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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Benchmark</title>
<meta name="description" content="automatically generated from '8060ce0b-6c33-41d9-b47f-e55326e9b359:benchmark.sagews' on CoCalc">
<meta name="date" content="2018-03-06T13:54:31">
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<div class="header">
<h1>Benchmark</h1>
<table class="header">
<tr><td>Author</td><td>Marcus Lenander</td></tr>
<tr><td>Date</td><td>2018-03-06T13:54:31</td></tr>
<tr><td>Project</td><td>8060ce0b-6c33-41d9-b47f-e55326e9b359</td></tr>
<tr><td>Location</td><td><a href="https:/localhost/projects/8060ce0b-6c33-41d9-b47f-e55326e9b359/files/benchmark.sagews">benchmark.sagews</a></td></tr>
<tr><td>Original file</td><td><a href="data:application/octet-stream;base64,︠513b474e-3b15-490f-8cdc-919d79e0d2a2︠
%md
# Benchmark
Here are the values used to benchmark the factorization functions
︡22802245-47c6-4c58-b697-2f275b7d035d︡{"done":true,"md":"# Benchmark\nHere are the values used to benchmark the factorization functions"}
︠037831ee-c983-41bf-a32a-637f8adb3794s︠
# This cell needs to be executed

iterations = 10

smallPrimes = ("small primes", [(2, [(481, [1, 13, 37])]), (3, [(31093, [1, 31, 17, 59])]), (4, [(1213045, [1, 37, 5, 83, 79])]), (5, [(15001613, [1, 31, 37, 29, 11, 41])]), (6, [(3429238769, [1, 47, 97, 59, 11, 19, 61])]), (7, [(206397809105, [1, 37, 79, 5, 53, 41, 67, 97])]), (8, [(7311461300687, [1, 41, 23, 73, 41, 59, 83, 23, 23])]), (9, [(472213574958521, [1, 41, 53, 37, 47, 61, 11, 71, 61, 43])]), (10, [(3443187949695, [1, 29, 43, 83, 5, 73, 41, 13, 3, 19, 3])]), (11, [(309773094336642695, [1, 5, 97, 11, 31, 83, 97, 31, 89, 43, 53, 37])]), (12, [(62263002262083735, [1, 47, 83, 17, 41, 59, 59, 43, 3, 7, 47, 31, 5])]), (13, [(666536544405580303, [1, 31, 23, 7, 47, 23, 67, 37, 37, 19, 13, 41, 19, 7])]), (14, [(56142059257389353853, [1, 3, 37, 11, 37, 19, 97, 11, 31, 53, 31, 67, 11, 71, 23])]), (15, [(3173389011480824657829, [1, 3, 79, 59, 53, 31, 7, 23, 43, 73, 11, 71, 3, 71, 31, 53])]), (16, [(15863359163742166197825, [1, 37, 3, 19, 61, 5, 11, 79, 79, 67, 3, 71, 5, 71, 97, 43, 17])]), (17, [(3839358256056932827602345, [1, 67, 17, 29, 19, 53, 41, 19, 19, 37, 73, 89, 13, 5, 53, 3, 73, 43])]), (18, [(18710317739887802052740556555, [1, 97, 89, 89, 83, 59, 5, 79, 59, 73, 13, 11, 31, 31, 29, 3, 89, 67, 41])]), (19, [(155903632515187552359018988575, [1, 97, 43, 47, 89, 97, 11, 73, 73, 61, 3, 37, 29, 61, 73, 5, 5, 67, 29, 37])]), (20, [(53620794966136160429097776631, [1, 23, 3, 79, 23, 43, 89, 61, 59, 3, 23, 71, 41, 97, 13, 11, 17, 37, 29, 47, 13])])])

mediumPrimes = ("medium primes", [(2, [(9505247, [1, 1427, 6661])]), (3, [(112377214483, [1, 4451, 7607, 3319])]), (4, [(113332156404307, [1, 4007, 3539, 2903, 2753])]), (5, [(4298836929253947781, [1, 8429, 7417, 5039, 1867, 7309])]), (6, [(11038759956959519253043, [1, 4909, 7307, 1597, 3733, 7243, 7127])]), (7, [(353271001154438218427229539, [1, 8167, 2687, 5483, 7253, 5807, 7127, 9781])]), (8, [(858069121139663326922589137543, [1, 9137, 9463, 3967, 8737, 4349, 5003, 2243, 5867])]), (9, [(131563435713374902721110800493303, [1, 5923, 6907, 8317, 1151, 1787, 5479, 9929, 2287, 1511])]), (10, [(2528123531806453766378415166939107671, [1, 9749, 2069, 5879, 8377, 2683, 2267, 4919, 3637, 4703, 4973])]), (11, [(98861961050577963648512453904444483679, [1, 1283, 2203, 9533, 1303, 2239, 1523, 5009, 1429, 4253, 2791, 9719])]), (12, [(3699719069641057612942949836474926656811572189, [1, 9133, 9967, 5879, 6547, 8929, 2351, 8681, 6857, 9719, 7583, 3461, 3313])]), (13, [(9297901936182093694009454599759344878967851169253, [1, 3947, 8599, 3109, 4999, 5581, 8629, 5953, 8069, 6829, 9677, 5197, 8059, 2753])]), (14, [(2987283285112052856777637490953875990300408162464831, [1, 1523, 7043, 1889, 7507, 6133, 3253, 3797, 1877, 3463, 7253, 9281, 7243, 8837, 9257])]), (15, [(14046255291904838561381033780082793879910682609073503319, [1, 2003, 9479, 8677, 4733, 1279, 3947, 5431, 9421, 9059, 9377, 4817, 1663, 3221, 8111, 3923])]), (16, [(1672833210619559517657260567204379601678267615743624567961, [1, 9883, 6067, 1559, 1009, 7069, 2213, 8713, 1601, 9491, 7369, 1327, 6701, 3359, 6871, 2039, 2777])]), (17, [(212010140415468603762770884867770164189873990478028538128651543, [1, 7757, 1721, 9343, 2521, 6793, 8017, 8117, 2879, 6491, 3637, 3319, 3677, 5711, 7681, 3433, 2087, 5851])]), (18, [(29763544558056708909351290167863189328280637881745015028766377567, [1, 3793, 3323, 7841, 9949, 1181, 6659, 5171, 2011, 1861, 3547, 2887, 2131, 4801, 2243, 2141, 5843, 9349, 7237])]), (19, [(183733102700898942618853672482178977569632673473846394890208044869833, [1, 1861, 6997, 1459, 7103, 8191, 6883, 1499, 1123, 2069, 8563, 4091, 7699, 4027, 5813, 2099, 8803, 5821, 2753, 3709])]), (20, [(4315581732420458239176904986420389625324862838223258879737740116751534309, [1, 4933, 9473, 2753, 7949, 1223, 1213, 1447, 9689, 2647, 7177, 4421, 7883, 7883, 4673, 7253, 4787, 2713, 8929, 2693, 3673])])])

largePrimes = ("large primes", [(2, [(4063375517, [1, 78439, 51803])]), (3, [(522742080565357, [1, 71167, 82051, 89521])]), (4, [(52187387971275982093, [1, 89753, 95717, 64693, 93901])]), (5, [(1162300682477934084344741, [1, 65183, 73883, 57397, 78803, 53359])]), (6, [(188904463700616439184603915519, [1, 77339, 67523, 99577, 59333, 64577, 94811])]), (7, [(10382597739368109104150090934175379, [1, 88321, 75787, 62417, 55117, 56179, 83399, 96233])]), (8, [(2236854499510418655753593501324101562419, [1, 91433, 96221, 73477, 94543, 80489, 73063, 67619, 92041])]), (9, [(35042439864356271632594896096225381140303727, [1, 93077, 63391, 71261, 50909, 67979, 75307, 54403, 61007, 96353])]), (10, [(9938019912957784649301000808068798240941672975269, [1, 94793, 50909, 88667, 75377, 74231, 75553, 99571, 86509, 89959, 70901])]), (11, [(187109892613625880027947942540002116725379107367853319, [1, 53611, 60659, 85313, 88609, 71089, 75133, 53267, 66851, 99041, 80603, 50129])]), (12, [(49161767109869991125387613590249904971687586373477597553749, [1, 88211, 97073, 79111, 80777, 51859, 99767, 84869, 80963, 75937, 91369, 52027, 70009])]), (13, [(986007145146192555084662271727905179607731398501077146686982027, [1, 88241, 72559, 86239, 92459, 57097, 63647, 96167, 54541, 67219, 70439, 50123, 66083, 64609])]), (14, [(122656733660163473018814025422928703405374994772383697825517039916327, [1, 68389, 86539, 63493, 56377, 61001, 60217, 85361, 58393, 65701, 99251, 94049, 70289, 77711, 94397])]), (15, [(7842053712205825701754260824788620754149912403029793155702700015604989373, [1, 81101, 82387, 92399, 88903, 67567, 60037, 96797, 60161, 58229, 58243, 76333, 84181, 67927, 58403, 69959])]), (16, [(414983958423876613281406476811736161578168944722930828312908133102632845752703, [1, 92083, 56477, 94573, 67187, 83177, 88471, 52951, 55579, 71597, 66179, 59671, 59729, 69481, 97583, 54623, 92717])]), (17, [(53002745697331794043197162487408577583597259117156412795445234494802005531541655757, [1, 51949, 81689, 71089, 81737, 60659, 93179, 70489, 90547, 62189, 92647, 64123, 75239, 90841, 88129, 74653, 57119, 62791])]), (18, [(2774325281122485998802780772219788618613994707680106838689326624193111749855341451994853, [1, 62081, 94229, 70313, 50513, 69247, 67531, 74903, 84827, 75037, 57697, 58789, 78779, 50909, 88819, 99923, 90353, 59627, 92077])]), (19, [(81814093803623318906242340014181655977264794640309240515571248892045623493330471152004211349, [1, 63629, 76597, 60761, 85223, 63611, 82039, 75431, 52501, 77351, 54547, 60139, 80387, 51721, 59093, 65537, 66587, 81817, 91961, 76631])]), (20, [(4759420676774002917027080074804196749925026162216764903500438803531064867662815998548224047575111, [1, 51193, 63617, 74827, 77239, 65761, 71011, 82613, 77719, 99709, 85213, 95959, 54787, 56503, 53503, 61553, 60689, 67033, 64513, 58831, 65713])])])

largerPrimes = ('Larger primes', [(2, [(187186702751, [1, 590377, 317063])]), (3, [(227610837550458559, [1, 345461, 887483, 742393])]), (4, [(70258793277571237647233, [1, 899981, 280607, 312353, 890683])]), (5, [(28721678110719749295143472251, [1, 252323, 322589, 562259, 826169, 759623])]), (6, [(16584959865789562307773297581668989, [1, 526199, 772097, 347519, 284857, 826759, 498779])]), (7, [(40135231725177170651266451927317370040017, [1, 689917, 363037, 462571, 805559, 561367, 823201, 930571])]), (8, [(13543477157075511779696540916677807232136281983, [1, 369841, 369079, 898481, 593171, 673613, 333197, 874127, 948901])]), (9, [(21868276789400720715203792286586485297210926281696241, [1, 508867, 666031, 911839, 521657, 319981, 592597, 776357, 947389, 972611])]), (10, [(3398638008982066688531884463264580936942051180990210108323, [1, 655243, 756373, 805219, 655859, 563197, 592087, 467101, 333331, 364031, 687023])]), (11, [(9136943238414668122038298815310911346194279867410940342650742671, [1, 741457, 386333, 423887, 741869, 752281, 938323, 933847, 548567, 636953, 986351, 446477])]), (12, [(38071366054007302601960554011850986602984984747338895665946437878377453, [1, 779189, 507691, 750961, 875417, 967427, 371251, 857737, 943073, 943363, 895087, 761861, 783283])]), (13, [(368625134734142995123626326808047577046599110832420111833822347712566666853, [1, 409063, 634079, 260263, 620887, 744407, 440183, 971171, 755737, 654679, 556093, 968593, 293483, 353359])]), (14, [(350789352401366415305072032960473921257900088976055701075698491956756257404655481, [1, 746483, 585587, 530851, 555349, 751259, 378949, 404843, 937823, 447683, 444817, 511289, 644291, 603731, 635879])]), (15, [(431463623920866689805584050956253221308032437458060677109830929906624804391812275410793, [1, 533747, 682333, 828067, 484751, 446261, 578687, 977147, 283831, 564979, 690163, 836863, 327017, 693403, 794153, 701257])]), (16, [(3090895415152262211627476518158103729565126064320269607944002601270807904266490336040532453091, [1, 729761, 596009, 627481, 812963, 576757, 711679, 825983, 955613, 911593, 587959, 700759, 767623, 268979, 651821, 858763, 990523])]), (17, [(1881182900515253077657544850252234921978522056443095815660055032303071363462608086772712619979929, [1, 765283, 360959, 399181, 468653, 287849, 481297, 382351, 711727, 261917, 846983, 754463, 346711, 346217, 541201, 990377, 338027, 265261])]), (18, [(23169284855147410245104557782459930672656640958302012768111347982308836202807150642723443947428384991983, [1, 428899, 979543, 314243, 947819, 441121, 954277, 304709, 620717, 427877, 399689, 415343, 289181, 985063, 883429, 840979, 488011, 665153, 476587])]), (19, [(14148962297868150427488880128423453856260378948237916062898523907220089968114112210934057887773724022523805637, [1, 289249, 679417, 535481, 947539, 832757, 934537, 424829, 280451, 990893, 300319, 404321, 384547, 424223, 340387, 624097, 839207, 793999, 901717, 610837])]), (20, [(729883933457870363432152113700293245237626872643614401017049987282050216103044544786654875010234935256140803954547, [1, 704321, 342799, 581447, 842249, 257837, 938219, 255349, 266009, 265709, 725341, 452033, 692717, 464923, 648007, 795307, 476659, 314399, 367687, 518579, 909203])])])

largestPrimes = ("largest primes", [(2, [(156522823147269816284598631312951810612882615746935161032701, [1, 272431619873581157551105550911, 574539854147262640021933661891])]), (3, [(33874806091130475009235697120079470280226688813077808889362612187330734249556669208421939, [1, 155903459436988767034958394683, 785575136929393571457349360969, 276588001275352182296868615457])])])

print "Stored number suite - re run if needed"
︡1f67ffce-63e0-40af-a571-ace142f1c321︡{"stdout":"Stored number suite - re run if needed\n"}︡{"done":true}︡
︠18531ca3-d578-4c3c-91c6-d6573a15ee4cs︠
smallClosePrimes = ('Small close primes', [(2, [(187, [1, 11, 17]), (221, [1, 13, 17])]), (3, [(1463, [1, 11, 19, 7]), (1183, [1, 13, 13, 7])]), (4, [(23023, [1, 11, 23, 7, 13]), (18515, [1, 5, 23, 7, 23])]), (5, [(161733, [1, 11, 13, 13, 29, 3]), (252655, [1, 5, 23, 13, 13, 13])]), (6, [(1154725, [1, 5, 13, 5, 17, 11, 19]), (955695, [1, 5, 29, 13, 13, 3, 13])]), (7, [(7743087, [1, 3, 31, 11, 29, 3, 29, 3]), (40602639, [1, 11, 29, 11, 19, 7, 29, 3])]), (8, [(107279613, [1, 3, 23, 3, 23, 7, 37, 3, 29]), (283487325, [1, 3, 17, 11, 41, 5, 17, 5, 29])]), (9, [(935717625, [1, 5, 43, 5, 29, 3, 23, 3, 29, 5]), (878332455, [1, 7, 17, 5, 31, 11, 13, 3, 37, 3])]), (10, [(24451456575, [1, 3, 17, 7, 13, 5, 43, 13, 29, 5, 13]), (1748802168425, [1, 13, 41, 5, 47, 13, 41, 5, 31, 13, 13])]), (11, [(6148592793, [1, 3, 19, 3, 31, 3, 19, 7, 19, 3, 17, 3]), (433954018575, [1, 3, 29, 5, 23, 11, 47, 5, 47, 7, 17, 3])]), (12, [(2336441234985, [1, 13, 37, 5, 19, 11, 13, 3, 41, 3, 19, 3, 17]), (6169110180975, [1, 3, 41, 3, 29, 7, 31, 5, 19, 7, 47, 5, 17])]), (13, [(19600594410375, [1, 5, 29, 3, 37, 11, 29, 5, 19, 3, 47, 5, 19, 3]), (27464992644375, [1, 3, 13, 11, 47, 5, 13, 5, 29, 3, 47, 5, 41, 5])]), (14, [(979848317369025, [1, 5, 23, 3, 59, 5, 17, 13, 59, 3, 23, 3, 29, 3, 41]), (16313742837926625, [1, 5, 23, 13, 61, 5, 53, 3, 31, 5, 43, 7, 53, 7, 13])]), (15, [(276612138433767825, [1, 3, 41, 13, 67, 3, 67, 5, 41, 3, 53, 13, 43, 5, 47, 3]), (480388899282435, [1, 11, 29, 3, 29, 3, 31, 5, 13, 3, 29, 3, 23, 3, 53, 3])]), (16, [(13042072935932625, [1, 3, 31, 5, 23, 3, 31, 3, 19, 3, 31, 3, 13, 5, 43, 5, 59]), (382555146521019375, [1, 3, 29, 5, 61, 3, 71, 3, 23, 5, 61, 5, 19, 3, 37, 5, 61])]), (17, [(3312499880682759375, [1, 5, 19, 3, 47, 5, 47, 5, 29, 7, 79, 3, 73, 3, 47, 5, 17, 5]), (1706485929231344625, [1, 13, 67, 5, 43, 5, 53, 3, 19, 3, 47, 3, 17, 3, 17, 7, 47, 5])]), (18, [(1174450948827771103125, [1, 5, 31, 3, 23, 5, 13, 5, 23, 7, 79, 5, 59, 5, 19, 13, 71, 13, 79]), (201675564824001357375, [1, 5, 31, 13, 19, 3, 67, 5, 37, 5, 61, 3, 23, 3, 71, 13, 13, 11, 17])]), (19, [(2896784440836584878125, [1, 5, 73, 5, 67, 5, 53, 5, 23, 13, 41, 7, 73, 5, 17, 3, 41, 7, 13, 3]), (1890142883084170567125, [1, 3, 67, 3, 13, 5, 29, 3, 79, 3, 47, 3, 79, 13, 61, 7, 17, 5, 89, 5])]), (20, [(65022163146983219653125, [1, 5, 43, 5, 59, 3, 61, 3, 97, 5, 59, 13, 31, 3, 83, 3, 29, 5, 23, 5, 13]), (32369441131223583393825, [1, 5, 29, 3, 97, 13, 19, 3, 41, 3, 71, 3, 53, 3, 37, 7, 17, 3, 53, 5, 71])]), (2, [(961, [1, 31, 31]), (1147, [1, 31, 37])]), (3, [(33263, [1, 29, 37, 31]), (27869, [1, 31, 31, 29])]), (4, [(494209, [1, 19, 37, 19, 37]), (847757, [1, 29, 41, 23, 31])]), (5, [(14253769, [1, 17, 43, 17, 37, 31]), (21859867, [1, 31, 31, 23, 43, 23])]), (6, [(272897651, [1, 13, 47, 17, 47, 13, 43]), (424808137, [1, 19, 43, 13, 37, 23, 47])]), (7, [(7642399589, [1, 11, 43, 23, 43, 17, 31, 31]), (8418710641, [1, 31, 47, 11, 53, 11, 53, 17])]), (8, [(705261876527, [1, 19, 47, 13, 61, 23, 43, 19, 53]), (343508150821, [1, 19, 43, 11, 61, 29, 41, 17, 31])]), (9, [(5001316620355, [1, 5, 61, 17, 53, 11, 53, 31, 53, 19]), (298235183875, [1, 5, 59, 19, 41, 5, 37, 5, 61, 23])]), (10, [(10840457019117, [1, 11, 37, 3, 31, 11, 37, 17, 53, 11, 71]), (32246166582465, [1, 11, 67, 3, 41, 5, 53, 19, 43, 31, 53])]), (11, [(131104352392575, [1, 17, 47, 29, 73, 17, 53, 3, 31, 5, 37, 5]), (318821990728325, [1, 31, 53, 19, 37, 5, 31, 5, 41, 7, 73, 17])]), (12, [(8917467228811725, [1, 29, 41, 5, 79, 3, 41, 23, 31, 5, 43, 19, 53]), (2047407165326187, [1, 23, 31, 7, 53, 3, 41, 19, 71, 3, 71, 3, 73])]), (13, [(6224134475718818659, [1, 13, 47, 11, 71, 23, 83, 23, 37, 17, 67, 19, 53, 7]), (51245303801837145, [1, 17, 53, 7, 83, 7, 73, 11, 43, 13, 31, 5, 67, 3])]), (14, [(108043090363342428225, [1, 5, 73, 29, 59, 19, 71, 31, 61, 3, 83, 5, 47, 19, 61]), (3926065196602313399917, [1, 17, 47, 23, 83, 19, 61, 23, 31, 17, 71, 29, 53, 23, 73])]), (15, [(22027411283540928125, [1, 23, 83, 5, 31, 23, 47, 5, 89, 5, 71, 7, 47, 5, 53, 5]), (177118086912132284625, [1, 3, 59, 7, 89, 23, 89, 5, 71, 29, 53, 23, 61, 5, 41, 5])]), (16, [(23707258426609810843125, [1, 5, 101, 23, 83, 17, 89, 5, 67, 5, 71, 29, 97, 5, 79, 3, 41]), (2031893035845148045125, [1, 3, 47, 3, 41, 5, 73, 5, 67, 23, 71, 19, 73, 19, 73, 5, 61])]), (17, [(36236921442400155709375, [1, 5, 71, 5, 101, 19, 67, 5, 41, 23, 43, 11, 79, 13, 47, 5, 59, 5]), (95484403968664676886375, [1, 31, 31, 5, 89, 3, 47, 5, 83, 13, 67, 29, 53, 5, 37, 31, 71, 7])]), (18, [(68449749435915415117875, [1, 13, 101, 23, 59, 3, 43, 5, 41, 3, 31, 13, 43, 3, 67, 5, 83, 5, 67]), (19589478089411820609060525, [1, 5, 107, 3, 97, 23, 47, 29, 31, 5, 89, 19, 103, 3, 31, 17, 83, 11, 103])]), (19, [(17459425383139545183002625, [1, 5, 53, 3, 61, 5, 101, 13, 73, 19, 59, 7, 103, 11, 101, 5, 41, 11, 53, 7]), (253868269728472313813110875, [1, 5, 59, 3, 67, 5, 67, 29, 41, 13, 109, 19, 47, 13, 73, 31, 43, 5, 79, 17])]), (20, [(10019176560312034400567595, [1, 3, 47, 3, 83, 5, 47, 19, 103, 29, 41, 3, 31, 3, 61, 3, 43, 3, 79, 17, 59]), (215947535722966231822673332275, [1, 5, 109, 17, 43, 23, 47, 23, 79, 11, 83, 17, 113, 17, 61, 17, 83, 3, 107, 5, 67])])])

