This figure creates a black dot for each prime number. The numbers are plotted as a square spiral starting on the red dot and extending around it.
It is curious to notice that you can discover some oblique directions that are very dense in terms of prime occurence.
Are primes not so uniformely distributed?
| <!DOCTYPE html> | |
| <svg width="960" height="500"> | |
| <g id='sandbox' transform='translate('+[960/2, 500/2]+')'> | |
| </g> | |
| </svg> | |
| <script src="https://d3js.org/d3.v4.min.js"></script> | |
| <script> | |
| const maxLayers=1000; | |
| const svg = d3.select('#sandbox'); | |
| const primes=[2, 3]; | |
| function isPrime(number) { | |
| if (number<4) return true; | |
| const limit = Math.sqrt(number); | |
| for(var primeIdx=0; primeIdx<primes.length && primes[primeIdx]<=limit; primeIdx++) { | |
| const prime=primes[primeIdx]; | |
| if (number%prime==0) { | |
| return false; | |
| } | |
| } | |
| primes.push(number); | |
| return true; | |
| } | |
| function yPos(cnt,layer, total) { | |
| //there is a axial symetry. Let's start in a corner | |
| const halfCount=total/2; //we are sure it is an even number | |
| const half = (Math.floor(cnt/halfCount)%2==0)?1:-1; | |
| //the y pos is limited to layer*2+1 | |
| const y=Math.min(layer*2, cnt%halfCount); | |
| return half*(y-layer); | |
| } | |
| function xPos(cnt,layer, total) { | |
| //the position is the same with a phase of a quarter | |
| return yPos(cnt+total/4, layer, total); | |
| } | |
| svg.append('circle').attr('r', 3) | |
| .attr('fill', 'red') | |
| .attr('cx', 0) | |
| .attr('cy', 0); | |
| const zoom=1; | |
| const layer = d3.range(maxLayers); //layer is the level from the center | |
| let current=1; | |
| layer.map(l=>{ | |
| const totalPointCount = l*8; | |
| const count=d3.range(totalPointCount); // count of points per layer | |
| for (let c=0;c<totalPointCount; c++) { | |
| if (isPrime(current++)) { | |
| svg.append('circle').attr('r', 1) | |
| .attr('cx', zoom*xPos(c, l, totalPointCount)) | |
| .attr('cy', zoom*yPos(c, l, totalPointCount)); | |
| } | |
| }; | |
| }); | |
| console.log("displayed primes="+primes.length) | |
| </script> |