{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Spiral primes (Euler Problem 58)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "[https://projecteuler.net/problem=58](https://projecteuler.net/problem=58)\n", "\n", "Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.\n", "\n", "37 36 35 34 33 32 31\n", "38 17 16 15 14 13 30\n", "39 18 5 4 3 12 29\n", "40 19 6 1 2 11 28\n", "41 20 7 8 9 10 27\n", "42 21 22 23 24 25 26\n", "43 44 45 46 47 48 49\n", "\n", "It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.\n", "\n", "If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "completion_date": "", "kernelspec": { "display_name": "Python 3", "language": "python3.6", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" }, "tags": [] }, "nbformat": 4, "nbformat_minor": 2 }