2d:null 2e:["$","title",null,{"children":"Mutations of Digits of Primes | Bryan | Observable"}] 33:[] 31:{"id":"0204140b3ed01ec1","slug":"digits-of-primes","title":"Mutations of Digits of Primes","thumbnail":"c2f5c303d443da5c9b7ed6902afc8278316aa31ecc1fa19971c2e53f6a8a85cd","access_level":"public","create_time":"$D2018-04-04T04:25:10.434Z","update_time":"$D2018-04-05T22:38:21.184Z","view_time":null,"first_public_time":"$D2018-04-05T05:43:06.710Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"a8afac7fc0f0a766","login":"bbischof","name":"Bryan","avatar_url":"https://avatars-next.observableusercontent.com/c71257ace95ae262b20ea3ea4f4b2a09891e92c86bf45e64d1b97d82d212a332","tier":"starter_2024"},"version":301,"publish_version":301,"role":null,"authored":false,"authors":[{"type":"individual","id":"32ac87846a6eed40","login":"bbischof","name":"Bryan","avatar_url":"https://avatars-next.observableusercontent.com/c71257ace95ae262b20ea3ea4f4b2a09891e92c86bf45e64d1b97d82d212a332","tier":null}],"members":[{"type":"individual","id":"32ac87846a6eed40","login":"bbischof","name":"Bryan","avatar_url":"https://avatars-next.observableusercontent.com/c71257ace95ae262b20ea3ea4f4b2a09891e92c86bf45e64d1b97d82d212a332","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Mutations of Digits of Primes","cells":[{"id":0,"value":"md`# Mutations of Digits of Primes`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"viewof n = slider(\n {\n min: 2, \n max: 5, \n step: 1, \n value: 2,\n title: \"Let n =\", \n description: \"Number of Digits (warning, big numbers are slow!)\"\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"incdec('n', viewof n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"md`The primes with ${n} digits are: `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"primes = getPrimesWithNDigits(n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"md`If we reverse their digits, are they still prime?`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"emirps_booleans = primes.map(x => emirp(x))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"md`What if we rotate their digits?`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"viewof number_of_shifts = slider(\n {\n min: 1, \n max: n-1, \n step: 1, \n value: this ? this.value : 1,\n title: \"Number of shifts:\", \n description: \"How many digits we shift by\"\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"incdec('number of shifts', viewof number_of_shifts)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"shifted_primes = primes.map(x => x.toString().substr(number_of_shifts) + x.toString().substr(0, number_of_shifts))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"shifted_booleans = primes.map(x => shiftPrime(x))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":283,"value":"md`Finally, let's think about permutations of the digits:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":256,"value":"viewof r = radio({title: 'Permutation options:', options: buttons, value: buttons[0]})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":285,"value":"md`## Which kind of digit mutation would you like to visualize?`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":261,"value":"viewof tp = radio({title: 'Types of primes:', options: types_of_prime, value: types_of_prime[0]})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"chart = {\n let square_width = (height*2-300)/(prime_data).length\n let square_height = (height/2)-30\n \n function color(value) {\n if (value==0) {\n\t return 'blue'\n }\n if (value==1) {\n \treturn 'yellow'\n }\n\t};\n \n const svg = d3.select(DOM.svg(width, height/2))\n \n let rectangles = svg.selectAll(\"rect\")\n .data(prime_data)\n .enter()\n .append(\"rect\"); \n rectangles\n .attr(\"x\", function(d){\n return d.i * square_width-100; \n })\n .attr(\"y\", function(d){\n return 0 * square_height; \n })\n .attr(\"width\", square_width)\n .attr(\"height\", square_height). \n style(\"fill\", function(d){\n return color(d[tp]); \n }); \n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":296,"value":"incdec('n', viewof n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":287,"value":"md`## The Innards(helper functions and variables):`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":75,"value":"prime_data = range(Math.pow(10, n-1), Math.pow(10, n)-1).map(\n x => ({\n 'i': x, \n 'shifts': number_of_shifts,\n 'prime': isPrime(x),\n 'emirp': emirp(x),\n 'shifted_prime': shiftPrime(x, number_of_shifts),\n 'permuted_prime': isPrime(permute_number(x))\n })\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"function getAllPermutations(string) {\n var results = [];\n\n if (string.length === 1) {\n results.push(string);\n return results;\n }\n\n for (var i = 0; i < string.length; i++) {\n var firstChar = string[i];\n var charsLeft = string.substring(0, i) + string.substring(i + 1);\n var innerPermutations = getAllPermutations(charsLeft);\n for (var j = 0; j < innerPermutations.length; j++) {\n results.push(firstChar + innerPermutations[j]);\n }\n }\n return results;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":238,"value":"function permute_number(i) {\n return r.split(\"\").map(x => i.toString().charAt(x-1)).join(\"\")\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":266,"value":"types_of_prime = [\"prime\", \"emirp\", \"shifted_prime\", \"permuted_prime\"]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":161,"value":"buttons = getAllPermutations(range(1,n).join(\"\")).map(x => \"(\"+x+\")\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":91,"value":"function shiftPrime(x, shift) {\n return isPrime(x.toString().substr(number_of_shifts) + x.toString().substr(0, number_of_shifts))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"function emirp(x){\n return isPrime(x.toString().split(\"\").reverse().join(\"\"))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":78,"value":"function range(start, end) {\n return Array(end - start + 1).fill().map((_, idx) => start + idx)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"function incdec(name, view) {\n const form = html``;\n form.inc.addEventListener(\"click\", () => update(view, view.value + 1));\n form.dec.addEventListener(\"click\", () => update(view, view.value - 1));\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"function update(view, value) {\n view.input.value = value;\n view.dispatchEvent(new CustomEvent(\"input\"));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"import {radio} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"function isPrime(number) {\n var start = 2;\n while (start <= Math.sqrt(number)) {\n if (number % start++ < 1) return false;\n }\n return number > 1;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"function getPrimes(start, finish) {\n var realStart = (start <= finish) ? start : finish;\n var realEnd = (start > finish) ? start : finish;\n var numbers = [];\n \n for(var current = realStart; current <= realEnd; current++) {\n if(isPrime(current)) {\n numbers.push(current);\n }\n }\n return numbers\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"function getPrimesWithNDigits(n){\n return getPrimes(Math.pow(10, n-1)-1, Math.pow(10, n)-1)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"height = 600","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"gen = require(\"generatorics\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":107,"value":"d3 = require(\"https://d3js.org/d3.v5.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 32:"$31:body"