mediumClosePrimes = ("Medium close primes", [(2, [(316933, [1, 557, 569]), (313591, [1, 557, 563])]), (3, [(171534277, [1, 557, 563, 547]), (173971709, [1, 557, 571, 547])]), (4, [(94758693241, [1, 541, 569, 541, 569]), (100381676093, [1, 557, 571, 547, 577])]), (5, [(56670957560149, [1, 563, 587, 563, 563, 541]), (55737645509339, [1, 563, 563, 547, 571, 563])]), (6, [(33960079475671199, [1, 557, 563, 547, 593, 563, 593]), (28590087506703829, [1, 541, 593, 521, 569, 521, 577])]), (7, [(16668687877305357367, [1, 547, 593, 547, 593, 547, 569, 509]), (14895421562352162947, [1, 523, 563, 523, 587, 541, 563, 541])]), (8, [(8825598186724532340139, [1, 503, 577, 563, 601, 503, 593, 503, 599]), (8056030357210311798593, [1, 509, 571, 541, 563, 509, 587, 541, 563])]), (9, [(5176371113800439756757811, [1, 523, 569, 503, 593, 547, 587, 547, 607, 547]), (4307414133054528902898431, [1, 547, 577, 503, 569, 547, 569, 503, 563, 541])]), (10, [(2472832340955827717218826729, [1, 499, 571, 541, 599, 491, 577, 563, 569, 491, 601]), (2584284171184513506455410453, [1, 503, 613, 509, 599, 563, 569, 499, 607, 491, 577])]), (11, [(1910856948409986584271742351543, [1, 521, 577, 547, 563, 563, 577, 541, 617, 563, 607, 557]), (1332882535090650712169308963739, [1, 487, 613, 547, 613, 503, 563, 487, 617, 557, 563, 499])]), (12, [(852196735493924940848986241767987, [1, 541, 613, 487, 617, 491, 587, 523, 613, 523, 563, 523, 601]), (752546528211330815497003845481997, [1, 479, 593, 503, 587, 491, 587, 503, 607, 541, 587, 547, 587])]), (13, [(413424284293138931542565906706071669, [1, 491, 587, 487, 617, 541, 607, 487, 587, 557, 617, 479, 571, 541]), (422612439674921629650938136476012611, [1, 523, 569, 541, 577, 541, 571, 523, 613, 487, 569, 563, 563, 523])]), (14, [(457153207646831573744181522153370927673, [1, 547, 619, 547, 641, 563, 607, 547, 593, 563, 631, 509, 619, 503, 617]), (259918970541028265619885810519171604529, [1, 557, 631, 541, 593, 487, 563, 503, 619, 503, 617, 467, 631, 503, 587])]), (15, [(109868336528703352227207124944087831704269, [1, 463, 599, 509, 631, 467, 617, 487, 643, 563, 563, 487, 607, 541, 563, 479]), (142219206797328060675174570040656920579167, [1, 479, 613, 547, 587, 557, 601, 479, 587, 499, 571, 479, 643, 563, 593, 547])]), (16, [(76820202531067992349805610678707511043871803, [1, 547, 587, 509, 569, 491, 613, 491, 607, 547, 601, 487, 643, 487, 617, 463, 643]), (84353082637098915851350715686631411152617919, [1, 499, 593, 541, 613, 523, 601, 557, 593, 491, 587, 521, 587, 491, 599, 521, 613])]), (17, [(29867711038615093175665393861938141536525529539, [1, 541, 607, 479, 577, 557, 599, 467, 647, 463, 577, 461, 607, 499, 617, 457, 617, 503]), (32160416498806182862863819430142025959220975101, [1, 449, 613, 509, 631, 461, 613, 499, 601, 541, 599, 461, 617, 487, 631, 503, 599, 503])]), (18, [(19956848495929281188644811212469947126676084328359, [1, 449, 601, 563, 659, 467, 587, 461, 577, 509, 659, 467, 577, 479, 641, 499, 653, 503, 601]), (21117036798239547259422495410311750799350659014713, [1, 487, 593, 541, 571, 449, 601, 487, 643, 521, 617, 463, 619, 457, 659, 503, 563, 541, 659])]), (19, [(13264396535897727373516274848984084788966136163607509, [1, 503, 613, 461, 659, 461, 659, 563, 569, 461, 647, 521, 653, 523, 607, 449, 631, 541, 631, 467]), (12747441328106451238259995492136682019426946134615741, [1, 461, 593, 503, 619, 479, 653, 521, 659, 563, 641, 541, 617, 457, 571, 499, 607, 439, 599, 557])]), (20, [(5156986434929461169796816182749562003267982133556328449, [1, 463, 571, 439, 661, 433, 607, 457, 617, 509, 641, 467, 659, 457, 661, 557, 661, 499, 619, 439, 599]), (4889610655414411472658135732868818020771788946718976949, [1, 503, 673, 487, 569, 479, 617, 491, 653, 457, 613, 461, 563, 479, 673, 509, 569, 433, 571, 487, 673])]), (2, [(1142761, [1, 1069, 1069]), (1136347, [1, 1063, 1069])]), (3, [(1228276303, [1, 1063, 1087, 1063]), (1235209189, [1, 1063, 1087, 1069])]), (4, [(1334677393237, [1, 1063, 1093, 1051, 1093]), (1332235165619, [1, 1063, 1091, 1051, 1093])]), (5, [(1402629106625399, [1, 1063, 1091, 1049, 1097, 1051]), (1418937909399427, [1, 1069, 1093, 1051, 1087, 1063])]), (6, [(1597798805102350891, [1, 1069, 1093, 1063, 1097, 1069, 1097]), (1520005874460943489, [1, 1069, 1069, 1061, 1087, 1061, 1087])]), (7, [(1603168127794699290541, [1, 1063, 1103, 1051, 1109, 1033, 1093, 1039]), (1612842382725010293011, [1, 1033, 1097, 1069, 1091, 1049, 1109, 1049])]), (8, [(1718598263073818570384887, [1, 1031, 1097, 1069, 1091, 1063, 1093, 1049, 1069]), (1757529589061923699888087, [1, 1049, 1097, 1063, 1087, 1039, 1093, 1061, 1097])]), (9, [(1824913317720944628804183853, [1, 1051, 1109, 1033, 1097, 1063, 1091, 1051, 1091, 1039]), (1766115859678499030090922409, [1, 1061, 1091, 1063, 1069, 1033, 1091, 1039, 1091, 1051])]), (10, [(2044146205511432560530644353003, [1, 1061, 1123, 1019, 1093, 1069, 1087, 1039, 1109, 1019, 1129]), (2023343565385497662573424982849, [1, 1049, 1069, 1049, 1129, 1051, 1117, 1039, 1093, 1069, 1069])]), (11, [(2138146560514888959638653203727999, [1, 1033, 1093, 1033, 1117, 1049, 1093, 1061, 1129, 1069, 1097, 1019]), (2047088725942481982714204169717471, [1, 1061, 1123, 1031, 1123, 1019, 1069, 1051, 1069, 1061, 1069, 1069])]), (12, [(2353583186144653289501714282050393409, [1, 1049, 1087, 1021, 1153, 1049, 1103, 1051, 1093, 1051, 1091, 1019, 1129]), (2275159985769061830987258016478931859, [1, 1063, 1097, 1031, 1103, 1063, 1103, 1021, 1091, 1051, 1109, 1009, 1117])]), (13, [(2492097436003839540838892538978283235653, [1, 1039, 1103, 1039, 1117, 1039, 1123, 1051, 1093, 1019, 1069, 1069, 1123, 1069]), (2083445330217309788943292916425765482277, [1, 1039, 1091, 1013, 1123, 1031, 1097, 1033, 1093, 1019, 1123, 1021, 1069, 1013])]), (14, [(3026567709449547952359333008027322113358461, [1, 1061, 1117, 1033, 1109, 1061, 1153, 1013, 1117, 1051, 1087, 1013, 1153, 1069, 1129]), (2882599589709110224249733588127180959062163, [1, 1013, 1097, 1033, 1109, 1063, 1123, 1063, 1087, 1063, 1151, 1061, 1109, 1049, 1087])]), (15, [(2784085616184428897659292570343329087575063793, [1, 1039, 1163, 997, 1087, 1009, 1109, 1009, 1151, 997, 1093, 1031, 1181, 1039, 1151, 1031]), (2623289042257046506415381707180861391182863277, [1, 991, 1091, 997, 1129, 1069, 1163, 1049, 1093, 1021, 1093, 1019, 1091, 1051, 1091, 1063])]), (16, [(3309498666165362973713994449803606500505059524969, [1, 1051, 1103, 1049, 1151, 1021, 1129, 1063, 1109, 1063, 1103, 1009, 1151, 983, 1091, 1061, 1123]), (3007559565989492190685682333633142659992222889983, [1, 991, 1153, 1013, 1103, 1069, 1109, 1039, 1151, 983, 1153, 1051, 1123, 983, 1109, 1033, 1103])]), (17, [(3337430374387820187766404846559737967472421425519377, [1, 1061, 1193, 1009, 1171, 1069, 1097, 971, 1093, 1061, 1091, 1019, 1187, 1033, 1109, 983, 1103, 1031]), (3009463694645099549214603933901886663401681206188531, [1, 1031, 1091, 1039, 1163, 1019, 1151, 1061, 1129, 1069, 1123, 1013, 1069, 977, 1109, 1019, 1117, 983])]), (18, [(3205474017206716910525999363197509384671530933913244179, [1, 1069, 1093, 991, 1163, 991, 1103, 971, 1087, 1061, 1069, 1039, 1087, 1063, 1091, 1019, 1087, 1051, 1193]), (3838143684519378674624606833998765033603759339155011169, [1, 1049, 1097, 991, 1193, 1021, 1151, 1069, 1093, 1021, 1181, 977, 1103, 1069, 1093, 1061, 1201, 977, 1087])]), (19, [(3630505250586537380826457274577452415857434807088548791649, [1, 1021, 1109, 1009, 1153, 967, 1163, 1009, 1123, 953, 1201, 1021, 1093, 997, 1171, 1033, 1109, 1019, 1171, 1061]), (3328634472598003887835597528525093350883513224862826212061, [1, 971, 1091, 1039, 1201, 1031, 1213, 1061, 1153, 997, 1103, 953, 1153, 977, 1091, 997, 1097, 1039, 1151, 977])]), (20, [(3055878534232886887533008275157224451264024556815840381056001, [1, 977, 1117, 977, 1117, 983, 1187, 971, 1093, 971, 1087, 1069, 1109, 953, 1097, 1051, 1093, 1069, 1193, 991, 1091]), (4003992205233808349893596129588063075763059241015453817988877, [1, 1033, 1069, 1031, 1163, 997, 1187, 953, 1087, 1039, 1129, 1049, 1069, 1031, 1213, 1013, 1109, 1039, 1181, 997, 1091])])])

largeClosePrimes = ("Large close primes", [(2, [(865712929, [1, 29423, 29423]), (865712929, [1, 29423, 29423])]), (3, [(25454551017407, [1, 29411, 29437, 29401]), (25454551017407, [1, 29401, 29437, 29411])]), (4, [(748949254585166161, [1, 29411, 29437, 29401, 29423]), (749815315379647091, [1, 29423, 29429, 29411, 29443])]), (5, [(22042301982094473596467, [1, 29389, 29437, 29401, 29453, 29423]), (22037819908204262231501, [1, 29411, 29453, 29399, 29423, 29411])]), (6, [(647625188777536523967038123, [1, 29389, 29437, 29387, 29429, 29399, 29443]), (648727214546027169234119857, [1, 29411, 29443, 29401, 29443, 29399, 29437])]), (7, [(19047305219120345130931560910901, [1, 29401, 29437, 29399, 29437, 29401, 29437, 29383]), (19122506962371043582760416155121, [1, 29423, 29473, 29399, 29483, 29399, 29423, 29411])]), (8, [(562143099156355627345058252853193301, [1, 29423, 29443, 29363, 29483, 29411, 29429, 29383, 29473]), (562829942618851054761838008402259709, [1, 29363, 29483, 29401, 29501, 29401, 29443, 29399, 29453])]), (9, [(16549917550139176331089539530499288572021, [1, 29389, 29437, 29423, 29501, 29347, 29443, 29383, 29527, 29399]), (16494942489066181415143190513104903497931, [1, 29387, 29443, 29387, 29501, 29383, 29473, 29347, 29443, 29387])]), (10, [(483818446645921223916066574454799803265926869, [1, 29399, 29443, 29383, 29423, 29411, 29423, 29347, 29443, 29387, 29423]), (490367376997778494257114997680532736329945909, [1, 29387, 29483, 29401, 29501, 29423, 29531, 29389, 29501, 29389, 29473])]), (11, [(14298066897873419916925610084596585019684404299577, [1, 29363, 29437, 29339, 29443, 29333, 29531, 29411, 29537, 29347, 29483, 29411]), (14320484452966964226830269428065419115967575823307, [1, 29399, 29527, 29389, 29537, 29399, 29501, 29383, 29423, 29347, 29443, 29333])]), (12, [(422988549701602021708072490756282881304545627458255859, [1, 29363, 29453, 29401, 29453, 29389, 29567, 29423, 29531, 29363, 29429, 29423, 29423]), (423761271786225112222217862150288564714519017380395689, [1, 29411, 29537, 29401, 29483, 29383, 29537, 29339, 29473, 29411, 29527, 29333, 29437])]), (13, [(12293239381581520625704123339024990495993226167931711051791, [1, 29363, 29443, 29347, 29537, 29401, 29423, 29347, 29531, 29311, 29423, 29311, 29443, 29399]), (12451198379061059764624491385115885732898863931874087138687, [1, 29363, 29569, 29347, 29429, 29339, 29567, 29423, 29483, 29363, 29527, 29423, 29483, 29339])]), (14, [(366249931054054855918254086215217231707917666117006778977380909, [1, 29347, 29569, 29423, 29443, 29333, 29527, 29387, 29567, 29399, 29429, 29327, 29527, 29339, 29453]), (367896370789011152412608731303715436991394396657947014758999489, [1, 29303, 29501, 29399, 29537, 29387, 29567, 29389, 29473, 29311, 29527, 29399, 29483, 29399, 29527])]), (15, [(10644894953985381764687625074094294366413635557060109122838940666171, [1, 29297, 29443, 29333, 29453, 29311, 29527, 29311, 29527, 29387, 29527, 29303, 29567, 29383, 29453, 29311]), (10685620363611581349723712362560065711947054666446884334157352103099, [1, 29399, 29453, 29399, 29531, 29399, 29443, 29311, 29453, 29297, 29531, 29297, 29573, 29389, 29473, 29297])]), (16, [(318513253747377908211654512553364042173627257881988069391587768229583691, [1, 29423, 29501, 29423, 29537, 29401, 29573, 29399, 29501, 29311, 29429, 29363, 29483, 29303, 29423, 29411, 29569]), (318010433938975531069970467031819358831170737214531625647265186479508697, [1, 29347, 29573, 29327, 29423, 29333, 29501, 29327, 29443, 29387, 29581, 29423, 29573, 29399, 29537, 29347, 29483])]), (17, [(9274924513456323558811589191670119099925691334742148666185537727889128732529, [1, 29423, 29599, 29269, 29531, 29339, 29483, 29333, 29443, 29333, 29537, 29387, 29443, 29399, 29453, 29311, 29599, 29287]), (9306534270861220085725248728885553486460012328605762858906957840590239358497, [1, 29389, 29567, 29363, 29423, 29269, 29483, 29423, 29437, 29363, 29567, 29333, 29581, 29399, 29527, 29339, 29537, 29269])]), (18, [(273447555319424943187398893784654666306360710336455357136751751809036563020145951, [1, 29389, 29473, 29387, 29501, 29327, 29611, 29327, 29537, 29339, 29537, 29251, 29423, 29423, 29473, 29251, 29527, 29303, 29573]), (273777364729800462429940443288730515555346668606062214085557317040304257088157639, [1, 29423, 29429, 29287, 29611, 29311, 29531, 29347, 29581, 29303, 29429, 29333, 29531, 29287, 29501, 29327, 29587, 29303, 29567])]), (19, [(8092813032034752870137381401915653543865243380513951917556601612686501897877155480529, [1, 29383, 29611, 29389, 29581, 29287, 29531, 29401, 29501, 29297, 29453, 29327, 29611, 29411, 29453, 29383, 29453, 29387, 29537, 29251]), (8101465846655008560733288209269117691483784364549949754676618472732876797621084547241, [1, 29399, 29573, 29339, 29567, 29251, 29423, 29347, 29443, 29389, 29573, 29333, 29567, 29347, 29573, 29327, 29501, 29401, 29629, 29297])]), (20, [(234378162774272083465819585268149691307105050863628353375341774554968068447199162285443833, [1, 29287, 29483, 29251, 29453, 29389, 29483, 29339, 29501, 29333, 29537, 29269, 29437, 29339, 29501, 29297, 29453, 29401, 29537, 29383, 29531]), (234135764547596304524147681265747540452786682840147054666671262723031988066482413301913669, [1, 29339, 29531, 29297, 29567, 29231, 29567, 29297, 29423, 29339, 29443, 29231, 29587, 29311, 29567, 29311, 29599, 29399, 29453, 29231, 29453])]), (2, [(1621270081, [1, 40253, 40277]), (1621270081, [1, 40253, 40277])]), (3, [(65260984570493, [1, 40253, 40277, 40253]), (65241529329521, [1, 40253, 40277, 40241])]), (4, [(2628907540960158751, [1, 40253, 40283, 40241, 40289]), (2628515975157071569, [1, 40241, 40289, 40253, 40277])]), (5, [(105663786523994505249787, [1, 40237, 40283, 40231, 40277, 40231]), (105747846551901297102991, [1, 40253, 40277, 40241, 40283, 40237])]), (6, [(4276777994168845795685084369, [1, 40213, 40357, 40253, 40357, 40277, 40277]), (4261730664682637298515573083, [1, 40237, 40277, 40231, 40277, 40213, 40357])]), (7, [(171675339450528779010130577717441, [1, 40231, 40351, 40237, 40289, 40277, 40277, 40213]), (171725964673339015282431048008621, [1, 40237, 40343, 40213, 40361, 40231, 40289, 40213])]), (8, [(6940328532425640161878617107022831931, [1, 40241, 40387, 40277, 40351, 40213, 40277, 40213, 40343]), (6937928030201461327568435740563312701, [1, 40213, 40357, 40241, 40361, 40253, 40343, 40231, 40289])]), (9, [(278783934216210794061753445528460285077843, [1, 40237, 40283, 40177, 40423, 40237, 40289, 40213, 40423, 40189]), (280201693317557732699734499983537650751331, [1, 40277, 40361, 40277, 40423, 40213, 40361, 40237, 40289, 40237])]), (10, [(11266035858555712572848498785608957810155199769, [1, 40277, 40361, 40241, 40277, 40169, 40427, 40231, 40343, 40213, 40343]), (11248748165423422014156975262092465859284398131, [1, 40277, 40361, 40193, 40289, 40189, 40343, 40213, 40361, 40237, 40357])]), (11, [(452365647933365700184455164174376023053860917287901, [1, 40177, 40387, 40277, 40283, 40189, 40357, 40231, 40343, 40163, 40387, 40241]), (449701911482155772128565847368365973030290463048771, [1, 40189, 40351, 40253, 40289, 40189, 40283, 40193, 40343, 40193, 40351, 40163])]), (12, [(18313458677768241029361126067868713086248286672636815087, [1, 40237, 40429, 40277, 40357, 40241, 40351, 40253, 40283, 40231, 40289, 40213, 40357]), (18250572437229924758295006051459000197191942489816056329, [1, 40213, 40361, 40231, 40283, 40231, 40361, 40177, 40277, 40153, 40433, 40237, 40423])]), (13, [(738365424372328155516200875596859028033712185143813239636697, [1, 40241, 40427, 40189, 40343, 40253, 40427, 40237, 40357, 40189, 40433, 40213, 40351, 40177]), (735286352707701561586078679475095075815643479401450265856257, [1, 40153, 40459, 40241, 40459, 40193, 40289, 40237, 40289, 40153, 40387, 40169, 40387, 40253])]), (14, [(29373297580035069399879971437182275084191326425505542159180637071, [1, 40213, 40289, 40129, 40283, 40129, 40387, 40241, 40361, 40153, 40429, 40129, 40277, 40169, 40427]), (29909068422978136679310036940712188458368142913407434306408958727, [1, 40177, 40433, 40189, 40429, 40193, 40423, 40277, 40429, 40241, 40343, 40237, 40427, 40189, 40357])]), (15, [(1190308734806001452624428419210166831878447638583765709998701699322677, [1, 40163, 40471, 40153, 40429, 40241, 40283, 40277, 40289, 40151, 40459, 40241, 40343, 40127, 40343, 40169]), (1191197716982639111892135143689621152800042059925150289986504827047163, [1, 40189, 40289, 40129, 40283, 40241, 40289, 40213, 40427, 40151, 40483, 40277, 40459, 40129, 40357, 40253])]), (16, [(48142145059544319190375895840285035420345008460652389028989842839589161101, [1, 40151, 40283, 40213, 40423, 40277, 40423, 40241, 40459, 40169, 40433, 40151, 40343, 40163, 40427, 40151, 40277]), (48304323928051683956152914371144110851492525150491340507493386931312814789, [1, 40241, 40433, 40123, 40459, 40153, 40283, 40241, 40429, 40151, 40483, 40169, 40357, 40193, 40429, 40189, 40387])]), (17, [(1947163081288901745447679864902656801561849466655905426788125701187223499442883, [1, 40253, 40483, 40127, 40387, 40111, 40277, 40213, 40493, 40129, 40433, 40253, 40459, 40277, 40487, 40231, 40289, 40129]), (1950193563503571247994675503760211420163920048052169513812618570297657545722893, [1, 40231, 40427, 40111, 40427, 40127, 40487, 40231, 40459, 40237, 40351, 40129, 40427, 40231, 40277, 40277, 40423, 40241])]), (18, [(78936951915049847226243400827108784756556544200163394380642260866249453916058775541, [1, 40253, 40471, 40099, 40343, 40129, 40433, 40231, 40471, 40237, 40361, 40213, 40471, 40213, 40471, 40237, 40351, 40099, 40487]), (78951094094132040233040058707045915482428704964122655414198932241792706059352696417, [1, 40123, 40429, 40127, 40423, 40153, 40483, 40151, 40427, 40193, 40487, 40189, 40357, 40123, 40471, 40231, 40499, 40253, 40459])]), (19, [(3128927636109278291345269400034681971656783052672880042429271967052894323478553387411493, [1, 40123, 40471, 40253, 40277, 40111, 40289, 40177, 40387, 40093, 40283, 40177, 40429, 40193, 40387, 40231, 40471, 40099, 40499, 40253]), (3146520128824371716207725209907584052952049742107680993674409723280717068075495166986423, [1, 40213, 40289, 40189, 40483, 40127, 40277, 40163, 40429, 40163, 40487, 40193, 40433, 40129, 40289, 40277, 40483, 40093, 40459, 40253])]), (20, [(128852600609349526097437512679089470899860629063921966904451544951666329006154974515208595849, [1, 40099, 40471, 40241, 40357, 40237, 40361, 40277, 40423, 40087, 40519, 40241, 40429, 40087, 40499, 40169, 40499, 40189, 40507, 40213, 40471]), (126062316213731487422916572994986948260691672311530813690188127109530700932036759345668642767, [1, 40189, 40433, 40277, 40343, 40153, 40387, 40169, 40357, 40093, 40499, 40127, 40387, 40087, 40499, 40087, 40493, 40111, 40283, 40087, 40433])])])

