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p058.py
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p058.py
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# -*- coding: utf-8 -*-
"""
Created on Thu May 16 14:22:55 2013
@author: guillermo
"""
def isprime(n):
'''check if integer n is a prime'''
# make sure n is a positive integer
n = abs(int(n))
# 0 and 1 are not primes
if n < 2:
return False
# 2 is the only even prime number
if n == 2:
return True
# all other even numbers are not primes
if not n & 1:
return False
# range starts with 3 and only needs to go up the squareroot of n
# for all odd numbers
for x in range(3, int(n**0.5)+1, 2):
if n % x == 0:
return False
return True
valores = [3]
def actvalores(n):
for i in range (0,n):
x = valores[i]
valores.append(int(x) + 8*(i+2) - 6)
def valor(n):
#da el valor de la esquina menor de la iteracion n
return valores[n]
nprimos = []
ntotal = [1]
def addnumbers(n):
#añade los correspondientes numeros a las listas para la iteracion n
x = valor(n)
if (isprime(x)):
nprimos.append(x)
if (isprime(x + 2*(n+1))):
nprimos.append(x + 2*(n+1))
if (isprime(x + 4*(n+1))):
nprimos.append(x + 4*(n+1))
if (isprime(x + 6*(n+1))):
nprimos.append(x + 6*(n+1))
ntotal.append(x)
ntotal.append(x+2*n)
ntotal.append(x+4*n)
ntotal.append(x+6*n)
actvalores(20000)
#valores contiene los 20000 primeros valores menores de las esquinas
#number obtained by bruteforcing
addnumbers(0)
cont = 1
while double(len(nprimos))/double(len(ntotal)) > 0.1:
addnumbers(cont)
cont = cont + 1
print 2*cont + 1