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<!doctype html><html lang="en"><head><meta charset="utf-8">
<title>Interactive Prime Number Patterns</title>
<!-- MIT license, https://github.com/neoneye/interactive-prime-number-patterns -->
<meta name="viewport" content="width=device-width, initial-scale=1">
<!-- Uses https://github.com/chartjs/Chart.js -->
<script src="https://cdn.jsdelivr.net/npm/chart.js@2.8.0"></script>
<style>
html {
background-color: white;
font-family: system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica,Arial,sans-serif,Segoe UI Emoji,Segoe UI Symbol;
}
html, body, .main-row-container {
height: 100%;
margin: 0;
}
html, body {
/* disable scrolling */
overflow: hidden;
}
.main-row-container {
display: flex;
flex-direction: column;
justify-content: flex-start;
align-items: stretch;
align-content: stretch;
}
.main-row-item {
flex-grow: 0;
flex-shrink: 0;
flex-basis: 0;
}
.main-row-item-growable {
flex-grow: 1;
position: relative;
padding-top: 10px;
}
.value-container {
display: flex;
padding-left: 10px;
padding-right: 10px;
}
.value-container-item {
flex: 1;
}
.slider-container {
height: 25px;
padding-top: 10px;
padding-left: 10px;
padding-right: 10px;
}
.slider {
width: 100%;
}
#slider0value {
font-weight: bold;
}
#overlay-bottom-right {
position: absolute;
right: 0;
bottom: 0;
}
.overlay-inner {
padding: 10px;
background: rgba(128, 128, 128, 0.2);
}
</style>
<script>
var config = {
type: 'scatter',
data: {
datasets: []
},
options: {
animation: false,
responsive: true,
maintainAspectRatio: false,
tooltips: {
mode: 'point',
callbacks: {
label: function(tooltipItem, data) {
var pointItem = data.datasets[tooltipItem.datasetIndex].data[tooltipItem.index];
var s = pointItem.label;
var is_string = (typeof s == 'string') || (s instanceof String);
if (is_string) {
return s;
} else {
return "x: " + pointItem.x + " y: " + pointItem.y;
}
}
},
},
legend: {
display: false,
},
title: {
display: true,
text: 'a(n) = floor(frac(k * (n+offset)) * prime(n+1)).',
fontColor: 'rgba(0,0,0,1.0)',
position: 'bottom',
fontSize: 25,
}
}
};
function isPrime(num) {
for ( var i = 2; i < num; i++ ) {
if ( num % i === 0 ) {
return false;
}
}
return true;
}
function computePrimes(count) {
var ary = [2];
for ( var i = 3; true; i+=2 ) {
if ( isPrime(i) ) {
ary.push(i);
if (ary.length >= count) {
break;
}
}
}
return ary;
}
function rebuildChart(primes, k, offset) {
var chart = window.myChart;
const count = primes.length;
const base = 1;
// const base = 2.71828182845904;
var dataAll = [];
for ( var i = 0; i < count; i+=1 ) {
const prime0 = primes[i];
const prime1 = primes[i + 1];
const primeGap = prime1 - prime0;
const n = i + offset;
const factor = ((n * k) % base);
const value = factor * prime0;
const y = Math.floor(value);
dict = {
x: i,
y: y,
label: `a(${i}) = floor(frac(${k} * ${n}) * ${prime0}) = ${y}`,
primeGap: primeGap,
};
dataAll.push(dict);
}
const showTwinPrimes = false;
// const showTwinPrimes = true;
var dataHighlight = [];
var dataNotHighlight = [];
if (showTwinPrimes) {
for ( var i = 0; i < dataAll.length; i += 1 ) {
const data = dataAll[i];
if (data.primeGap == 2) {
dataHighlight.push(data);
} else {
dataNotHighlight.push(data);
}
}
}
const datasetAll = {
label: 'All',
backgroundColor: 'rgba(25,25,25,1.0)',
pointRadius: 1,
pointHitRadius: 5,
borderWidth: 0,
data: dataAll,
};
const datasetHighlight = {
label: 'Highlight',
backgroundColor: 'rgba(25,25,25,1.0)',
pointRadius: 2,
pointHitRadius: 5,
borderWidth: 0,
data: dataHighlight,
};
const datasetNotHighlight = {
label: 'Not Highlight',
backgroundColor: 'rgba(180,180,180,1.0)',
pointRadius: 1,
pointHitRadius: 5,
borderWidth: 0,
data: dataNotHighlight,
};
while (chart.data.datasets.length > 0) {
chart.data.datasets.pop();
}
if (showTwinPrimes) {
chart.data.datasets.push(datasetHighlight);
chart.data.datasets.push(datasetNotHighlight);
} else {
chart.data.datasets.push(datasetAll);
}
chart.update();
}
var slider0Handler = function() {
console.log("do nothing");
};