print "stored close number suite - re run if needed"
︡bd6d7519-1b35-4711-a53f-1d74173d8968︡{"stdout":"stored close number suite - re run if needed\n"}︡{"done":true}︡
︠fc11521b-f6e7-4eac-acd9-d5c658748d99i︠
# This cell needs to be executed

def plotMinMaxAverage(benchmark):
    dataMin = []
    dataMax = []
    dataAverage = []

    for numberOfFactors, min, max, average in benchmarks:
        dataMin.append([numberOfFactors, min.totalTime["default"]])
        dataMax.append([numberOfFactors, max.totalTime["default"]])
        dataAverage.append([numberOfFactors, average.totalTime["default"]])
        #print "for %d factors:"%numberOfFactors
        #print "min", min
        #print "max", max
        #print "average", average

    minPlot = scatter_plot(dataMin, markersize = 5, scale = "linear", xmin = 2, ymin=0, facecolor="green", edgecolor="green")
    maxPlot = scatter_plot(dataMax, markersize = 5, scale = "linear", xmin = 2, ymin=0, facecolor="red", edgecolor="red")
    averagePlot = scatter_plot(dataAverage, markersize =5, scale = "linear", xmin = 2, ymin=0, facecolor="blue", edgecolor="blue")

    html("<font color='green'>minimum</font><br/><font color='red'>maximum</font><br/><font color='blue'>average</font>")

    return (minPlot, maxPlot, averagePlot)

print "defined plot function - re run if needed"
︡54cee9e2-f58c-497a-9116-05611f711f8e︡{"stdout":"defined plot function - re run if needed\n"}︡{"done":true}︡
︠0b40494b-e32b-47e4-899a-674ffa089d15︠

︡1143503d-0dfa-4171-a6c8-a5735823e868︡{"done":true}︡
︠9347994e-8446-486d-b055-7cf13e70d84ei︠
%md
## Trial Division
︡3815f2d8-a8d9-482c-bb07-a496fd690c20︡{"done":true,"md":"## Trial Division"}
︠219255df-7a33-4c28-b7e4-824e637a013c︠
from trial_division import *

benchmarks = TrialDivision.benchmark(smallPrimes, iterations)

examplePlot = '''
minPlot, maxPlot, averagePlot = plotMinMaxAverage(benchmarks)

print "Regular trial division, small primes"
minPlot + maxPlot + averagePlot

benchmarks = TrialDivision.benchmark(smallPrimes, iterations, {"modified": True})
minPlot, maxPlot, averagePlot = plotMinMaxAverage(benchmarks)

print "Primes only trial division, small primes\n"
minPlot + maxPlot + averagePlot
'''
︡e3f7af6e-2271-459e-bbc5-ef2ac52cea0d︡{"done":true}︡
︠8381e20e-774f-40b9-9bc1-74866114a09e︠
from trial_division import *

benchmarks = TrialDivision.benchmark(smallClosePrimes, iterations)
print "small primes"

benchmarks = TrialDivision.benchmark(smallClosePrimes, iterations, {"modified": True})
print "small primes"
︡ad9c120e-44cf-480e-b199-ae279624e98d︡{"stdout":"small primes\n"}︡{"stdout":"small primes\n"}︡{"done":true}︡
︠e920037c-25fd-4ba3-a296-a37ca0f5dadf︠
%md
Observationer trial division:
I och med att Trial Division hittar den minsta faktorn först så vet den att ingen annan faktor är mindre, därför kan den börja räkna från den hittade faktorn nästa gång istället för 0
︡76c8f62f-0006-427b-ad9e-9ce4a85afd6c︡
︠7da2602d-d0e3-4eef-afb3-f45a2db598dbi︠
%md
## Fermat's Factorization
︡1d70e3aa-f9c3-45dd-b19d-014107894b1a︡{"done":true,"md":"## Fermat's Factorization"}
︠c81e81ef-e521-429d-8fc0-b96231f59970︠
from fermats_factorization import *

# Klarade ej att slutföra 4 factors medium primes under > 11 timmar!

benchmarks = FermatsFactorization.benchmark(smallPrimes, iterations)
print "small primes"
benchmarks = FermatsFactorization.benchmark(mediumPrimes, iterations)
print "medium primes"
benchmarks = FermatsFactorization.benchmark(largePrimes, iterations)
print "large primes"
benchmarks = FermatsFactorization.benchmark(largerPrimes, iterations)
print "larger primes"

benchmarks = FermatsFactorization.benchmark(smallClosePrimes, iterations)
print "close small primes"
benchmarks = FermatsFactorization.benchmark(mediumClosePrimes, iterations)
print "close medium primes"
benchmarks = FermatsFactorization.benchmark(largeClosePrimes, iterations)
print "close large primes"
︡fa5b2078-d67c-4d3c-ae4d-3a2c84ce1034︡{"stderr":"Error in lines 2-2\n"}︡{"stderr":"Traceback (most recent call last):\n  File \"/usr/local/sage/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 995, in execute\n    exec compile(block+'\\n', '', 'single') in namespace, locals\n  File \"\", line 1, in <module>\n  File \"factorization_function.py\", line 79, in benchmark\n    resultingFactors, b = self.factorize(n, true, **optionalArgs)\n  File \"fermats_factorization.py\", line 77, in factorize\n    possibleFactors = self.getOneFactor(a, benchmark)\n  File \"fermats_factorization.py\", line 32, in getOneFactor\n    benchmark.iterate()\n  File \"src/cysignals/signals.pyx\", line 251, in cysignals.signals.python_check_interrupt (build/src/cysignals/signals.c:2721)\n  File \"src/cysignals/signals.pyx\", line 94, in cysignals.signals.sig_raise_exception (build/src/cysignals/signals.c:1328)\nKeyboardInterrupt\n"}︡{"done":true}︡
︠efb9d8f0-3810-47b0-b4a4-a6fb911107cc︠
%md
observationer fermats:

av någon anledning verkar small primes 9 och 15 faktorer ta extra lång tid. Varför?

En optimering av fermats hade varit att börja räkna ifrån n:te roten ur det sammansatta talet. där n är antalet faktorer.

Udda antal faktorer går jävligt mycket långsammare.
︡28e19006-6988-47db-b2ce-ee6f5e9056c1︡
︠7edfd4e3-f582-4de3-ad74-3c5eb8a645b0i︠

%md
## Pollards Rho Algorithm
︡0face64e-e61d-41ba-87ea-0adbdc8622dc︡{"done":true,"md":"## Pollards Rho Algorithm"}
︠98c7831e-5b96-4b53-9863-268d7f6bcfab︠
from pollards_rho_algorithm import *

benchmarks = PollardsRhoAlgorithm.benchmark(smallPrimes, iterations)
print "small primes"
︡1ea413a9-a265-4b80-b3cd-61bec14218c5︡{"stdout":"small primes\n"}︡{"done":true}︡
︠0d28dcbf-ac0a-454c-94d6-8924ccd1ece1︠
︡8216fdce-0a19-408b-a966-4889e530491d︡
︠9ad8fdc4-7071-4568-9a12-75fb30a060a7i︠
%md
## Lenstras
︡f7a3a515-e036-4c55-8537-e4f7e4771b59︡{"done":true,"md":"## Lenstras"}
︠829afeb3-5ad8-402c-a540-98e48f3e0afc︠
from lenstras_elliptic_curve_factorization import *
#benchmarks = LenstrasEllipticCurveFactorization.benchmark(smallPrimes, iterations, {"maximumIterations": -1})
#values = map(lambda x: x[3].totalTime["default"], benchmarks)
#print sum(values)/len(values)


benchmarks = LenstrasEllipticCurveFactorization.benchmark(largerPrimes, iterations, {"maximumIterations": -1})
values = map(lambda x: x[3].totalTime["default"], benchmarks)
print sum(values)/len(values)

x = """
for i in [1, 2, 5, 10, 50, 100, 1000, -1]:
    print i,
    benchmarks = LenstrasEllipticCurveFactorization.benchmark(smallPrimes, iterations, {"maximumIterations": i})
    values = map(lambda x: x[3].totalTime["default"], benchmarks)
    print sum(values)/len(values)
"""
︡657c4faa-6e98-4c6b-8439-497ee33d218d︡{"stdout":"39.1989332011\n"}︡{"done":true}︡
︠b5f7e70c-659b-4187-8a4a-b562120e97cc︠
1 0.00392751317275
2 0.00423920154572
5 0.00414510526155
10 0.00408152279101
50 0.00364659710934
100 0.00381851321773
1000 0.00402681074644
︡a7b9c01e-ee05-4dc2-90c1-3a6adab8bc38︡
︠d85853df-011b-48df-8cba-66d5868634bc︠
1 0.00383018819909
2 0.0042179722535
5 0.00391916475798
10 0.00397971805773
50 0.00365026875546
100 0.00352077860581
1000 0.00339124202728
︡a6fcf9b9-7867-447b-a851-4383672a8550︡
︠28cbc7f3-65db-4f36-8f56-e6ee9542187a︠
1 0.00396525985316
2 0.00439642730512
5 0.00393485395532
10 0.00405216217041
50 0.00363662493856
100 0.00342771881505
1000 0.00337653912996
-1 0.178503995193
︡a9351fe1-7c76-4dff-bcc3-ef840b557d02︡
︠5b5b66aa-9e88-4122-960b-9c8f94934739i︠
%md
Lenstras observationer:
att sänka maximum iterations innebär att fler iterationer körs (totalt, inte per "omgång") - detta innebär att fler primtester körs.

Det skulle gå att använda ett såll (marcus lägger till om GitHub-lösningen). Istället för att gå till alla punkter kan man ta primtal.

Teori:
Att 5 är bättre än 1 och 2 iterationer kan ha att göra med att det är först då det börjar löna sig med primtalstester. Det är generellt bättra att ha få iterationer och försöka forcera faktorer, men primtestet håller då tillbaka prestandan. Att exempelvis lägga till en flagga första gången ett tal är primtestat skulle kunna resultera i att tal inte behöver primtestas mer än en gång, men ändå kunna testa enbart en iteration av algoritmen.

Literatur har tytt på att algoritmen kan vara snabbare om man avbryter efter n försök (sqrt(n)) och kör om igen för att få nya slumpvariabler. Vid imperisk studie hittade vi.... Vi såg dock att sqrt(n) presterade klart sämst. Detta visade sig ha med jämförelse av int och cocalcs integer med decimaler som blir vid sqrt(n). int(i) < int(ceil(sqrt(n))) är alltså snabbare (med en faktor av ≈60!!!) än int(i) < sqrt(n) trots att sqrt(n) enbart beräknas en enda gång!
︡1133b299-83ef-4277-9476-37e48b139d1c︡{"done":true,"md":"Lenstras observationer:\natt sänka maximum iterations innebär att fler iterationer körs (totalt, inte per \"omgång\") - detta innebär att fler primtester körs.\n\nDet skulle gå att använda ett såll (marcus lägger till om GitHub-lösningen). Istället för att gå till alla punkter kan man ta primtal.\n\nTeori:\nAtt 5 är bättre än 1 och 2 iterationer kan ha att göra med att det är först då det börjar löna sig med primtalstester. Det är generellt bättra att ha få iterationer och försöka forcera faktorer, men primtestet håller då tillbaka prestandan. Att exempelvis lägga till en flagga första gången ett tal är primtestat skulle kunna resultera i att tal inte behöver primtestas mer än en gång, men ändå kunna testa enbart en iteration av algoritmen.\n\nLiteratur har tytt på att algoritmen kan vara snabbare om man avbryter efter n försök (sqrt(n)) och kör om igen för att få nya slumpvariabler. Vid imperisk studie hittade vi.... Vi såg dock att sqrt(n) presterade klart sämst. Detta visade sig ha med jämförelse av int och cocalcs integer med decimaler som blir vid sqrt(n). int(i) < int(ceil(sqrt(n))) är alltså snabbare (med en faktor av ≈60!!!) än int(i) < sqrt(n) trots att sqrt(n) enbart beräknas en enda gång!"}
︠b47cf34e-1b83-47d3-8523-5c051fa7a3c8︠
%md
## Run all
︡3a9702e3-d07a-45ba-888d-df39d0b35d7a︡{"done":true,"md":"## Run all"}
︠9deb2d03-0f89-4087-88d8-942cece20f9br︠
from fermats_factorization import *
from pollards_rho_algorithm import *
from lenstras_elliptic_curve_factorization import *

benchmarks = FermatsFactorization.benchmark(smallClosePrimes, iterations)
print "close small primes"
benchmarks = FermatsFactorization.benchmark(mediumClosePrimes, iterations)
print "close medium primes"
benchmarks = FermatsFactorization.benchmark(largeClosePrimes, iterations)
print "close large primes"
print "fermats"

print "pollards"
benchmarks = PollardsRhoAlgo.benchmark(smallPrimes, iterations)
print "small primes"
benchmarks = PollardsRhoAlgorithm.benchmark(mediumPrimes, iterations)
print "medium primes"
benchmarks = PollardsRhoAlgorithm.benchmark(largePrimes, iterations)
print "large primes"
benchmarks = PollardsRhoAlgorithm.benchmark(largerPrimes, iterations)
print "larger primes"

benchmarks = PollardsRhoAlgorithm.benchmark(smallClosePrimes, iterations)
print "close small primes"
benchmarks = PollardsRhoAlgorithm.benchmark(mediumClosePrimes, iterations)
print "close medium primes"
benchmarks = PollardsRhoAlgorithm.benchmark(largeClosePrimes, iterations)
print "close large primes"
print "pollards"

print "lenstras"
benchmarks = LenstrasEllipticCurveFactorization.benchmark(smallPrimes, iterations)
print "small primes"
benchmarks = LenstrasEllipticCurveFactorization.benchmark(mediumPrimes, iterations)
print "medium primes"
benchmarks = LenstrasEllipticCurveFactorization.benchmark(largePrimes, iterations)
print "large primes"
benchmarks = LenstrasEllipticCurveFactorization.benchmark(largerPrimes, iterations)
print "larger primes"

benchmarks = LenstrasEllipticCurveFactorization.benchmark(smallClosePrimes, iterations)
print "close small primes"
benchmarks = LenstrasEllipticCurveFactorization.benchmark(mediumClosePrimes, iterations)
print "close medium primes"
benchmarks = LenstrasEllipticCurveFactorization.benchmark(largeClosePrimes, iterations)
print "close large primes"
print "lenstras"
︡0a6fced0-b458-4a7c-b3ec-a5e37e4ac016︡{"stdout":"close small primes\n"}︡{"stdout":"close small primes\n"}
︠85bd0330-3aeb-4c2c-950b-5fc18cb19418︠









" download="benchmark.sagews">benchmark.sagews</td></tr>
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<pre class="input"><code>%md</code><code><span class="cm-header cm-header-1">#</span><span class="cm-header cm-header-1"> </span><span class="cm-header cm-header-1">B</span><span class="cm-header cm-header-1">e</span><span class="cm-header cm-header-1">n</span><span class="cm-header cm-header-1">c</span><span class="cm-header cm-header-1">h</span><span class="cm-header cm-header-1">m</span><span class="cm-header cm-header-1">a</span><span class="cm-header cm-header-1">r</span><span class="cm-header cm-header-1">k</span></code><code>Here are the values used to benchmark the factorization functions</code></pre>
<div class="output md"><h1 id="benchmark">Benchmark</h1>
<p>Here are the values used to benchmark the factorization functions</p>
</div>
<pre class="input"><code><span class="cm-comment"># This cell needs to be executed</span></code><code></code><code><span class="cm-variable">iterations</span> = <span class="cm-number">10</span></code><code></code><code><span class="cm-variable">smallPrimes</span> = (<span class="cm-string">"small primes"</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">481</span>, [<span class="cm-number">1</span>, <span class="cm-number">13</span>, <span class="cm-number">37</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">31093</span>, [<span class="cm-number">1</span>, <span class="cm-number">31</span>, <span class="cm-number">17</span>, <span class="cm-number">59</span>])]), (<span class="cm-number">4</span>, [(<span class="cm-number">1213045</span>, [<span class="cm-number">1</span>, <span class="cm-number">37</span>, <span class="cm-number">5</span>, <span class="cm-number">83</span>, <span class="cm-number">79</span>])]), (<span class="cm-number">5</span>, [(<span class="cm-number">15001613</span>, [<span class="cm-number">1</span>, <span class="cm-number">31</span>, <span class="cm-number">37</span>, <span class="cm-number">29</span>, <span class="cm-number">11</span>, <span class="cm-number">41</span>])]), (<span class="cm-number">6</span>, [(<span class="cm-number">3429238769</span>, [<span class="cm-number">1</span>, <span class="cm-number">47</span>, <span class="cm-number">97</span>, <span class="cm-number">59</span>, <span class="cm-number">11</span>, <span class="cm-number">19</span>, <span class="cm-number">61</span>])]), (<span class="cm-number">7</span>, [(<span class="cm-number">206397809105</span>, [<span class="cm-number">1</span>, <span class="cm-number">37</span>, <span class="cm-number">79</span>, <span class="cm-number">5</span>, <span class="cm-number">53</span>, <span class="cm-number">41</span>, <span class="cm-number">67</span>, <span class="cm-number">97</span>])]), (<span class="cm-number">8</span>, [(<span class="cm-number">7311461300687</span>, [<span class="cm-number">1</span>, <span class="cm-number">41</span>, <span class="cm-number">23</span>, <span class="cm-number">73</span>, <span class="cm-number">41</span>, <span class="cm-number">59</span>, <span class="cm-number">83</span>, <span class="cm-number">23</span>, <span class="cm-number">23</span>])]), (<span class="cm-number">9</span>, [(<span class="cm-number">472213574958521</span>, [<span class="cm-number">1</span>, <span class="cm-number">41</span>, <span class="cm-number">53</span>, <span class="cm-number">37</span>, <span class="cm-number">47</span>, <span class="cm-number">61</span>, <span class="cm-number">11</span>, <span class="cm-number">71</span>, <span class="cm-number">61</span>, <span class="cm-number">43</span>])]), (<span class="cm-number">10</span>, [(<span class="cm-number">3443187949695</span>, [<span class="cm-number">1</span>, <span class="cm-number">29</span>, <span class="cm-number">43</span>, <span class="cm-number">83</span>, <span class="cm-number">5</span>, <span class="cm-number">73</span>, <span class="cm-number">41</span>, <span class="cm-number">13</span>, <span class="cm-number">3</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>])]), (<span class="cm-number">11</span>, [(<span class="cm-number">309773094336642695</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">97</span>, <span class="cm-number">11</span>, <span class="cm-number">31</span>, <span class="cm-number">83</span>, <span class="cm-number">97</span>, <span class="cm-number">31</span>, <span class="cm-number">89</span>, <span class="cm-number">43</span>, <span class="cm-number">53</span>, <span class="cm-number">37</span>])]), (<span class="cm-number">12</span>, [(<span class="cm-number">62263002262083735</span>, [<span class="cm-number">1</span>, <span class="cm-number">47</span>, <span class="cm-number">83</span>, <span class="cm-number">17</span>, <span class="cm-number">41</span>, <span class="cm-number">59</span>, <span class="cm-number">59</span>, <span class="cm-number">43</span>, <span class="cm-number">3</span>, <span class="cm-number">7</span>, <span class="cm-number">47</span>, <span class="cm-number">31</span>, <span class="cm-number">5</span>])]), (<span class="cm-number">13</span>, [(<span class="cm-number">666536544405580303</span>, [<span class="cm-number">1</span>, <span class="cm-number">31</span>, <span class="cm-number">23</span>, <span class="cm-number">7</span>, <span class="cm-number">47</span>, <span class="cm-number">23</span>, <span class="cm-number">67</span>, <span class="cm-number">37</span>, <span class="cm-number">37</span>, <span class="cm-number">19</span>, <span class="cm-number">13</span>, <span class="cm-number">41</span>, <span class="cm-number">19</span>, <span class="cm-number">7</span>])]), (<span class="cm-number">14</span>, [(<span class="cm-number">56142059257389353853</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">37</span>, <span class="cm-number">11</span>, <span class="cm-number">37</span>, <span class="cm-number">19</span>, <span class="cm-number">97</span>, <span class="cm-number">11</span>, <span class="cm-number">31</span>, <span class="cm-number">53</span>, <span class="cm-number">31</span>, <span class="cm-number">67</span>, <span class="cm-number">11</span>, <span class="cm-number">71</span>, <span class="cm-number">23</span>])]), (<span class="cm-number">15</span>, [(<span class="cm-number">3173389011480824657829</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">79</span>, <span class="cm-number">59</span>, <span class="cm-number">53</span>, <span class="cm-number">31</span>, <span class="cm-number">7</span>, <span class="cm-number">23</span>, <span class="cm-number">43</span>, <span class="cm-number">73</span>, <span class="cm-number">11</span>, <span class="cm-number">71</span>, <span class="cm-number">3</span>, <span class="cm-number">71</span>, <span class="cm-number">31</span>, <span class="cm-number">53</span>])]), (<span class="cm-number">16</span>, [(<span class="cm-number">15863359163742166197825</span>, [<span class="cm-number">1</span>, <span class="cm-number">37</span>, <span class="cm-number">3</span>, <span class="cm-number">19</span>, <span class="cm-number">61</span>, <span class="cm-number">5</span>, <span class="cm-number">11</span>, <span class="cm-number">79</span>, <span class="cm-number">79</span>, <span class="cm-number">67</span>, <span class="cm-number">3</span>, <span class="cm-number">71</span>, <span class="cm-number">5</span>, <span class="cm-number">71</span>, <span class="cm-number">97</span>, <span class="cm-number">43</span>, <span class="cm-number">17</span>])]), (<span class="cm-number">17</span>, [(<span class="cm-number">3839358256056932827602345</span>, [<span class="cm-number">1</span>, <span class="cm-number">67</span>, <span class="cm-number">17</span>, <span class="cm-number">29</span>, <span class="cm-number">19</span>, <span class="cm-number">53</span>, <span class="cm-number">41</span>, <span class="cm-number">19</span>, <span class="cm-number">19</span>, <span class="cm-number">37</span>, <span class="cm-number">73</span>, <span class="cm-number">89</span>, <span class="cm-number">13</span>, <span class="cm-number">5</span>, <span class="cm-number">53</span>, <span class="cm-number">3</span>, <span class="cm-number">73</span>, <span class="cm-number">43</span>])]), (<span class="cm-number">18</span>, [(<span class="cm-number">18710317739887802052740556555</span>, [<span class="cm-number">1</span>, <span class="cm-number">97</span>, <span class="cm-number">89</span>, <span class="cm-number">89</span>, <span class="cm-number">83</span>, <span class="cm-number">59</span>, <span class="cm-number">5</span>, <span class="cm-number">79</span>, <span class="cm-number">59</span>, <span class="cm-number">73</span>, <span class="cm-number">13</span>, <span class="cm-number">11</span>, <span class="cm-number">31</span>, <span class="cm-number">31</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">89</span>, <span class="cm-number">67</span>, <span class="cm-number">41</span>])]), (<span class="cm-number">19</span>, [(<span class="cm-number">155903632515187552359018988575</span>, [<span class="cm-number">1</span>, <span class="cm-number">97</span>, <span class="cm-number">43</span>, <span class="cm-number">47</span>, <span class="cm-number">89</span>, <span class="cm-number">97</span>, <span class="cm-number">11</span>, <span class="cm-number">73</span>, <span class="cm-number">73</span>, <span class="cm-number">61</span>, <span class="cm-number">3</span>, <span class="cm-number">37</span>, <span class="cm-number">29</span>, <span class="cm-number">61</span>, <span class="cm-number">73</span>, <span class="cm-number">5</span>, <span class="cm-number">5</span>, <span class="cm-number">67</span>, <span class="cm-number">29</span>, <span class="cm-number">37</span>])]), (<span class="cm-number">20</span>, [(<span class="cm-number">53620794966136160429097776631</span>, [<span class="cm-number">1</span>, <span class="cm-number">23</span>, <span class="cm-number">3</span>, <span class="cm-number">79</span>, <span class="cm-number">23</span>, <span class="cm-number">43</span>, <span class="cm-number">89</span>, <span class="cm-number">61</span>, <span class="cm-number">59</span>, <span class="cm-number">3</span>, <span class="cm-number">23</span>, <span class="cm-number">71</span>, <span class="cm-number">41</span>, <span class="cm-number">97</span>, <span class="cm-number">13</span>, <span class="cm-number">11</span>, <span class="cm-number">17</span>, <span class="cm-number">37</span>, <span class="cm-number">29</span>, <span class="cm-number">47</span>, <span class="cm-number">13</span>])])])</code><code></code><code><span class="cm-variable">mediumPrimes</span> = (<span class="cm-string">"medium primes"</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">9505247</span>, [<span class="cm-number">1</span>, <span class="cm-number">1427</span>, <span class="cm-number">6661</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">112377214483</span>, [<span class="cm-number">1</span>, <span class="cm-number">4451</span>, <span class="cm-number">7607</span>, <span class="cm-number">3319</span>])]), (<span class="cm-number">4</span>, [(<span class="cm-number">113332156404307</span>, [<span class="cm-number">1</span>, <span class="cm-number">4007</span>, <span class="cm-number">3539</span>, <span class="cm-number">2903</span>, <span class="cm-number">2753</span>])]), (<span class="cm-number">5</span>, [(<span class="cm-number">4298836929253947781</span>, [<span class="cm-number">1</span>, <span class="cm-number">8429</span>, <span class="cm-number">7417</span>, <span class="cm-number">5039</span>, <span class="cm-number">1867</span>, <span class="cm-number">7309</span>])]), (<span class="cm-number">6</span>, [(<span class="cm-number">11038759956959519253043</span>, [<span class="cm-number">1</span>, <span class="cm-number">4909</span>, <span class="cm-number">7307</span>, <span class="cm-number">1597</span>, <span class="cm-number">3733</span>, <span class="cm-number">7243</span>, <span class="cm-number">7127</span>])]), (<span class="cm-number">7</span>, [(<span class="cm-number">353271001154438218427229539</span>, [<span class="cm-number">1</span>, <span class="cm-number">8167</span>, <span class="cm-number">2687</span>, <span class="cm-number">5483</span>, <span class="cm-number">7253</span>, <span class="cm-number">5807</span>, <span class="cm-number">7127</span>, <span class="cm-number">9781</span>])]), (<span class="cm-number">8</span>, [(<span class="cm-number">858069121139663326922589137543</span>, [<span class="cm-number">1</span>, <span class="cm-number">9137</span>, <span class="cm-number">9463</span>, <span class="cm-number">3967</span>, <span class="cm-number">8737</span>, <span class="cm-number">4349</span>, <span class="cm-number">5003</span>, <span class="cm-number">2243</span>, <span class="cm-number">5867</span>])]), (<span class="cm-number">9</span>, [(<span class="cm-number">131563435713374902721110800493303</span>, [<span class="cm-number">1</span>, <span class="cm-number">5923</span>, <span class="cm-number">6907</span>, <span class="cm-number">8317</span>, <span class="cm-number">1151</span>, <span class="cm-number">1787</span>, <span class="cm-number">5479</span>, <span class="cm-number">9929</span>, <span class="cm-number">2287</span>, <span class="cm-number">1511</span>])]), (<span class="cm-number">10</span>, [(<span class="cm-number">2528123531806453766378415166939107671</span>, [<span class="cm-number">1</span>, <span class="cm-number">9749</span>, <span class="cm-number">2069</span>, <span class="cm-number">5879</span>, <span class="cm-number">8377</span>, <span class="cm-number">2683</span>, <span class="cm-number">2267</span>, <span class="cm-number">4919</span>, <span class="cm-number">3637</span>, <span class="cm-number">4703</span>, <span class="cm-number">4973</span>])]), (<span class="cm-number">11</span>, [(<span class="cm-number">98861961050577963648512453904444483679</span>, [<span class="cm-number">1</span>, <span class="cm-number">1283</span>, <span class="cm-number">2203</span>, <span class="cm-number">9533</span>, <span class="cm-number">1303</span>, <span class="cm-number">2239</span>, <span class="cm-number">1523</span>, <span class="cm-number">5009</span>, <span class="cm-number">1429</span>, <span class="cm-number">4253</span>, <span class="cm-number">2791</span>, <span class="cm-number">9719</span>])]), (<span class="cm-number">12</span>, [(<span class="cm-number">3699719069641057612942949836474926656811572189</span>, [<span class="cm-number">1</span>, <span class="cm-number">9133</span>, <span class="cm-number">9967</span>, <span class="cm-number">5879</span>, <span class="cm-number">6547</span>, <span class="cm-number">8929</span>, <span class="cm-number">2351</span>, <span class="cm-number">8681</span>, <span class="cm-number">6857</span>, <span class="cm-number">9719</span>, <span class="cm-number">7583</span>, <span class="cm-number">3461</span>, <span class="cm-number">3313</span>])]), (<span class="cm-number">13</span>, [(<span class="cm-number">9297901936182093694009454599759344878967851169253</span>, [<span class="cm-number">1</span>, <span class="cm-number">3947</span>, <span class="cm-number">8599</span>, <span class="cm-number">3109</span>, <span class="cm-number">4999</span>, <span class="cm-number">5581</span>, <span class="cm-number">8629</span>, <span class="cm-number">5953</span>, <span class="cm-number">8069</span>, <span class="cm-number">6829</span>, <span class="cm-number">9677</span>, <span class="cm-number">5197</span>, <span class="cm-number">8059</span>, <span class="cm-number">2753</span>])]), (<span class="cm-number">14</span>, [(<span class="cm-number">2987283285112052856777637490953875990300408162464831</span>, [<span class="cm-number">1</span>, <span class="cm-number">1523</span>, <span class="cm-number">7043</span>, <span class="cm-number">1889</span>, <span class="cm-number">7507</span>, <span class="cm-number">6133</span>, <span class="cm-number">3253</span>, <span class="cm-number">3797</span>, <span class="cm-number">1877</span>, <span class="cm-number">3463</span>, <span class="cm-number">7253</span>, <span class="cm-number">9281</span>, <span class="cm-number">7243</span>, <span class="cm-number">8837</span>, <span class="cm-number">9257</span>])]), (<span class="cm-number">15</span>, [(<span class="cm-number">14046255291904838561381033780082793879910682609073503319</span>, [<span class="cm-number">1</span>, <span class="cm-number">2003</span>, <span class="cm-number">9479</span>, <span class="cm-number">8677</span>, <span class="cm-number">4733</span>, <span class="cm-number">1279</span>, <span class="cm-number">3947</span>, <span class="cm-number">5431</span>, <span class="cm-number">9421</span>, <span class="cm-number">9059</span>, <span class="cm-number">9377</span>, <span class="cm-number">4817</span>, <span class="cm-number">1663</span>, <span class="cm-number">3221</span>, <span class="cm-number">8111</span>, <span class="cm-number">3923</span>])]), (<span class="cm-number">16</span>, [(<span class="cm-number">1672833210619559517657260567204379601678267615743624567961</span>, [<span class="cm-number">1</span>, <span class="cm-number">9883</span>, <span class="cm-number">6067</span>, <span class="cm-number">1559</span>, <span class="cm-number">1009</span>, <span class="cm-number">7069</span>, <span class="cm-number">2213</span>, <span class="cm-number">8713</span>, <span class="cm-number">1601</span>, <span class="cm-number">9491</span>, <span class="cm-number">7369</span>, <span class="cm-number">1327</span>, <span class="cm-number">6701</span>, <span class="cm-number">3359</span>, <span class="cm-number">6871</span>, <span class="cm-number">2039</span>, <span class="cm-number">2777</span>])]), (<span class="cm-number">17</span>, [(<span class="cm-number">212010140415468603762770884867770164189873990478028538128651543</span>, [<span class="cm-number">1</span>, <span class="cm-number">7757</span>, <span class="cm-number">1721</span>, <span class="cm-number">9343</span>, <span class="cm-number">2521</span>, <span class="cm-number">6793</span>, <span class="cm-number">8017</span>, <span class="cm-number">8117</span>, <span class="cm-number">2879</span>, <span class="cm-number">6491</span>, <span class="cm-number">3637</span>, <span class="cm-number">3319</span>, <span class="cm-number">3677</span>, <span class="cm-number">5711</span>, <span class="cm-number">7681</span>, <span class="cm-number">3433</span>, <span class="cm-number">2087</span>, <span class="cm-number">5851</span>])]), (<span class="cm-number">18</span>, [(<span class="cm-number">29763544558056708909351290167863189328280637881745015028766377567</span>, [<span class="cm-number">1</span>, <span class="cm-number">3793</span>, <span class="cm-number">3323</span>, <span class="cm-number">7841</span>, <span class="cm-number">9949</span>, <span class="cm-number">1181</span>, <span class="cm-number">6659</span>, <span class="cm-number">5171</span>, <span class="cm-number">2011</span>, <span class="cm-number">1861</span>, <span class="cm-number">3547</span>, <span class="cm-number">2887</span>, <span class="cm-number">2131</span>, <span class="cm-number">4801</span>, <span class="cm-number">2243</span>, <span class="cm-number">2141</span>, <span class="cm-number">5843</span>, <span class="cm-number">9349</span>, <span class="cm-number">7237</span>])]), (<span class="cm-number">19</span>, [(<span class="cm-number">183733102700898942618853672482178977569632673473846394890208044869833</span>, [<span class="cm-number">1</span>, <span class="cm-number">1861</span>, <span class="cm-number">6997</span>, <span class="cm-number">1459</span>, <span class="cm-number">7103</span>, <span class="cm-number">8191</span>, <span class="cm-number">6883</span>, <span class="cm-number">1499</span>, <span class="cm-number">1123</span>, <span class="cm-number">2069</span>, <span class="cm-number">8563</span>, <span class="cm-number">4091</span>, <span class="cm-number">7699</span>, <span class="cm-number">4027</span>, <span class="cm-number">5813</span>, <span class="cm-number">2099</span>, <span class="cm-number">8803</span>, <span class="cm-number">5821</span>, <span class="cm-number">2753</span>, <span class="cm-number">3709</span>])]), (<span class="cm-number">20</span>, [(<span class="cm-number">4315581732420458239176904986420389625324862838223258879737740116751534309</span>, [<span class="cm-number">1</span>, <span class="cm-number">4933</span>, <span class="cm-number">9473</span>, <span class="cm-number">2753</span>, <span class="cm-number">7949</span>, <span class="cm-number">1223</span>, <span class="cm-number">1213</span>, <span class="cm-number">1447</span>, <span class="cm-number">9689</span>, <span class="cm-number">2647</span>, <span class="cm-number">7177</span>, <span class="cm-number">4421</span>, <span class="cm-number">7883</span>, <span class="cm-number">7883</span>, <span class="cm-number">4673</span>, <span class="cm-number">7253</span>, <span class="cm-number">4787</span>, <span class="cm-number">2713</span>, <span class="cm-number">8929</span>, <span class="cm-number">2693</span>, <span class="cm-number">3673</span>])])])</code><code></code><code><span class="cm-variable">largePrimes</span> = (<span class="cm-string">"large primes"</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">4063375517</span>, [<span class="cm-number">1</span>, <span class="cm-number">78439</span>, <span class="cm-number">51803</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">522742080565357</span>, [<span class="cm-number">1</span>, <span class="cm-number">71167</span>, <span class="cm-number">82051</span>, <span class="cm-number">89521</span>])]), (<span class="cm-number">4</span>, [(<span class="cm-number">52187387971275982093</span>, [<span class="cm-number">1</span>, <span class="cm-number">89753</span>, <span class="cm-number">95717</span>, <span class="cm-number">64693</span>, <span class="cm-number">93901</span>])]), (<span class="cm-number">5</span>, [(<span class="cm-number">1162300682477934084344741</span>, [<span class="cm-number">1</span>, <span class="cm-number">65183</span>, <span class="cm-number">73883</span>, <span class="cm-number">57397</span>, <span class="cm-number">78803</span>, <span class="cm-number">53359</span>])]), (<span class="cm-number">6</span>, [(<span class="cm-number">188904463700616439184603915519</span>, [<span class="cm-number">1</span>, <span class="cm-number">77339</span>, <span class="cm-number">67523</span>, <span class="cm-number">99577</span>, <span class="cm-number">59333</span>, <span class="cm-number">64577</span>, <span class="cm-number">94811</span>])]), (<span class="cm-number">7</span>, [(<span class="cm-number">10382597739368109104150090934175379</span>, [<span class="cm-number">1</span>, <span class="cm-number">88321</span>, <span class="cm-number">75787</span>, <span class="cm-number">62417</span>, <span class="cm-number">55117</span>, <span class="cm-number">56179</span>, <span class="cm-number">83399</span>, <span class="cm-number">96233</span>])]), (<span class="cm-number">8</span>, [(<span class="cm-number">2236854499510418655753593501324101562419</span>, [<span class="cm-number">1</span>, <span class="cm-number">91433</span>, <span class="cm-number">96221</span>, <span class="cm-number">73477</span>, <span class="cm-number">94543</span>, <span class="cm-number">80489</span>, <span class="cm-number">73063</span>, <span