var updateChart = function() {
console.log("do nothing");
};
function setK(k) {
var slider = document.getElementById("slider0");
slider.value = (k * 10000) % 10000;
var value = document.getElementById("slider0value");
value.innerText = `${k}`;
window.chartParameterK = k;
updateChart();
}
function setK_1div3() {
setK(0.333333333333333);
}
function setK_EulersNumber() {
setK(2.7182818284);
}
function setK_Pi() {
setK(3.1415926535);
}
function setK_A085849() {
setK(0.353236371854); // https://oeis.org/A085849
}
function setK_Sqrt2() {
setK(1.4142135623730951); // https://oeis.org/A002193
}
function setK_GoldenRatio() {
setK(1.61803398874); // https://oeis.org/A001622
}
function setK_EulerMascheroni() {
setK(0.577215664); // https://oeis.org/A001620
}
function setTermCount(termCount) {
window.termCount = termCount;
updateChart();
}
window.onload = function() {
var ctx = document.getElementById('canvas').getContext('2d');
window.myChart = new Chart(ctx, config);
window.termCount = 1000;
window.chartParameterK = 0.3333;
window.chartParameterOffset = 0;
const primes = computePrimes(10001);
let slider0 = document.getElementById("slider0");
let slider1 = document.getElementById("slider1");
let value0 = document.getElementById("slider0value");
let value1 = document.getElementById("slider1value");
updateChart = function() {
const slicedArrayPrimes = primes.slice(0, window.termCount);
rebuildChart(slicedArrayPrimes, window.chartParameterK, window.chartParameterOffset);
};
slider0Handler = function() {
var slider0value = slider0.value;
var value = parseInt(slider0value);
let value_integer = Math.floor(value / 10000);
let value_frac = value % 10000;
let value_frac_string = value_frac.toString().padStart(4, "0");
window.chartParameterK = value / 10000.0;
value0.innerHTML = `${value_integer}.${value_frac_string}`;
};
slider1Handler = function() {
var slider1value = slider1.value;
var offset = parseInt(slider1value);
value1.innerHTML = `${offset}`;
window.chartParameterOffset = offset;
};
slider0.oninput = function() {
slider0Handler();
updateChart();
};
slider1.oninput = function() {
slider1Handler();
updateChart();
};
slider0Handler();
slider1Handler();
setK_A085849();
};
</script>
</head>
<body>
<div class="main-row-container">
<div class="main-row-item">
<div class="slider-container">
<input type="range" min="0" max="10000" value="5000" class="slider" id="slider0">
</div>
</div>
<div class="main-row-item">
<div class="value-container">
<div class="value-container-item slidevalue">
<span>k</span> = <span id="slider0value">VALUE</span>
</div>
<div class="value-container-item">
set k:
<button onclick="setK_Pi()">Pi</button>
<button onclick="setK_1div3()">1/3</button>
<button onclick="setK_A085849()">A085849</button>
<button onclick="setK_Sqrt2()">sqrt(2)</button>
<button onclick="setK_EulerMascheroni()">Euler–Mascheroni</button>
<button onclick="setK_GoldenRatio()">Golden Ratio</button>
<button onclick="setK_EulersNumber()">e</button>
</div>
</div>
</div>
<div class="main-row-item">
<div class="slider-container">
<input type="range" min="-50" max="50" value="0" class="slider" id="slider1">
</div>
</div>
<div class="main-row-item">
<div class="value-container">
<div class="value-container-item slidevalue">
<span>offset</span> = <span id="slider1value">VALUE</span>
</div>
<div class="value-container-item">
number of terms:
<button onclick="setTermCount(100)">100</button>
<button onclick="setTermCount(200)">200</button>
<button onclick="setTermCount(500)">500</button>
<button onclick="setTermCount(1000)">1000</button>
<button onclick="setTermCount(2000)">2000</button>
<button onclick="setTermCount(5000)">5000</button>
<button onclick="setTermCount(10000)">10000</button>
</div>
</div>
</div>
<div class="main-row-item-growable">
<canvas id="canvas"></canvas>
</div>
</div>
<div id="overlay-bottom-right">
<div class="overlay-inner"><a href="https://github.com/neoneye/interactive-prime-number-patterns">This project is open source</a></div>
</div>
</body>
</html>