class="cm-number">67619</span>, <span class="cm-number">92041</span>])]), (<span class="cm-number">9</span>, [(<span class="cm-number">35042439864356271632594896096225381140303727</span>, [<span class="cm-number">1</span>, <span class="cm-number">93077</span>, <span class="cm-number">63391</span>, <span class="cm-number">71261</span>, <span class="cm-number">50909</span>, <span class="cm-number">67979</span>, <span class="cm-number">75307</span>, <span class="cm-number">54403</span>, <span class="cm-number">61007</span>, <span class="cm-number">96353</span>])]), (<span class="cm-number">10</span>, [(<span class="cm-number">9938019912957784649301000808068798240941672975269</span>, [<span class="cm-number">1</span>, <span class="cm-number">94793</span>, <span class="cm-number">50909</span>, <span class="cm-number">88667</span>, <span class="cm-number">75377</span>, <span class="cm-number">74231</span>, <span class="cm-number">75553</span>, <span class="cm-number">99571</span>, <span class="cm-number">86509</span>, <span class="cm-number">89959</span>, <span class="cm-number">70901</span>])]), (<span class="cm-number">11</span>, [(<span class="cm-number">187109892613625880027947942540002116725379107367853319</span>, [<span class="cm-number">1</span>, <span class="cm-number">53611</span>, <span class="cm-number">60659</span>, <span class="cm-number">85313</span>, <span class="cm-number">88609</span>, <span class="cm-number">71089</span>, <span class="cm-number">75133</span>, <span class="cm-number">53267</span>, <span class="cm-number">66851</span>, <span class="cm-number">99041</span>, <span class="cm-number">80603</span>, <span class="cm-number">50129</span>])]), (<span class="cm-number">12</span>, [(<span class="cm-number">49161767109869991125387613590249904971687586373477597553749</span>, [<span class="cm-number">1</span>, <span class="cm-number">88211</span>, <span class="cm-number">97073</span>, <span class="cm-number">79111</span>, <span class="cm-number">80777</span>, <span class="cm-number">51859</span>, <span class="cm-number">99767</span>, <span class="cm-number">84869</span>, <span class="cm-number">80963</span>, <span class="cm-number">75937</span>, <span class="cm-number">91369</span>, <span class="cm-number">52027</span>, <span class="cm-number">70009</span>])]), (<span class="cm-number">13</span>, [(<span class="cm-number">986007145146192555084662271727905179607731398501077146686982027</span>, [<span class="cm-number">1</span>, <span class="cm-number">88241</span>, <span class="cm-number">72559</span>, <span class="cm-number">86239</span>, <span class="cm-number">92459</span>, <span class="cm-number">57097</span>, <span class="cm-number">63647</span>, <span class="cm-number">96167</span>, <span class="cm-number">54541</span>, <span class="cm-number">67219</span>, <span class="cm-number">70439</span>, <span class="cm-number">50123</span>, <span class="cm-number">66083</span>, <span class="cm-number">64609</span>])]), (<span class="cm-number">14</span>, [(<span class="cm-number">122656733660163473018814025422928703405374994772383697825517039916327</span>, [<span class="cm-number">1</span>, <span class="cm-number">68389</span>, <span class="cm-number">86539</span>, <span class="cm-number">63493</span>, <span class="cm-number">56377</span>, <span class="cm-number">61001</span>, <span class="cm-number">60217</span>, <span class="cm-number">85361</span>, <span class="cm-number">58393</span>, <span class="cm-number">65701</span>, <span class="cm-number">99251</span>, <span class="cm-number">94049</span>, <span class="cm-number">70289</span>, <span class="cm-number">77711</span>, <span class="cm-number">94397</span>])]), (<span class="cm-number">15</span>, [(<span class="cm-number">7842053712205825701754260824788620754149912403029793155702700015604989373</span>, [<span class="cm-number">1</span>, <span class="cm-number">81101</span>, <span class="cm-number">82387</span>, <span class="cm-number">92399</span>, <span class="cm-number">88903</span>, <span class="cm-number">67567</span>, <span class="cm-number">60037</span>, <span class="cm-number">96797</span>, <span class="cm-number">60161</span>, <span class="cm-number">58229</span>, <span class="cm-number">58243</span>, <span class="cm-number">76333</span>, <span class="cm-number">84181</span>, <span class="cm-number">67927</span>, <span class="cm-number">58403</span>, <span class="cm-number">69959</span>])]), (<span class="cm-number">16</span>, [(<span class="cm-number">414983958423876613281406476811736161578168944722930828312908133102632845752703</span>, [<span class="cm-number">1</span>, <span class="cm-number">92083</span>, <span class="cm-number">56477</span>, <span class="cm-number">94573</span>, <span class="cm-number">67187</span>, <span class="cm-number">83177</span>, <span class="cm-number">88471</span>, <span class="cm-number">52951</span>, <span class="cm-number">55579</span>, <span class="cm-number">71597</span>, <span class="cm-number">66179</span>, <span class="cm-number">59671</span>, <span class="cm-number">59729</span>, <span class="cm-number">69481</span>, <span class="cm-number">97583</span>, <span class="cm-number">54623</span>, <span class="cm-number">92717</span>])]), (<span class="cm-number">17</span>, [(<span class="cm-number">53002745697331794043197162487408577583597259117156412795445234494802005531541655757</span>, [<span class="cm-number">1</span>, <span class="cm-number">51949</span>, <span class="cm-number">81689</span>, <span class="cm-number">71089</span>, <span class="cm-number">81737</span>, <span class="cm-number">60659</span>, <span class="cm-number">93179</span>, <span class="cm-number">70489</span>, <span class="cm-number">90547</span>, <span class="cm-number">62189</span>, <span class="cm-number">92647</span>, <span class="cm-number">64123</span>, <span class="cm-number">75239</span>, <span class="cm-number">90841</span>, <span class="cm-number">88129</span>, <span class="cm-number">74653</span>, <span class="cm-number">57119</span>, <span class="cm-number">62791</span>])]), (<span class="cm-number">18</span>, [(<span class="cm-number">2774325281122485998802780772219788618613994707680106838689326624193111749855341451994853</span>, [<span class="cm-number">1</span>, <span class="cm-number">62081</span>, <span class="cm-number">94229</span>, <span class="cm-number">70313</span>, <span class="cm-number">50513</span>, <span class="cm-number">69247</span>, <span class="cm-number">67531</span>, <span class="cm-number">74903</span>, <span class="cm-number">84827</span>, <span class="cm-number">75037</span>, <span class="cm-number">57697</span>, <span class="cm-number">58789</span>, <span class="cm-number">78779</span>, <span class="cm-number">50909</span>, <span class="cm-number">88819</span>, <span class="cm-number">99923</span>, <span class="cm-number">90353</span>, <span class="cm-number">59627</span>, <span class="cm-number">92077</span>])]), (<span class="cm-number">19</span>, [(<span class="cm-number">81814093803623318906242340014181655977264794640309240515571248892045623493330471152004211349</span>, [<span class="cm-number">1</span>, <span class="cm-number">63629</span>, <span class="cm-number">76597</span>, <span class="cm-number">60761</span>, <span class="cm-number">85223</span>, <span class="cm-number">63611</span>, <span class="cm-number">82039</span>, <span class="cm-number">75431</span>, <span class="cm-number">52501</span>, <span class="cm-number">77351</span>, <span class="cm-number">54547</span>, <span class="cm-number">60139</span>, <span class="cm-number">80387</span>, <span class="cm-number">51721</span>, <span class="cm-number">59093</span>, <span class="cm-number">65537</span>, <span class="cm-number">66587</span>, <span class="cm-number">81817</span>, <span class="cm-number">91961</span>, <span class="cm-number">76631</span>])]), (<span class="cm-number">20</span>, [(<span class="cm-number">4759420676774002917027080074804196749925026162216764903500438803531064867662815998548224047575111</span>, [<span class="cm-number">1</span>, <span class="cm-number">51193</span>, <span class="cm-number">63617</span>, <span class="cm-number">74827</span>, <span class="cm-number">77239</span>, <span class="cm-number">65761</span>, <span class="cm-number">71011</span>, <span class="cm-number">82613</span>, <span class="cm-number">77719</span>, <span class="cm-number">99709</span>, <span class="cm-number">85213</span>, <span class="cm-number">95959</span>, <span class="cm-number">54787</span>, <span class="cm-number">56503</span>, <span class="cm-number">53503</span>, <span class="cm-number">61553</span>, <span class="cm-number">60689</span>, <span class="cm-number">67033</span>, <span class="cm-number">64513</span>, <span class="cm-number">58831</span>, <span class="cm-number">65713</span>])])])</code><code></code><code><span class="cm-variable">largerPrimes</span> = (<span class="cm-string">'Larger primes'</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">187186702751</span>, [<span class="cm-number">1</span>, <span class="cm-number">590377</span>, <span class="cm-number">317063</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">227610837550458559</span>, [<span class="cm-number">1</span>, <span class="cm-number">345461</span>, <span class="cm-number">887483</span>, <span class="cm-number">742393</span>])]), (<span class="cm-number">4</span>, [(<span class="cm-number">70258793277571237647233</span>, [<span class="cm-number">1</span>, <span class="cm-number">899981</span>, <span class="cm-number">280607</span>, <span class="cm-number">312353</span>, <span class="cm-number">890683</span>])]), (<span class="cm-number">5</span>, [(<span class="cm-number">28721678110719749295143472251</span>, [<span class="cm-number">1</span>, <span class="cm-number">252323</span>, <span class="cm-number">322589</span>, <span class="cm-number">562259</span>, <span class="cm-number">826169</span>, <span class="cm-number">759623</span>])]), (<span class="cm-number">6</span>, [(<span class="cm-number">16584959865789562307773297581668989</span>, [<span class="cm-number">1</span>, <span class="cm-number">526199</span>, <span class="cm-number">772097</span>, <span class="cm-number">347519</span>, <span class="cm-number">284857</span>, <span class="cm-number">826759</span>, <span class="cm-number">498779</span>])]), (<span class="cm-number">7</span>, [(<span class="cm-number">40135231725177170651266451927317370040017</span>, [<span class="cm-number">1</span>, <span class="cm-number">689917</span>, <span class="cm-number">363037</span>, <span class="cm-number">462571</span>, <span class="cm-number">805559</span>, <span class="cm-number">561367</span>, <span class="cm-number">823201</span>, <span class="cm-number">930571</span>])]), (<span class="cm-number">8</span>, [(<span class="cm-number">13543477157075511779696540916677807232136281983</span>, [<span class="cm-number">1</span>, <span class="cm-number">369841</span>, <span class="cm-number">369079</span>, <span class="cm-number">898481</span>, <span class="cm-number">593171</span>, <span class="cm-number">673613</span>, <span class="cm-number">333197</span>, <span class="cm-number">874127</span>, <span class="cm-number">948901</span>])]), (<span class="cm-number">9</span>, [(<span class="cm-number">21868276789400720715203792286586485297210926281696241</span>, [<span class="cm-number">1</span>, <span class="cm-number">508867</span>, <span class="cm-number">666031</span>, <span class="cm-number">911839</span>, <span class="cm-number">521657</span>, <span class="cm-number">319981</span>, <span class="cm-number">592597</span>, <span class="cm-number">776357</span>, <span class="cm-number">947389</span>, <span class="cm-number">972611</span>])]), (<span class="cm-number">10</span>, [(<span class="cm-number">3398638008982066688531884463264580936942051180990210108323</span>, [<span class="cm-number">1</span>, <span class="cm-number">655243</span>, <span class="cm-number">756373</span>, <span class="cm-number">805219</span>, <span class="cm-number">655859</span>, <span class="cm-number">563197</span>, <span class="cm-number">592087</span>, <span class="cm-number">467101</span>, <span class="cm-number">333331</span>, <span class="cm-number">364031</span>, <span class="cm-number">687023</span>])]), (<span class="cm-number">11</span>, [(<span class="cm-number">9136943238414668122038298815310911346194279867410940342650742671</span>, [<span class="cm-number">1</span>, <span class="cm-number">741457</span>, <span class="cm-number">386333</span>, <span class="cm-number">423887</span>, <span class="cm-number">741869</span>, <span class="cm-number">752281</span>, <span class="cm-number">938323</span>, <span class="cm-number">933847</span>, <span class="cm-number">548567</span>, <span class="cm-number">636953</span>, <span class="cm-number">986351</span>, <span class="cm-number">446477</span>])]), (<span class="cm-number">12</span>, [(<span class="cm-number">38071366054007302601960554011850986602984984747338895665946437878377453</span>, [<span class="cm-number">1</span>, <span class="cm-number">779189</span>, <span class="cm-number">507691</span>, <span class="cm-number">750961</span>, <span class="cm-number">875417</span>, <span class="cm-number">967427</span>, <span class="cm-number">371251</span>, <span class="cm-number">857737</span>, <span class="cm-number">943073</span>, <span class="cm-number">943363</span>, <span class="cm-number">895087</span>, <span class="cm-number">761861</span>, <span class="cm-number">783283</span>])]), (<span class="cm-number">13</span>, [(<span class="cm-number">368625134734142995123626326808047577046599110832420111833822347712566666853</span>, [<span class="cm-number">1</span>, <span class="cm-number">409063</span>, <span class="cm-number">634079</span>, <span class="cm-number">260263</span>, <span class="cm-number">620887</span>, <span class="cm-number">744407</span>, <span class="cm-number">440183</span>, <span class="cm-number">971171</span>, <span class="cm-number">755737</span>, <span class="cm-number">654679</span>, <span class="cm-number">556093</span>, <span class="cm-number">968593</span>, <span class="cm-number">293483</span>, <span class="cm-number">353359</span>])]), (<span class="cm-number">14</span>, [(<span class="cm-number">350789352401366415305072032960473921257900088976055701075698491956756257404655481</span>, [<span class="cm-number">1</span>, <span class="cm-number">746483</span>, <span class="cm-number">585587</span>, <span class="cm-number">530851</span>, <span class="cm-number">555349</span>, <span class="cm-number">751259</span>, <span class="cm-number">378949</span>, <span class="cm-number">404843</span>, <span class="cm-number">937823</span>, <span class="cm-number">447683</span>, <span class="cm-number">444817</span>, <span class="cm-number">511289</span>, <span class="cm-number">644291</span>, <span class="cm-number">603731</span>, <span class="cm-number">635879</span>])]), (<span class="cm-number">15</span>, [(<span class="cm-number">431463623920866689805584050956253221308032437458060677109830929906624804391812275410793</span>, [<span class="cm-number">1</span>, <span class="cm-number">533747</span>, <span class="cm-number">682333</span>, <span class="cm-number">828067</span>, <span class="cm-number">484751</span>, <span class="cm-number">446261</span>, <span class="cm-number">578687</span>, <span class="cm-number">977147</span>, <span class="cm-number">283831</span>, <span class="cm-number">564979</span>, <span class="cm-number">690163</span>, <span class="cm-number">836863</span>, <span class="cm-number">327017</span>, <span class="cm-number">693403</span>, <span class="cm-number">794153</span>, <span class="cm-number">701257</span>])]), (<span class="cm-number">16</span>, [(<span class="cm-number">3090895415152262211627476518158103729565126064320269607944002601270807904266490336040532453091</span>, [<span class="cm-number">1</span>, <span class="cm-number">729761</span>, <span class="cm-number">596009</span>, <span class="cm-number">627481</span>, <span class="cm-number">812963</span>, <span class="cm-number">576757</span>, <span class="cm-number">711679</span>, <span class="cm-number">825983</span>, <span class="cm-number">955613</span>, <span class="cm-number">911593</span>, <span class="cm-number">587959</span>, <span class="cm-number">700759</span>, <span class="cm-number">767623</span>, <span class="cm-number">268979</span>, <span class="cm-number">651821</span>, <span class="cm-number">858763</span>, <span class="cm-number">990523</span>])]), (<span class="cm-number">17</span>, [(<span class="cm-number">1881182900515253077657544850252234921978522056443095815660055032303071363462608086772712619979929</span>, [<span class="cm-number">1</span>, <span class="cm-number">765283</span>, <span class="cm-number">360959</span>, <span class="cm-number">399181</span>, <span class="cm-number">468653</span>, <span class="cm-number">287849</span>, <span class="cm-number">481297</span>, <span class="cm-number">382351</span>, <span class="cm-number">711727</span>, <span class="cm-number">261917</span>, <span class="cm-number">846983</span>, <span class="cm-number">754463</span>, <span class="cm-number">346711</span>, <span class="cm-number">346217</span>, <span class="cm-number">541201</span>, <span class="cm-number">990377</span>, <span class="cm-number">338027</span>, <span class="cm-number">265261</span>])]), (<span class="cm-number">18</span>, [(<span class="cm-number">23169284855147410245104557782459930672656640958302012768111347982308836202807150642723443947428384991983</span>, [<span class="cm-number">1</span>, <span class="cm-number">428899</span>, <span class="cm-number">979543</span>, <span class="cm-number">314243</span>, <span class="cm-number">947819</span>, <span class="cm-number">441121</span>, <span class="cm-number">954277</span>, <span class="cm-number">304709</span>, <span class="cm-number">620717</span>, <span class="cm-number">427877</span>, <span class="cm-number">399689</span>, <span class="cm-number">415343</span>, <span class="cm-number">289181</span>, <span class="cm-number">985063</span>, <span class="cm-number">883429</span>, <span class="cm-number">840979</span>, <span class="cm-number">488011</span>, <span class="cm-number">665153</span>, <span class="cm-number">476587</span>])]), (<span class="cm-number">19</span>, [(<span class="cm-number">14148962297868150427488880128423453856260378948237916062898523907220089968114112210934057887773724022523805637</span>, [<span class="cm-number">1</span>, <span class="cm-number">289249</span>, <span class="cm-number">679417</span>, <span class="cm-number">535481</span>, <span class="cm-number">947539</span>, <span class="cm-number">832757</span>, <span class="cm-number">934537</span>, <span class="cm-number">424829</span>, <span class="cm-number">280451</span>, <span class="cm-number">990893</span>, <span class="cm-number">300319</span>, <span class="cm-number">404321</span>, <span class="cm-number">384547</span>, <span class="cm-number">424223</span>, <span class="cm-number">340387</span>, <span class="cm-number">624097</span>, <span class="cm-number">839207</span>, <span class="cm-number">793999</span>, <span class="cm-number">901717</span>, <span class="cm-number">610837</span>])]), (<span class="cm-number">20</span>, [(<span class="cm-number">729883933457870363432152113700293245237626872643614401017049987282050216103044544786654875010234935256140803954547</span>, [<span class="cm-number">1</span>, <span class="cm-number">704321</span>, <span class="cm-number">342799</span>, <span class="cm-number">581447</span>, <span class="cm-number">842249</span>, <span class="cm-number">257837</span>, <span class="cm-number">938219</span>, <span class="cm-number">255349</span>, <span class="cm-number">266009</span>, <span class="cm-number">265709</span>, <span class="cm-number">725341</span>, <span class="cm-number">452033</span>, <span class="cm-number">692717</span>, <span class="cm-number">464923</span>, <span class="cm-number">648007</span>, <span class="cm-number">795307</span>, <span class="cm-number">476659</span>, <span class="cm-number">314399</span>, <span class="cm-number">367687</span>, <span class="cm-number">518579</span>, <span class="cm-number">909203</span>])])])</code><code></code><code><span class="cm-variable">largestPrimes</span> = (<span class="cm-string">"largest primes"</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">156522823147269816284598631312951810612882615746935161032701</span>, [<span class="cm-number">1</span>, <span class="cm-number">272431619873581157551105550911</span>, <span class="cm-number">574539854147262640021933661891</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">33874806091130475009235697120079470280226688813077808889362612187330734249556669208421939</span>, [<span class="cm-number">1</span>, <span class="cm-number">155903459436988767034958394683</span>, <span class="cm-number">785575136929393571457349360969</span>, <span class="cm-number">276588001275352182296868615457</span>])])])</code><code></code><code><span class="cm-keyword">print</span> <span class="cm-string">"Stored number suite - re run if needed"</span></code></pre>
<div class="output stdout">Stored number suite - re run if needed
</div>
<pre class="input"><code><span class="cm-variable">smallClosePrimes</span> = (<span class="cm-string">'Small close primes'</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">187</span>, [<span class="cm-number">1</span>, <span class="cm-number">11</span>, <span class="cm-number">17</span>]), (<span class="cm-number">221</span>, [<span class="cm-number">1</span>, <span class="cm-number">13</span>, <span class="cm-number">17</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">1463</span>, [<span class="cm-number">1</span>, <span class="cm-number">11</span>, <span class="cm-number">19</span>, <span class="cm-number">7</span>]), (<span class="cm-number">1183</span>, [<span class="cm-number">1</span>, <span class="cm-number">13</span>, <span class="cm-number">13</span>, <span class="cm-number">7</span>])]), (<span class="cm-number">4</span>, [(<span class="cm-number">23023</span>, [<span class="cm-number">1</span>, <span class="cm-number">11</span>, <span class="cm-number">23</span>, <span class="cm-number">7</span>, <span class="cm-number">13</span>]), (<span class="cm-number">18515</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">23</span>, <span class="cm-number">7</span>, <span class="cm-number">23</span>])]), (<span class="cm-number">5</span>, [(<span class="cm-number">161733</span>, [<span class="cm-number">1</span>, <span class="cm-number">11</span>, <span class="cm-number">13</span>, <span class="cm-number">13</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>]), (<span class="cm-number">252655</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">23</span>, <span class="cm-number">13</span>, <span class="cm-number">13</span>, <span class="cm-number">13</span>])]), (<span class="cm-number">6</span>, [(<span class="cm-number">1154725</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">13</span>, <span class="cm-number">5</span>, <span class="cm-number">17</span>, <span class="cm-number">11</span>, <span class="cm-number">19</span>]), (<span class="cm-number">955695</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">29</span>, <span class="cm-number">13</span>, <span class="cm-number">13</span>, <span class="cm-number">3</span>, <span class="cm-number">13</span>])]), (<span class="cm-number">7</span>, [(<span class="cm-number">7743087</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">11</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>]), (<span class="cm-number">40602639</span>, [<span class="cm-number">1</span>, <span class="cm-number">11</span>, <span class="cm-number">29</span>, <span class="cm-number">11</span>, <span class="cm-number">19</span>, <span class="cm-number">7</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>])]), (<span class="cm-number">8</span>, [(<span class="cm-number">107279613</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">23</span>, <span class="cm-number">3</span>, <span class="cm-number">23</span>, <span class="cm-number">7</span>, <span class="cm-number">37</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>]), (<span class="cm-number">283487325</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">17</span>, <span class="cm-number">11</span>, <span class="cm-number">41</span>, <span class="cm-number">5</span>, <span class="cm-number">17</span>, <span class="cm-number">5</span>, <span class="cm-number">29</span>])]), (<span class="cm-number">9</span>, [(<span class="cm-number">935717625</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">43</span>, <span class="cm-number">5</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">23</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">5</span>]), (<span class="cm-number">878332455</span>, [<span class="cm-number">1</span>, <span class="cm-number">7</span>, <span class="cm-number">17</span>, <span class="cm-number">5</span>, <span class="cm-number">31</span>, <span class="cm-number">11</span>, <span class="cm-number">13</span>, <span class="cm-number">3</span>, <span class="cm-number">37</span>, <span class="cm-number">3</span>])]), (<span class="cm-number">10</span>, [(<span class="cm-number">24451456575</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">17</span>, <span class="cm-number">7</span>, <span class="cm-number">13</span>, <span class="cm-number">5</span>, <span class="cm-number">43</span>, <span class="cm-number">13</span>, <span class="cm-number">29</span>, <span class="cm-number">5</span>, <span class="cm-number">13</span>]), (<span class="cm-number">1748802168425</span>, [<span class="cm-number">1</span>, <span class="cm-number">13</span>, <span class="cm-number">41</span>, <span class="cm-number">5</span>, <span class="cm-number">47</span>, <span class="cm-number">13</span>, <span class="cm-number">41</span>, <span class="cm-number">5</span>, <span class="cm-number">31</span>, <span class="cm-number">13</span>, <span class="cm-number">13</span>])]), (<span class="cm-number">11</span>, [(<span class="cm-number">6148592793</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">3</span>, <span class="cm-number">19</span>, <span class="cm-number">7</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">17</span>, <span class="cm-number">3</span>]), (<span class="cm-number">433954018575</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">5</span>, <span class="cm-number">23</span>, <span class="cm-number">11</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">47</span>, <span class="cm-number">7</span>, <span class="cm-number">17</span>, <span class="cm-number">3</span>])]), (<span class="cm-number">12</span>, [(<span class="cm-number">2336441234985</span>, [<span class="cm-number">1</span>, <span class="cm-number">13</span>, <span class="cm-number">37</span>, <span class="cm-number">5</span>, <span class="cm-number">19</span>, <span class="cm-number">11</span>, <span class="cm-number">13</span>, <span class="cm-number">3</span>, <span class="cm-number">41</span>, <span class="cm-number">3</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">17</span>]), (<span class="cm-number">6169110180975</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">41</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">7</span>, <span class="cm-number">31</span>, <span class="cm-number">5</span>, <span class="cm-number">19</span>, <span class="cm-number">7</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">17</span>])]), (<span class="cm-number">13</span>, [(<span class="cm-number">19600594410375</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">37</span>, <span class="cm-number">11</span>, <span class="cm-number">29</span>, <span class="cm-number">5</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>]), (<span class="cm-number">27464992644375</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">13</span>, <span class="cm-number">11</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">13</span>, <span class="cm-number">5</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">41</span>, <span class="cm-number">5</span>])]), (<span class="cm-number">14</span>, [(<span class="cm-number">979848317369025</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">23</span>, <span class="cm-number">3</span>, <span class="cm-number">59</span>, <span class="cm-number">5</span>, <span class="cm-number">17</span>, <span class="cm-number">13</span>, <span class="cm-number">59</span>, <span class="cm-number">3</span>, <span class="cm-number">23</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">41</span>]), (<span class="cm-number">16313742837926625</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">23</span>, <span class="cm-number">13</span>, <span class="cm-number">61</span>, <span class="cm-number">5</span>, <span class="cm-number">53</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">5</span>, <span class="cm-number">43</span>, <span class="cm-number">7</span>, <span class="cm-number">53</span>, <span class="cm-number">7</span>, <span class="cm-number">13</span>])]), (<span class="cm-number">15</span>, [(<span class="cm-number">276612138433767825</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">41</span>, <span class="cm-number">13</span>, <span class="cm-number">67</span>, <span class="cm-number">3</span>, <span class="cm-number">67</span>, <span class="cm-number">5</span>, <span class="cm-number">41</span>, <span class="cm-number">3</span>, <span class="cm-number">53</span>, <span class="cm-number">13</span>, <span class="cm-number">43</span>, <span class="cm-number">5</span>, <span class="cm-number">47</span>, <span class="cm-number">3</span>]), (<span class="cm-number">480388899282435</span>, [<span class="cm-number">1</span>, <span class="cm-number">11</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">5</span>, <span class="cm-number">13</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">3</span>, <span class="cm-number">23</span>, <span class="cm-number">3</span>, <span class="cm-number">53</span>, <span class="cm-number">3</span>])]), (<span class="cm-number">16</span>, [(<span class="cm-number">13042072935932625</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">5</span>, <span class="cm-number">23</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">3</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">3</span>, <span class="cm-number">13</span>, <span class="cm-number">5</span>, <span class="cm-number">43</span>, <span class="cm-number">5</span>, <span class="cm-number">59</span>]), (<span class="cm-number">382555146521019375</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">29</span>, <span class="cm-number">5</span>, <span class="cm-number">61</span>, <span class="cm-number">3</span>, <span class="cm-number">71</span>, <span class="cm-number">3</span>, <span class="cm-number">23</span>, <span class="cm-number">5</span>, <span class="cm-number">61</span>, <span class="cm-number">5</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">37</span>, <span class="cm-number">5</span>, <span class="cm-number">61</span>])]), (<span class="cm-number">17</span>, [(<span class="cm-number">3312499880682759375</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">29</span>, <span class="cm-number">7</span>, <span class="cm-number">79</span>, <span class="cm-number">3</span>, <span class="cm-number">73</span>, <span class="cm-number">3</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>, <span class="cm-number">17</span>, <span class="cm-number">5</span>]), (<span class="cm-number">1706485929231344625</span>, [<span class="cm-number">1</span>, <span class="cm-number">13</span>, <span class="cm-number">67</span>, <span class="cm-number">5</span>, <span class="cm-number">43</span>, <span class="cm-number">5</span>, <span class="cm-number">53</span>, <span class="cm-number">3</span>, <span class="cm-number">19</span>, <span class="cm-number">3</span>, <span class="cm-number">47</span>, <span class="cm-number">3</span>, <span class="cm-number">17</span>, <span class="cm-number">3</span>, <span class="cm-number">17</span>, <span class="cm-number">7</span>, <span class="cm-number">47</span>, <span class="cm-number">5</span>])]), (<span class="cm-number">18</span>, [(<span 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class="cm-number">3</span>, <span class="cm-number">43</span>, <span class="cm-number">5</span>, <span class="cm-number">41</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">13</span>, <span class="cm-number">43</span>, <span class="cm-number">3</span>, <span class="cm-number">67</span>, <span class="cm-number">5</span>, <span class="cm-number">83</span>, <span class="cm-number">5</span>, <span class="cm-number">67</span>]), (<span class="cm-number">19589478089411820609060525</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">107</span>, <span class="cm-number">3</span>, <span class="cm-number">97</span>, <span class="cm-number">23</span>, <span class="cm-number">47</span>, <span class="cm-number">29</span>, <span class="cm-number">31</span>, <span class="cm-number">5</span>, <span class="cm-number">89</span>, <span class="cm-number">19</span>, <span class="cm-number">103</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">17</span>, <span class="cm-number">83</span>, <span class="cm-number">11</span>, <span class="cm-number">103</span>])]), (<span class="cm-number">19</span>, [(<span class="cm-number">17459425383139545183002625</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">53</span>, <span class="cm-number">3</span>, <span class="cm-number">61</span>, <span class="cm-number">5</span>, <span class="cm-number">101</span>, <span class="cm-number">13</span>, <span class="cm-number">73</span>, <span class="cm-number">19</span>, <span class="cm-number">59</span>, <span class="cm-number">7</span>, <span class="cm-number">103</span>, <span class="cm-number">11</span>, <span class="cm-number">101</span>, <span class="cm-number">5</span>, <span class="cm-number">41</span>, <span class="cm-number">11</span>, <span class="cm-number">53</span>, <span class="cm-number">7</span>]), (<span class="cm-number">253868269728472313813110875</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">59</span>, <span class="cm-number">3</span>, <span class="cm-number">67</span>, <span class="cm-number">5</span>, <span class="cm-number">67</span>, <span class="cm-number">29</span>, <span class="cm-number">41</span>, <span class="cm-number">13</span>, <span class="cm-number">109</span>, <span class="cm-number">19</span>, <span class="cm-number">47</span>, <span class="cm-number">13</span>, <span class="cm-number">73</span>, <span class="cm-number">31</span>, <span class="cm-number">43</span>, <span class="cm-number">5</span>, <span class="cm-number">79</span>, <span class="cm-number">17</span>])]), (<span class="cm-number">20</span>, [(<span class="cm-number">10019176560312034400567595</span>, [<span class="cm-number">1</span>, <span class="cm-number">3</span>, <span class="cm-number">47</span>, <span class="cm-number">3</span>, <span class="cm-number">83</span>, <span class="cm-number">5</span>, <span class="cm-number">47</span>, <span class="cm-number">19</span>, <span class="cm-number">103</span>, <span class="cm-number">29</span>, <span class="cm-number">41</span>, <span class="cm-number">3</span>, <span class="cm-number">31</span>, <span class="cm-number">3</span>, <span class="cm-number">61</span>, <span class="cm-number">3</span>, <span class="cm-number">43</span>, <span class="cm-number">3</span>, <span class="cm-number">79</span>, <span class="cm-number">17</span>, <span class="cm-number">59</span>]), (<span class="cm-number">215947535722966231822673332275</span>, [<span class="cm-number">1</span>, <span class="cm-number">5</span>, <span class="cm-number">109</span>, <span class="cm-number">17</span>, <span class="cm-number">43</span>, <span class="cm-number">23</span>, <span class="cm-number">47</span>, <span class="cm-number">23</span>, <span class="cm-number">79</span>, <span class="cm-number">11</span>, <span class="cm-number">83</span>, <span class="cm-number">17</span>, <span class="cm-number">113</span>, <span class="cm-number">17</span>, <span class="cm-number">61</span>, <span class="cm-number">17</span>, <span class="cm-number">83</span>, <span class="cm-number">3</span>, <span class="cm-number">107</span>, <span class="cm-number">5</span>, <span class="cm-number">67</span>])])])</code><code></code><code><span class="cm-variable">mediumClosePrimes</span> = (<span class="cm-string">"Medium close primes"</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">316933</span>, [<span class="cm-number">1</span>, <span class="cm-number">557</span>, <span class="cm-number">569</span>]), (<span class="cm-number">313591</span>, [<span class="cm-number">1</span>, <span class="cm-number">557</span>, <span class="cm-number">563</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">171534277</span>, [<span class="cm-number">1</span>, <span class="cm-number">557</span>, <span class="cm-number">563</span>, <span class="cm-number">547</span>]), (<span class="cm-number">173971709</span>, [<span class="cm-number">1</span>, <span class="cm-number">557</span>, <span class="cm-number">571</span>, <span class="cm-number">547</span>])]), (<span class="cm-number">4</span>, [(<span class="cm-number">94758693241</span>, [<span class="cm-number">1</span>, <span class="cm-number">541</span>, <span class="cm-number">569</span>, <span class="cm-number">541</span>, <span class="cm-number">569</span>]), (<span class="cm-number">100381676093</span>, [<span class="cm-number">1</span>, <span class="cm-number">557</span>, <span class="cm-number">571</span>, <span class="cm-number">547</span>, <span class="cm-number">577</span>])]), (<span class="cm-number">5</span>, [(<span class="cm-number">56670957560149</span>, [<span class="cm-number">1</span>, <span class="cm-number">563</span>, <span class="cm-number">587</span>, <span class="cm-number">563</span>, <span class="cm-number">563</span>, <span class="cm-number">541</span>]), (<span class="cm-number">55737645509339</span>, [<span class="cm-number">1</span>, <span class="cm-number">563</span>, <span class="cm-number">563</span>, <span class="cm-number">547</span>, <span class="cm-number">571</span>, <span class="cm-number">563</span>])]), (<span class="cm-number">6</span>, [(<span class="cm-number">33960079475671199</span>, [<span class="cm-number">1</span>, <span class="cm-number">557</span>, <span class="cm-number">563</span>, <span class="cm-number">547</span>, <span class="cm-number">593</span>, <span class="cm-number">563</span>, <span class="cm-number">593</span>]), (<span class="cm-number">28590087506703829</span>, [<span class="cm-number">1</span>, <span class="cm-number">541</span>, <span class="cm-number">593</span>, <span class="cm-number">521</span>, <span class="cm-number">569</span>, <span class="cm-number">521</span>, <span class="cm-number">577</span>])]), (<span class="cm-number">7</span>, [(<span class="cm-number">16668687877305357367</span>, [<span class="cm-number">1</span>, <span class="cm-number">547</span>, <span class="cm-number">593</span>, <span class="cm-number">547</span>, <span class="cm-number">593</span>, <span class="cm-number">547</span>, <span class="cm-number">569</span>, <span class="cm-number">509</span>]), (<span class="cm-number">14895421562352162947</span>, [<span class="cm-number">1</span>, <span class="cm-number">523</span>, <span class="cm-number">563</span>, <span class="cm-number">523</span>, <span class="cm-number">587</span>, <span class="cm-number">541</span>, <span class="cm-number">563</span>, <span class="cm-number">541</span>])]), (<span class="cm-number">8</span>, [(<span class="cm-number">8825598186724532340139</span>, [<span class="cm-number">1</span>, <span class="cm-number">503</span>, <span class="cm-number">577</span>, <span class="cm-number">563</span>, <span class="cm-number">601</span>, <span class="cm-number">503</span>, <span class="cm-number">593</span>, <span class="cm-number">503</span>, <span class="cm-number">599</span>]), (<span class="cm-number">8056030357210311798593</span>, [<span class="cm-number">1</span>, <span class="cm-number">509</span>, <span class="cm-number">571</span>, <span class="cm-number">541</span>, <span class="cm-number">563</span>, <span class="cm-number">509</span>, <span class="cm-number">587</span>, <span class="cm-number">541</span>, <span class="cm-number">563</span>])]), (<span class="cm-number">9</span>, [(<span class="cm-number">5176371113800439756757811</span>, [<span class="cm-number">1</span>, <span class="cm-number">523</span>, <span class="cm-number">569</span>, <span class="cm-number">503</span>, <span class="cm-number">593</span>, <span class="cm-number">547</span>, <span class="cm-number">587</span>, <span class="cm-number">547</span>, <span class="cm-number">607</span>, <span class="cm-number">547</span>]), (<span class="cm-number">4307414133054528902898431</span>, [<span class="cm-number">1</span>, <span class="cm-number">547</span>, <span class="cm-number">577</span>, <span class="cm-number">503</span>, <span class="cm-number">569</span>, <span class="cm-number">547</span>, <span class="cm-number">569</span>, <span class="cm-number">503</span>, <span class="cm-number">563</span>, <span class="cm-number">541</span>])]), (<span class="cm-number">10</span>, [(<span class="cm-number">2472832340955827717218826729</span>, [<span class="cm-number">1</span>, <span class="cm-number">499</span>, <span class="cm-number">571</span>, <span class="cm-number">541</span>, <span class="cm-number">599</span>, <span class="cm-number">491</span>, <span class="cm-number">577</span>, <span class="cm-number">563</span>, <span class="cm-number">569</span>, <span class="cm-number">491</span>, <span class="cm-number">601</span>]), (<span class="cm-number">2584284171184513506455410453</span>, [<span class="cm-number">1</span>, <span class="cm-number">503</span>, <span class="cm-number">613</span>, <span class="cm-number">509</span>, <span class="cm-number">599</span>, <span class="cm-number">563</span>, <span class="cm-number">569</span>, <span class="cm-number">499</span>, <span class="cm-number">607</span>, <span class="cm-number">491</span>, <span class="cm-number">577</span>])]), (<span class="cm-number">11</span>, [(<span class="cm-number">1910856948409986584271742351543</span>, [<span class="cm-number">1</span>, <span class="cm-number">521</span>, <span class="cm-number">577</span>, <span class="cm-number">547</span>, <span class="cm-number">563</span>, <span class="cm-number">563</span>, <span class="cm-number">577</span>, <span class="cm-number">541</span>, <span class="cm-number">617</span>, <span class="cm-number">563</span>, <span class="cm-number">607</span>, <span class="cm-number">557</span>]), (<span class="cm-number">1332882535090650712169308963739</span>, [<span class="cm-number">1</span>, <span class="cm-number">487</span>, <span class="cm-number">613</span>, <span class="cm-number">547</span>, <span class="cm-number">613</span>, <span class="cm-number">503</span>, <span class="cm-number">563</span>, <span class="cm-number">487</span>, <span class="cm-number">617</span>, <span class="cm-number">557</span>, <span class="cm-number">563</span>, <span class="cm-number">499</span>])]), (<span class="cm-number">12</span>, [(<span class="cm-number">852196735493924940848986241767987</span>, [<span class="cm-number">1</span>, <span class="cm-number">541</span>, <span class="cm-number">613</span>, <span class="cm-number">487</span>, <span class="cm-number">617</span>, <span class="cm-number">491</span>, <span class="cm-number">587</span>, <span class="cm-number">523</span>, <span class="cm-number">613</span>, <span class="cm-number">523</span>, <span class="cm-number">563</span>, <span class="cm-number">523</span>, <span class="cm-number">601</span>]), (<span class="cm-number">752546528211330815497003845481997</span>, [<span class="cm-number">1</span>, <span class="cm-number">479</span>, <span class="cm-number">593</span>, <span class="cm-number">503</span>, <span class="cm-number">587</span>, <span class="cm-number">491</span>, <span class="cm-number">587</span>, <span class="cm-number">503</span>, <span class="cm-number">607</span>, <span class="cm-number">541</span>, <span class="cm-number">587</span>, <span class="cm-number">547</span>, <span class="cm-number">587</span>])]), (<span class="cm-number">13</span>, [(<span class="cm-number">413424284293138931542565906706071669</span>, [<span class="cm-number">1</span>, <span class="cm-number">491</span>, <span class="cm-number">587</span>, <span class="cm-number">487</span>, <span class="cm-number">617</span>, <span class="cm-number">541</span>, <span class="cm-number">607</span>, <span class="cm-number">487</span>, <span class="cm-number">587</span>, <span class="cm-number">557</span>, <span class="cm-number">617</span>, <span class="cm-number">479</span>, <span class="cm-number">571</span>, <span class="cm-number">541</span>]), (<span class="cm-number">422612439674921629650938136476012611</span>, [<span class="cm-number">1</span>, <span class="cm-number">523</span>, <span class="cm-number">569</span>, <span class="cm-number">541</span>, <span class="cm-number">577</span>, <span class="cm-number">541</span>, <span class="cm-number">571</span>, <span class="cm-number">523</span>, <span class="cm-number">613</span>, <span class="cm-number">487</span>, <span class="cm-number">569</span>, <span class="cm-number">563</span>, <span class="cm-number">563</span>, <span class="cm-number">523</span>])]), (<span class="cm-number">14</span>, [(<span class="cm-number">457153207646831573744181522153370927673</span>, [<span class="cm-number">1</span>, <span class="cm-number">547</span>, <span class="cm-number">619</span>, <span class="cm-number">547</span>, <span class="cm-number">641</span>, <span class="cm-number">563</span>, <span class="cm-number">607</span>, <span class="cm-number">547</span>, <span class="cm-number">593</span>, <span class="cm-number">563</span>, <span class="cm-number">631</span>, <span class="cm-number">509</span>, <span class="cm-number">619</span>, <span class="cm-number">503</span>, <span class="cm-number">617</span>]), (<span class="cm-number">259918970541028265619885810519171604529</span>, [<span class="cm-number">1</span>, <span class="cm-number">557</span>, <span class="cm-number">631</span>, <span class="cm-number">541</span>, <span class="cm-number">593</span>, <span class="cm-number">487</span>, <span class="cm-number">563</span>, <span class="cm-number">503</span>, <span class="cm-number">619</span>, <span class="cm-number">503</span>, <span class="cm-number">617</span>, <span class="cm-number">467</span>, <span class="cm-number">631</span>, <span class="cm-number">503</span>, <span class="cm-number">587</span>])]), (<span class="cm-number">15</span>, [(<span class="cm-number">109868336528703352227207124944087831704269</span>, [<span class="cm-number">1</span>, <span class="cm-number">463</span>, <span class="cm-number">599</span>, <span class="cm-number">509</span>, <span class="cm-number">631</span>, <span class="cm-number">467</span>, <span class="cm-number">617</span>, <span class="cm-number">487</span>, <span class="cm-number">643</span>, <span class="cm-number">563</span>, <span class="cm-number">563</span>, <span class="cm-number">487</span>, <span class="cm-number">607</span>, <span class="cm-number">541</span>, <span class="cm-number">563</span>, <span class="cm-number">479</span>]), (<span class="cm-number">142219206797328060675174570040656920579167</span>, [<span class="cm-number">1</span>, <span class="cm-number">479</span>, <span class="cm-number">613</span>, <span class="cm-number">547</span>, <span class="cm-number">587</span>, <span class="cm-number">557</span>, <span class="cm-number">601</span>, <span class="cm-number">479</span>, <span class="cm-number">587</span>, <span class="cm-number">499</span>, <span class="cm-number">571</span>, <span class="cm-number">479</span>, <span class="cm-number">643</span>, <span class="cm-number">563</span>, <span class="cm-number">593</span>, <span class="cm-number">547</span>])]), (<span class="cm-number">16</span>, [(<span class="cm-number">76820202531067992349805610678707511043871803</span>, [<span class="cm-number">1</span>, <span class="cm-number">547</span>, <span class="cm-number">587</span>, <span class="cm-number">509</span>, <span class="cm-number">569</span>, <span class="cm-number">491</span>, <span class="cm-number">613</span>, <span class="cm-number">491</span>, <span class="cm-number">607</span>, <span class="cm-number">547</span>, <span class="cm-number">601</span>, <span class="cm-number">487</span>, <span class="cm-number">643</span>, <span class="cm-number">487</span>, <span class="cm-number">617</span>, <span class="cm-number">463</span>, <span class="cm-number">643</span>]), (<span class="cm-number">84353082637098915851350715686631411152617919</span>, [<span class="cm-number">1</span>, <span class="cm-number">499</span>, <span class="cm-number">593</span>, <span class="cm-number">541</span>, <span class="cm-number">613</span>, <span class="cm-number">523</span>, <span class="cm-number">601</span>, <span class="cm-number">557</span>, <span class="cm-number">593</span>, <span class="cm-number">491</span>, <span class="cm-number">587</span>, <span class="cm-number">521</span>, <span class="cm-number">587</span>, <span class="cm-number">491</span>, <span class="cm-number">599</span>, <span class="cm-number">521</span>, <span class="cm-number">613</span>])]), (<span class="cm-number">17</span>, [(<span class="cm-number">29867711038615093175665393861938141536525529539</span>, [<span class="cm-number">1</span>, <span class="cm-number">541</span>, <span class="cm-number">607</span>, <span class="cm-number">479</span>, <span class="cm-number">577</span>, <span class="cm-number">557</span>, <span class="cm-number">599</span>, <span class="cm-number">467</span>, <span class="cm-number">647</span>, <span class="cm-number">463</span>, <span class="cm-number">577</span>, <span class="cm-number">461</span>, <span class="cm-number">607</span>, <span class="cm-number">499</span>, <span class="cm-number">617</span>, <span class="cm-number">457</span>, <span class="cm-number">617</span>, <span class="cm-number">503</span>]), (<span class="cm-number">32160416498806182862863819430142025959220975101</span>, [<span class="cm-number">1</span>, <span class="cm-number">449</span>, <span class="cm-number">613</span>, <span class="cm-number">509</span>, <span class="cm-number">631</span>, <span class="cm-number">461</span>, <span class="cm-number">613</span>, <span class="cm-number">499</span>, <span class="cm-number">601</span>, <span class="cm-number">541</span>, <span class="cm-number">599</span>, <span class="cm-number">461</span>, <span class="cm-number">617</span>, <span class="cm-number">487</span>, <span class="cm-number">631</span>, <span class="cm-number">503</span>, <span class="cm-number">599</span>, <span class="cm-number">503</span>])]), (<span class="cm-number">18</span>, [(<span class="cm-number">19956848495929281188644811212469947126676084328359</span>, [<span class="cm-number">1</span>, <span class="cm-number">449</span>, <span class="cm-number">601</span>, <span class="cm-number">563</span>, <span class="cm-number">659</span>, <span class="cm-number">467</span>, <span class="cm-number">587</span>, <span class="cm-number">461</span>, <span class="cm-number">577</span>, <span class="cm-number">509</span>, <span class="cm-number">659</span>, <span class="cm-number">467</span>, <span class="cm-number">577</span>, <span class="cm-number">479</span>, <span class="cm-number">641</span>, <span class="cm-number">499</span>, <span class="cm-number">653</span>, <span class="cm-number">503</span>, <span class="cm-number">601</span>]), (<span class="cm-number">21117036798239547259422495410311750799350659014713</span>, [<span class="cm-number">1</span>, <span class="cm-number">487</span>, <span class="cm-number">593</span>, <span class="cm-number">541</span>, <span class="cm-number">571</span>, <span class="cm-number">449</span>, <span class="cm-number">601</span>, <span class="cm-number">487</span>, <span class="cm-number">643</span>, <span class="cm-number">521</span>, <span class="cm-number">617</span>, <span class="cm-number">463</span>, <span class="cm-number">619</span>, <span class="cm-number">457</span>, <span class="cm-number">659</span>, <span class="cm-number">503</span>, <span class="cm-number">563</span>, <span class="cm-number">541</span>, <span class="cm-number">659</span>])]), (<span class="cm-number">19</span>, [(<span class="cm-number">13264396535897727373516274848984084788966136163607509</span>, [<span class="cm-number">1</span>, <span class="cm-number">503</span>, <span class="cm-number">613</span>, <span class="cm-number">461</span>, <span class="cm-number">659</span>, <span class="cm-number">461</span>, <span class="cm-number">659</span>, <span class="cm-number">563</span>, <span class="cm-number">569</span>, <span class="cm-number">461</span>, <span class="cm-number">647</span>, <span class="cm-number">521</span>, <span class="cm-number">653</span>, <span class="cm-number">523</span>, <span class="cm-number">607</span>, <span class="cm-number">449</span>, <span class="cm-number">631</span>, <span class="cm-number">541</span>, <span class="cm-number">631</span>, <span class="cm-number">467</span>]), (<span 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class="cm-number">997</span>, <span class="cm-number">1097</span>, <span class="cm-number">1039</span>, <span class="cm-number">1151</span>, <span class="cm-number">977</span>])]), (<span class="cm-number">20</span>, [(<span class="cm-number">3055878534232886887533008275157224451264024556815840381056001</span>, [<span class="cm-number">1</span>, <span class="cm-number">977</span>, <span class="cm-number">1117</span>, <span class="cm-number">977</span>, <span class="cm-number">1117</span>, <span class="cm-number">983</span>, <span class="cm-number">1187</span>, <span class="cm-number">971</span>, <span class="cm-number">1093</span>, <span class="cm-number">971</span>, <span class="cm-number">1087</span>, <span class="cm-number">1069</span>, <span class="cm-number">1109</span>, <span class="cm-number">953</span>, <span class="cm-number">1097</span>, <span class="cm-number">1051</span>, <span class="cm-number">1093</span>, <span class="cm-number">1069</span>, <span class="cm-number">1193</span>, <span class="cm-number">991</span>, <span class="cm-number">1091</span>]), (<span class="cm-number">4003992205233808349893596129588063075763059241015453817988877</span>, [<span class="cm-number">1</span>, <span class="cm-number">1033</span>, <span class="cm-number">1069</span>, <span class="cm-number">1031</span>, <span class="cm-number">1163</span>, <span class="cm-number">997</span>, <span class="cm-number">1187</span>, <span class="cm-number">953</span>, <span class="cm-number">1087</span>, <span class="cm-number">1039</span>, <span class="cm-number">1129</span>, <span class="cm-number">1049</span>, <span class="cm-number">1069</span>, <span class="cm-number">1031</span>, <span class="cm-number">1213</span>, <span class="cm-number">1013</span>, <span class="cm-number">1109</span>, <span class="cm-number">1039</span>, <span class="cm-number">1181</span>, <span class="cm-number">997</span>, <span class="cm-number">1091</span>])])])</code><code></code><code><span class="cm-variable">largeClosePrimes</span> = (<span class="cm-string">"Large close primes"</span>, [(<span class="cm-number">2</span>, [(<span class="cm-number">865712929</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29423</span>]), (<span class="cm-number">865712929</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29423</span>])]), (<span class="cm-number">3</span>, [(<span class="cm-number">25454551017407</span>, [<span class="cm-number">1</span>, <span class="cm-number">29411</span>, <span class="cm-number">29437</span>, <span class="cm-number">29401</span>]), (<span class="cm-number">25454551017407</span>, [<span class="cm-number">1</span>, <span class="cm-number">29401</span>, <span class="cm-number">29437</span>, <span class="cm-number">29411</span>])]), (<span class="cm-number">4</span>, [(<span class="cm-number">748949254585166161</span>, [<span class="cm-number">1</span>, <span class="cm-number">29411</span>, <span class="cm-number">29437</span>, <span class="cm-number">29401</span>, <span class="cm-number">29423</span>]), (<span class="cm-number">749815315379647091</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29429</span>, <span class="cm-number">29411</span>, <span class="cm-number">29443</span>])]), (<span class="cm-number">5</span>, [(<span class="cm-number">22042301982094473596467</span>, [<span class="cm-number">1</span>, <span class="cm-number">29389</span>, <span class="cm-number">29437</span>, <span class="cm-number">29401</span>, <span class="cm-number">29453</span>, <span class="cm-number">29423</span>]), (<span class="cm-number">22037819908204262231501</span>, [<span class="cm-number">1</span>, <span class="cm-number">29411</span>, <span class="cm-number">29453</span>, <span class="cm-number">29399</span>, <span class="cm-number">29423</span>, <span class="cm-number">29411</span>])]), (<span class="cm-number">6</span>, [(<span class="cm-number">647625188777536523967038123</span>, [<span class="cm-number">1</span>, <span class="cm-number">29389</span>, <span class="cm-number">29437</span>, <span class="cm-number">29387</span>, <span class="cm-number">29429</span>, <span class="cm-number">29399</span>, <span class="cm-number">29443</span>]), (<span class="cm-number">648727214546027169234119857</span>, [<span class="cm-number">1</span>, <span class="cm-number">29411</span>, <span class="cm-number">29443</span>, <span class="cm-number">29401</span>, <span class="cm-number">29443</span>, <span class="cm-number">29399</span>, <span class="cm-number">29437</span>])]), (<span class="cm-number">7</span>, [(<span class="cm-number">19047305219120345130931560910901</span>, [<span class="cm-number">1</span>, <span class="cm-number">29401</span>, <span class="cm-number">29437</span>, <span class="cm-number">29399</span>, <span class="cm-number">29437</span>, <span class="cm-number">29401</span>, <span class="cm-number">29437</span>, <span class="cm-number">29383</span>]), (<span class="cm-number">19122506962371043582760416155121</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29473</span>, <span class="cm-number">29399</span>, <span class="cm-number">29483</span>, <span class="cm-number">29399</span>, <span class="cm-number">29423</span>, <span class="cm-number">29411</span>])]), (<span class="cm-number">8</span>, [(<span class="cm-number">562143099156355627345058252853193301</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29443</span>, <span class="cm-number">29363</span>, <span class="cm-number">29483</span>, <span class="cm-number">29411</span>, <span class="cm-number">29429</span>, <span class="cm-number">29383</span>, <span class="cm-number">29473</span>]), (<span class="cm-number">562829942618851054761838008402259709</span>, [<span class="cm-number">1</span>, <span class="cm-number">29363</span>, <span class="cm-number">29483</span>, <span class="cm-number">29401</span>, <span class="cm-number">29501</span>, <span class="cm-number">29401</span>, <span class="cm-number">29443</span>, <span class="cm-number">29399</span>, <span class="cm-number">29453</span>])]), (<span class="cm-number">9</span>, [(<span class="cm-number">16549917550139176331089539530499288572021</span>, [<span class="cm-number">1</span>, <span class="cm-number">29389</span>, <span class="cm-number">29437</span>, <span class="cm-number">29423</span>, <span class="cm-number">29501</span>, <span class="cm-number">29347</span>, <span class="cm-number">29443</span>, <span class="cm-number">29383</span>, <span class="cm-number">29527</span>, <span class="cm-number">29399</span>]), (<span class="cm-number">16494942489066181415143190513104903497931</span>, [<span class="cm-number">1</span>, <span class="cm-number">29387</span>, <span class="cm-number">29443</span>, <span class="cm-number">29387</span>, <span class="cm-number">29501</span>, <span class="cm-number">29383</span>, <span class="cm-number">29473</span>, <span class="cm-number">29347</span>, <span class="cm-number">29443</span>, <span class="cm-number">29387</span>])]), (<span class="cm-number">10</span>, [(<span class="cm-number">483818446645921223916066574454799803265926869</span>, [<span class="cm-number">1</span>, <span class="cm-number">29399</span>, <span class="cm-number">29443</span>, <span class="cm-number">29383</span>, <span class="cm-number">29423</span>, <span class="cm-number">29411</span>, <span class="cm-number">29423</span>, <span class="cm-number">29347</span>, <span class="cm-number">29443</span>, <span class="cm-number">29387</span>, <span class="cm-number">29423</span>]), (<span class="cm-number">490367376997778494257114997680532736329945909</span>, [<span class="cm-number">1</span>, <span class="cm-number">29387</span>, <span class="cm-number">29483</span>, <span class="cm-number">29401</span>, <span class="cm-number">29501</span>, <span class="cm-number">29423</span>, <span class="cm-number">29531</span>, <span class="cm-number">29389</span>, <span class="cm-number">29501</span>, <span class="cm-number">29389</span>, <span class="cm-number">29473</span>])]), (<span class="cm-number">11</span>, [(<span class="cm-number">14298066897873419916925610084596585019684404299577</span>, [<span class="cm-number">1</span>, <span class="cm-number">29363</span>, <span class="cm-number">29437</span>, <span class="cm-number">29339</span>, <span class="cm-number">29443</span>, <span class="cm-number">29333</span>, <span class="cm-number">29531</span>, <span class="cm-number">29411</span>, <span class="cm-number">29537</span>, <span class="cm-number">29347</span>, <span class="cm-number">29483</span>, <span class="cm-number">29411</span>]), (<span class="cm-number">14320484452966964226830269428065419115967575823307</span>, [<span class="cm-number">1</span>, <span class="cm-number">29399</span>, <span class="cm-number">29527</span>, <span class="cm-number">29389</span>, <span class="cm-number">29537</span>, <span class="cm-number">29399</span>, <span class="cm-number">29501</span>, <span class="cm-number">29383</span>, <span class="cm-number">29423</span>, <span class="cm-number">29347</span>, <span class="cm-number">29443</span>, <span class="cm-number">29333</span>])]), (<span class="cm-number">12</span>, [(<span class="cm-number">422988549701602021708072490756282881304545627458255859</span>, [<span class="cm-number">1</span>, <span class="cm-number">29363</span>, <span class="cm-number">29453</span>, <span class="cm-number">29401</span>, <span class="cm-number">29453</span>, <span class="cm-number">29389</span>, <span class="cm-number">29567</span>, <span class="cm-number">29423</span>, <span class="cm-number">29531</span>, <span class="cm-number">29363</span>, <span class="cm-number">29429</span>, <span class="cm-number">29423</span>, <span class="cm-number">29423</span>]), (<span class="cm-number">423761271786225112222217862150288564714519017380395689</span>, [<span class="cm-number">1</span>, <span class="cm-number">29411</span>, <span class="cm-number">29537</span>, <span class="cm-number">29401</span>, <span class="cm-number">29483</span>, <span class="cm-number">29383</span>, <span class="cm-number">29537</span>, <span class="cm-number">29339</span>, <span class="cm-number">29473</span>, <span class="cm-number">29411</span>, <span class="cm-number">29527</span>, <span class="cm-number">29333</span>, <span class="cm-number">29437</span>])]), (<span class="cm-number">13</span>, [(<span class="cm-number">12293239381581520625704123339024990495993226167931711051791</span>, [<span class="cm-number">1</span>, <span class="cm-number">29363</span>, <span class="cm-number">29443</span>, <span class="cm-number">29347</span>, <span class="cm-number">29537</span>, <span class="cm-number">29401</span>, <span class="cm-number">29423</span>, <span class="cm-number">29347</span>, <span class="cm-number">29531</span>, <span class="cm-number">29311</span>, <span class="cm-number">29423</span>, <span class="cm-number">29311</span>, <span class="cm-number">29443</span>, <span class="cm-number">29399</span>]), (<span class="cm-number">12451198379061059764624491385115885732898863931874087138687</span>, [<span class="cm-number">1</span>, <span class="cm-number">29363</span>, <span class="cm-number">29569</span>, <span class="cm-number">29347</span>, <span class="cm-number">29429</span>, <span class="cm-number">29339</span>, <span class="cm-number">29567</span>, <span class="cm-number">29423</span>, <span class="cm-number">29483</span>, <span class="cm-number">29363</span>, <span class="cm-number">29527</span>, <span class="cm-number">29423</span>, <span class="cm-number">29483</span>, <span class="cm-number">29339</span>])]), (<span class="cm-number">14</span>, [(<span class="cm-number">366249931054054855918254086215217231707917666117006778977380909</span>, [<span class="cm-number">1</span>, <span class="cm-number">29347</span>, <span class="cm-number">29569</span>, <span class="cm-number">29423</span>, <span class="cm-number">29443</span>, <span class="cm-number">29333</span>, <span class="cm-number">29527</span>, <span class="cm-number">29387</span>, <span class="cm-number">29567</span>, <span class="cm-number">29399</span>, <span class="cm-number">29429</span>, <span class="cm-number">29327</span>, <span class="cm-number">29527</span>, <span class="cm-number">29339</span>, <span class="cm-number">29453</span>]), (<span class="cm-number">367896370789011152412608731303715436991394396657947014758999489</span>, [<span class="cm-number">1</span>, <span class="cm-number">29303</span>, <span class="cm-number">29501</span>, <span class="cm-number">29399</span>, <span class="cm-number">29537</span>, <span class="cm-number">29387</span>, <span class="cm-number">29567</span>, <span class="cm-number">29389</span>, <span class="cm-number">29473</span>, <span class="cm-number">29311</span>, <span class="cm-number">29527</span>, <span class="cm-number">29399</span>, <span class="cm-number">29483</span>, <span class="cm-number">29399</span>, <span class="cm-number">29527</span>])]), (<span class="cm-number">15</span>, [(<span class="cm-number">10644894953985381764687625074094294366413635557060109122838940666171</span>, [<span class="cm-number">1</span>, <span class="cm-number">29297</span>, <span class="cm-number">29443</span>, <span class="cm-number">29333</span>, <span class="cm-number">29453</span>, <span class="cm-number">29311</span>, <span class="cm-number">29527</span>, <span class="cm-number">29311</span>, <span class="cm-number">29527</span>, <span class="cm-number">29387</span>, <span class="cm-number">29527</span>, <span class="cm-number">29303</span>, <span class="cm-number">29567</span>, <span class="cm-number">29383</span>, <span class="cm-number">29453</span>, <span class="cm-number">29311</span>]), (<span class="cm-number">10685620363611581349723712362560065711947054666446884334157352103099</span>, [<span class="cm-number">1</span>, <span class="cm-number">29399</span>, <span class="cm-number">29453</span>, <span class="cm-number">29399</span>, <span class="cm-number">29531</span>, <span class="cm-number">29399</span>, <span class="cm-number">29443</span>, <span class="cm-number">29311</span>, <span class="cm-number">29453</span>, <span class="cm-number">29297</span>, <span class="cm-number">29531</span>, <span class="cm-number">29297</span>, <span class="cm-number">29573</span>, <span class="cm-number">29389</span>, <span class="cm-number">29473</span>, <span class="cm-number">29297</span>])]), (<span class="cm-number">16</span>, [(<span class="cm-number">318513253747377908211654512553364042173627257881988069391587768229583691</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29501</span>, <span class="cm-number">29423</span>, <span class="cm-number">29537</span>, <span class="cm-number">29401</span>, <span class="cm-number">29573</span>, <span class="cm-number">29399</span>, <span class="cm-number">29501</span>, <span class="cm-number">29311</span>, <span class="cm-number">29429</span>, <span class="cm-number">29363</span>, <span class="cm-number">29483</span>, <span class="cm-number">29303</span>, <span class="cm-number">29423</span>, <span class="cm-number">29411</span>, <span class="cm-number">29569</span>]), (<span class="cm-number">318010433938975531069970467031819358831170737214531625647265186479508697</span>, [<span class="cm-number">1</span>, <span class="cm-number">29347</span>, <span class="cm-number">29573</span>, <span class="cm-number">29327</span>, <span class="cm-number">29423</span>, <span class="cm-number">29333</span>, <span class="cm-number">29501</span>, <span class="cm-number">29327</span>, <span class="cm-number">29443</span>, <span class="cm-number">29387</span>, <span class="cm-number">29581</span>, <span class="cm-number">29423</span>, <span class="cm-number">29573</span>, <span class="cm-number">29399</span>, <span class="cm-number">29537</span>, <span class="cm-number">29347</span>, <span class="cm-number">29483</span>])]), (<span class="cm-number">17</span>, [(<span class="cm-number">9274924513456323558811589191670119099925691334742148666185537727889128732529</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29599</span>, <span class="cm-number">29269</span>, <span class="cm-number">29531</span>, <span class="cm-number">29339</span>, <span class="cm-number">29483</span>, <span class="cm-number">29333</span>, <span class="cm-number">29443</span>, <span class="cm-number">29333</span>, <span class="cm-number">29537</span>, <span class="cm-number">29387</span>, <span class="cm-number">29443</span>, <span class="cm-number">29399</span>, <span class="cm-number">29453</span>, <span class="cm-number">29311</span>, <span class="cm-number">29599</span>, <span class="cm-number">29287</span>]), (<span class="cm-number">9306534270861220085725248728885553486460012328605762858906957840590239358497</span>, [<span class="cm-number">1</span>, <span class="cm-number">29389</span>, <span class="cm-number">29567</span>, <span class="cm-number">29363</span>, <span class="cm-number">29423</span>, <span class="cm-number">29269</span>, <span class="cm-number">29483</span>, <span class="cm-number">29423</span>, <span class="cm-number">29437</span>, <span class="cm-number">29363</span>, <span class="cm-number">29567</span>, <span class="cm-number">29333</span>, <span class="cm-number">29581</span>, <span class="cm-number">29399</span>, <span class="cm-number">29527</span>, <span class="cm-number">29339</span>, <span class="cm-number">29537</span>, <span class="cm-number">29269</span>])]), (<span class="cm-number">18</span>, [(<span class="cm-number">273447555319424943187398893784654666306360710336455357136751751809036563020145951</span>, [<span class="cm-number">1</span>, <span class="cm-number">29389</span>, <span class="cm-number">29473</span>, <span class="cm-number">29387</span>, <span class="cm-number">29501</span>, <span class="cm-number">29327</span>, <span class="cm-number">29611</span>, <span class="cm-number">29327</span>, <span class="cm-number">29537</span>, <span class="cm-number">29339</span>, <span class="cm-number">29537</span>, <span class="cm-number">29251</span>, <span class="cm-number">29423</span>, <span class="cm-number">29423</span>, <span class="cm-number">29473</span>, <span class="cm-number">29251</span>, <span class="cm-number">29527</span>, <span class="cm-number">29303</span>, <span class="cm-number">29573</span>]), (<span class="cm-number">273777364729800462429940443288730515555346668606062214085557317040304257088157639</span>, [<span class="cm-number">1</span>, <span class="cm-number">29423</span>, <span class="cm-number">29429</span>, <span class="cm-number">29287</span>, <span class="cm-number">29611</span>, <span class="cm-number">29311</span>, <span class="cm-number">29531</span>, <span class="cm-number">29347</span>, <span class="cm-number">29581</span>, <span class="cm-number">29303</span>, <span class="cm-number">29429</span>, <span class="cm-number">29333</span>, <span class="cm-number">29531</span>, <span class="cm-number">29287</span>, <span class="cm-number">29501</span>, <span class="cm-number">29327</span>, <span class="cm-number">29587</span>, <span class="cm-number">29303</span>, <span class="cm-number">29567</span>])]), (<span class="cm-number">19</span>, [(<span class="cm-number">8092813032034752870137381401915653543865243380513951917556601612686501897877155480529</span>, [<span class="cm-number">1</span>, <span class="cm-number">29383</span>, <span class="cm-number">29611</span>, <span class="cm-number">29389</span>, <span class="cm-number">29581</span>, <span class="cm-number">29287</span>, <span class="cm-number">29531</span>, <span class="cm-number">29401</span>, <span class="cm-number">29501</span>, <span class="cm-number">29297</span>, <span class="cm-number">29453</span>, <span class="cm-number">29327</span>, <span class="cm-number">29611</span>, <span class="cm-number">29411</span>, <span class="cm-number">29453</span>, <span class="cm-number">29383</span>, <span class="cm-number">29453</span>, <span class="cm-number">29387</span>, <span class="cm-number">29537</span>, <span class="cm-number">29251</span>]), (<span class="cm-number">8101465846655008560733288209269117691483784364549949754676618472732876797621084547241</span>, [<span 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class="cm-number">40387</span>, <span class="cm-number">40093</span>, <span class="cm-number">40283</span>, <span class="cm-number">40177</span>, <span class="cm-number">40429</span>, <span class="cm-number">40193</span>, <span class="cm-number">40387</span>, <span class="cm-number">40231</span>, <span class="cm-number">40471</span>, <span class="cm-number">40099</span>, <span class="cm-number">40499</span>, <span class="cm-number">40253</span>]), (<span class="cm-number">3146520128824371716207725209907584052952049742107680993674409723280717068075495166986423</span>, [<span class="cm-number">1</span>, <span class="cm-number">40213</span>, <span class="cm-number">40289</span>, <span class="cm-number">40189</span>, <span class="cm-number">40483</span>, <span class="cm-number">40127</span>, <span class="cm-number">40277</span>, <span class="cm-number">40163</span>, <span class="cm-number">40429</span>, <span class="cm-number">40163</span>, <span class="cm-number">40487</span>, <span class="cm-number">40193</span>, <span class="cm-number">40433</span>, <span class="cm-number">40129</span>, <span class="cm-number">40289</span>, <span class="cm-number">40277</span>, <span class="cm-number">40483</span>, <span class="cm-number">40093</span>, <span class="cm-number">40459</span>, <span class="cm-number">40253</span>])]), (<span class="cm-number">20</span>, [(<span class="cm-number">128852600609349526097437512679089470899860629063921966904451544951666329006154974515208595849</span>, [<span class="cm-number">1</span>, <span class="cm-number">40099</span>, <span class="cm-number">40471</span>, <span class="cm-number">40241</span>, <span class="cm-number">40357</span>, <span class="cm-number">40237</span>, <span class="cm-number">40361</span>, <span class="cm-number">40277</span>, <span class="cm-number">40423</span>, <span class="cm-number">40087</span>, <span class="cm-number">40519</span>, <span class="cm-number">40241</span>, <span class="cm-number">40429</span>, <span class="cm-number">40087</span>, <span class="cm-number">40499</span>, <span class="cm-number">40169</span>, <span class="cm-number">40499</span>, <span class="cm-number">40189</span>, <span class="cm-number">40507</span>, <span class="cm-number">40213</span>, <span class="cm-number">40471</span>]), (<span class="cm-number">126062316213731487422916572994986948260691672311530813690188127109530700932036759345668642767</span>, [<span class="cm-number">1</span>, <span class="cm-number">40189</span>, <span class="cm-number">40433</span>, <span class="cm-number">40277</span>, <span class="cm-number">40343</span>, <span class="cm-number">40153</span>, <span class="cm-number">40387</span>, <span class="cm-number">40169</span>, <span class="cm-number">40357</span>, <span class="cm-number">40093</span>, <span class="cm-number">40499</span>, <span class="cm-number">40127</span>, <span class="cm-number">40387</span>, <span class="cm-number">40087</span>, <span class="cm-number">40499</span>, <span class="cm-number">40087</span>, <span class="cm-number">40493</span>, <span class="cm-number">40111</span>, <span class="cm-number">40283</span>, <span class="cm-number">40087</span>, <span class="cm-number">40433</span>])])])</code><code></code><code><span class="cm-keyword">print</span> <span class="cm-string">"stored close number suite - re run if needed"</span></code></pre>
<div class="output stdout">stored close number suite - re run if needed
</div>
<div class="output stdout">defined plot function - re run if needed
</div>
<pre class="input"><code></code></pre>
<div class="output md"><h2 id="trial-division">Trial Division</h2>
</div>
<pre class="input"><code><span class="cm-keyword">from</span> <span class="cm-variable">trial_division</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">TrialDivision</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallPrimes</span>, <span class="cm-variable">iterations</span>)</code><code></code><code><span class="cm-variable">examplePlot</span> = <span class="cm-string">'''</span></code><code><span class="cm-variable">minPlot</span>, <span class="cm-variable">maxPlot</span>, <span class="cm-variable">averagePlot</span> = <span class="cm-variable">plotMinMaxAverage</span>(<span class="cm-variable">benchmarks</span>)</code><code></code><code><span class="cm-keyword">print</span> <span class="cm-string">"Regular trial division, small primes"</span></code><code><span class="cm-variable">minPlot</span> <span class="cm-operator">+</span> <span class="cm-variable">maxPlot</span> <span class="cm-operator">+</span> <span class="cm-variable">averagePlot</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">TrialDivision</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallPrimes</span>, <span class="cm-variable">iterations</span>, {<span class="cm-string">"modified"</span>: <span class="cm-builtin">True</span>})</code><code><span class="cm-variable">minPlot</span>, <span class="cm-variable">maxPlot</span>, <span class="cm-variable">averagePlot</span> = <span class="cm-variable">plotMinMaxAverage</span>(<span class="cm-variable">benchmarks</span>)</code><code></code><code><span class="cm-keyword">print</span> <span class="cm-string">"Primes only trial division, small primes\n"</span></code><code><span class="cm-variable">minPlot</span> <span class="cm-operator">+</span> <span class="cm-variable">maxPlot</span> <span class="cm-operator">+</span> <span class="cm-variable">averagePlot</span></code><code><span class="cm-string">'''</span></code></pre>
<pre class="input"><code><span class="cm-keyword">from</span> <span class="cm-variable">trial_division</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">TrialDivision</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"small primes"</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">TrialDivision</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallClosePrimes</span>, <span class="cm-variable">iterations</span>, {<span class="cm-string">"modified"</span>: <span class="cm-builtin">True</span>})</code><code><span class="cm-keyword">print</span> <span class="cm-string">"small primes"</span></code></pre>
<div class="output stdout">small primes
small primes
</div>
<pre class="input"><code>%md</code><code>Observationer trial division:</code><code>I och med att Trial Division hittar den minsta faktorn först så vet den att ingen annan faktor är mindre, därför kan den börja räkna från den hittade faktorn nästa gång istället för 0</code></pre>
<div class="output md"><h2 id="fermat-s-factorization">Fermat's Factorization</h2>
</div>
<pre class="input"><code><span class="cm-keyword">from</span> <span class="cm-variable">fermats_factorization</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code></code><code><span class="cm-comment"># Klarade ej att slutföra 4 factors medium primes under > 11 timmar!</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"small primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">mediumPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"medium primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"large primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largerPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"larger primes"</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close small primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">mediumClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close medium primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largeClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close large primes"</span></code></pre>
<div class="output stderr">Error in lines 2-2
</div>
<div class="output stderr">Traceback (most recent call last):
File "/usr/local/sage/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
File "factorization_function.py", line 79, in benchmark
resultingFactors, b = self.factorize(n, true, **optionalArgs)
File "fermats_factorization.py", line 77, in factorize
possibleFactors = self.getOneFactor(a, benchmark)
File "fermats_factorization.py", line 32, in getOneFactor
benchmark.iterate()
File "src/cysignals/signals.pyx", line 251, in cysignals.signals.python_check_interrupt (build/src/cysignals/signals.c:2721)
File "src/cysignals/signals.pyx", line 94, in cysignals.signals.sig_raise_exception (build/src/cysignals/signals.c:1328)
KeyboardInterrupt
</module></div>
<pre class="input"><code>%md</code><code>observationer fermats:</code><code></code><code>av någon anledning verkar small primes 9 och 15 faktorer ta extra lång tid. Varför?</code><code></code><code>En optimering av fermats hade varit att börja räkna ifrån n:te roten ur det sammansatta talet. där n är antalet faktorer.</code><code></code><code>Udda antal faktorer går jävligt mycket långsammare. för att för fyra faktorer -- -- | -- -- och för 5 faktorer -- -- -|- -- -- Så man måste gå en halv extra.</code></pre>
<pre class="input"><code></code></pre>
<div class="output md"><h2 id="pollards-rho-algorithm">Pollards Rho Algorithm</h2>
</div>
<pre class="input"><code><span class="cm-keyword">from</span> <span class="cm-variable">pollards_rho_algorithm</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgorithm</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"small primes"</span></code></pre>
<div class="output stdout">small primes
</div>
<div class="output md"><h2 id="lenstras">Lenstras</h2>
</div>
<pre class="input"><code><span class="cm-keyword">from</span> <span class="cm-variable">lenstras_elliptic_curve_factorization</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code><span class="cm-comment">#benchmarks = LenstrasEllipticCurveFactorization.benchmark(smallPrimes, iterations, {"maximumIterations": -1})</span></code><code><span class="cm-comment">#values = map(lambda x: x[3].totalTime["default"], benchmarks)</span></code><code><span class="cm-comment">#print sum(values)/len(values)</span></code><code></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largerPrimes</span>, <span class="cm-variable">iterations</span>, {<span class="cm-string">"maximumIterations"</span>: <span class="cm-operator">-</span><span class="cm-number">1</span>})</code><code><span class="cm-variable">values</span> = <span class="cm-builtin">map</span>(<span class="cm-keyword">lambda</span> <span class="cm-variable">x</span>: <span class="cm-variable">x</span>[<span class="cm-number">3</span>].<span class="cm-variable">totalTime</span>[<span class="cm-string">"default"</span>], <span class="cm-variable">benchmarks</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-builtin">sum</span>(<span class="cm-variable">values</span>)<span class="cm-operator">/</span><span class="cm-builtin">len</span>(<span class="cm-variable">values</span>)</code><code></code><code><span class="cm-variable">x</span> = <span class="cm-string">"""</span></code><code><span class="cm-keyword">for</span> <span class="cm-variable">i</span> <span class="cm-keyword">in</span> [<span class="cm-number">1</span>, <span class="cm-number">2</span>, <span class="cm-number">5</span>, <span class="cm-number">10</span>, <span class="cm-number">50</span>, <span class="cm-number">100</span>, <span class="cm-number">1000</span>, <span class="cm-operator">-</span><span class="cm-number">1</span>]:</code><code> <span class="cm-keyword">print</span> <span class="cm-variable">i</span>,</code><code> <span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallPrimes</span>, <span class="cm-variable">iterations</span>, {<span class="cm-string">"maximumIterations"</span>: <span class="cm-variable">i</span>})</code><code> <span class="cm-variable">values</span> = <span class="cm-builtin">map</span>(<span class="cm-keyword">lambda</span> <span class="cm-variable">x</span>: <span class="cm-variable">x</span>[<span class="cm-number">3</span>].<span class="cm-variable">totalTime</span>[<span class="cm-string">"default"</span>], <span class="cm-variable">benchmarks</span>)</code><code> <span class="cm-keyword">print</span> <span class="cm-builtin">sum</span>(<span class="cm-variable">values</span>)<span class="cm-operator">/</span><span class="cm-builtin">len</span>(<span class="cm-variable">values</span>)</code><code><span class="cm-string">"""</span></code></pre>
<div class="output stdout">39.1989332011
</div>
<pre class="input"><code><span class="cm-number">1</span> <span class="cm-number">0.00392751317275</span></code><code><span class="cm-number">2</span> <span class="cm-number">0.00423920154572</span></code><code><span class="cm-number">5</span> <span class="cm-number">0.00414510526155</span></code><code><span class="cm-number">10</span> <span class="cm-number">0.00408152279101</span></code><code><span class="cm-number">50</span> <span class="cm-number">0.00364659710934</span></code><code><span class="cm-number">100</span> <span class="cm-number">0.00381851321773</span></code><code><span class="cm-number">1000</span> <span class="cm-number">0.00402681074644</span></code></pre>
<pre class="input"><code><span class="cm-number">1</span> <span class="cm-number">0.00383018819909</span></code><code><span class="cm-number">2</span> <span class="cm-number">0.0042179722535</span></code><code><span class="cm-number">5</span> <span class="cm-number">0.00391916475798</span></code><code><span class="cm-number">10</span> <span class="cm-number">0.00397971805773</span></code><code><span class="cm-number">50</span> <span class="cm-number">0.00365026875546</span></code><code><span class="cm-number">100</span> <span class="cm-number">0.00352077860581</span></code><code><span class="cm-number">1000</span> <span class="cm-number">0.00339124202728</span></code></pre>
<pre class="input"><code><span class="cm-number">1</span> <span class="cm-number">0.00396525985316</span></code><code><span class="cm-number">2</span> <span class="cm-number">0.00439642730512</span></code><code><span class="cm-number">5</span> <span class="cm-number">0.00393485395532</span></code><code><span class="cm-number">10</span> <span class="cm-number">0.00405216217041</span></code><code><span class="cm-number">50</span> <span class="cm-number">0.00363662493856</span></code><code><span class="cm-number">100</span> <span class="cm-number">0.00342771881505</span></code><code><span class="cm-number">1000</span> <span class="cm-number">0.00337653912996</span></code><code><span class="cm-operator">-</span><span class="cm-number">1</span> <span class="cm-number">0.178503995193</span></code></pre>
<div class="output md"><p>Lenstras observationer:
att sänka maximum iterations innebär att fler iterationer körs (totalt, inte per "omgång") - detta innebär att fler primtester körs.</p>
<p>Det skulle gå att använda ett såll (marcus lägger till om GitHub-lösningen). Istället för att gå till alla punkter kan man ta primtal.</p>
<p>Teori:
Att 5 är bättre än 1 och 2 iterationer kan ha att göra med att det är först då det börjar löna sig med primtalstester. Det är generellt bättra att ha få iterationer och försöka forcera faktorer, men primtestet håller då tillbaka prestandan. Att exempelvis lägga till en flagga första gången ett tal är primtestat skulle kunna resultera i att tal inte behöver primtestas mer än en gång, men ändå kunna testa enbart en iteration av algoritmen.</p>
<p>Literatur har tytt på att algoritmen kan vara snabbare om man avbryter efter n försök (sqrt(n)) och kör om igen för att få nya slumpvariabler. Vid imperisk studie hittade vi.... Vi såg dock att sqrt(n) presterade klart sämst. Detta visade sig ha med jämförelse av int och cocalcs integer med decimaler som blir vid sqrt(n). int(i) < int(ceil(sqrt(n))) är alltså snabbare (med en faktor av ≈60!!!) än int(i) < sqrt(n) trots att sqrt(n) enbart beräknas en enda gång!</p>
</div>
<pre class="input"><code>%md</code><code><span class="cm-header cm-header-2">#</span><span class="cm-header cm-header-2">#</span><span class="cm-header cm-header-2"> </span><span class="cm-header cm-header-2">R</span><span class="cm-header cm-header-2">u</span><span class="cm-header cm-header-2">n</span><span class="cm-header cm-header-2"> </span><span class="cm-header cm-header-2">a</span><span class="cm-header cm-header-2">l</span><span class="cm-header cm-header-2">l</span></code></pre>
<div class="output md"><h2 id="run-all">Run all</h2>
</div>
<pre class="input"><code><span class="cm-keyword">from</span> <span class="cm-variable">fermats_factorization</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code><span class="cm-keyword">from</span> <span class="cm-variable">pollards_rho_algorithm</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code><span class="cm-keyword">from</span> <span class="cm-variable">lenstras_elliptic_curve_factorization</span> <span class="cm-keyword">import</span> <span class="cm-operator">*</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close small primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">mediumClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close medium primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">FermatsFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largeClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close large primes"</span></code><code><span class="cm-keyword">print</span> <span class="cm-string">"fermats"</span></code><code></code><code><span class="cm-keyword">print</span> <span class="cm-string">"pollards"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgo</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"small primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgorithm</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">mediumPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"medium primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgorithm</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"large primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgorithm</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largerPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"larger primes"</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgorithm</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close small primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgorithm</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">mediumClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close medium primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">PollardsRhoAlgorithm</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largeClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close large primes"</span></code><code><span class="cm-keyword">print</span> <span class="cm-string">"pollards"</span></code><code></code><code><span class="cm-keyword">print</span> <span class="cm-string">"lenstras"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"small primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">mediumPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"medium primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"large primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largerPrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"larger primes"</span></code><code></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">smallClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close small primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">mediumClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close medium primes"</span></code><code><span class="cm-variable">benchmarks</span> = <span class="cm-variable">LenstrasEllipticCurveFactorization</span>.<span class="cm-variable">benchmark</span>(<span class="cm-variable">largeClosePrimes</span>, <span class="cm-variable">iterations</span>)</code><code><span class="cm-keyword">print</span> <span class="cm-string">"close large primes"</span></code><code><span class="cm-keyword">print</span> <span class="cm-string">"lenstras"</span></code></pre>
<div class="output stdout">close small primes
close small primes
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