126 lines
3.0 KiB
Markdown
126 lines
3.0 KiB
Markdown
---
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id: 5900f39f1000cf542c50feb2
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title: 'Problem 51: Prime digit replacements'
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challengeType: 5
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forumTopicId: 302162
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dashedName: problem-51-prime-digit-replacements
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---
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# --description--
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By replacing the 1st digit of the 2-digit number \*3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
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By replacing the 3rd and 4th digits of 56\*\*3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property.
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Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an `n` prime value family.
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# --hints--
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`primeDigitReplacements(6)` should return a number.
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```js
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assert(typeof primeDigitReplacements(6) === 'number');
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```
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`primeDigitReplacements(6)` should return `13`.
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```js
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assert.strictEqual(primeDigitReplacements(6), 13);
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```
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`primeDigitReplacements(7)` should return `56003`.
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```js
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assert.strictEqual(primeDigitReplacements(7), 56003);
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```
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`primeDigitReplacements(8)` should return `121313`.
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```js
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assert.strictEqual(primeDigitReplacements(8), 121313);
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```
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# --seed--
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## --seed-contents--
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```js
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function primeDigitReplacements(n) {
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return true;
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}
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primeDigitReplacements(6);
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```
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# --solutions--
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```js
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function primeDigitReplacements(n) {
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function isNFamily(number, primesMap, n) {
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const prime = number.toString();
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const lastDigit = prime[prime.length - 1];
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return (
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doesReplacingMakeFamily(prime, '0', primesMap, n) ||
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(lastDigit !== '1' &&
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doesReplacingMakeFamily(prime, '1', primesMap, n)) ||
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doesReplacingMakeFamily(prime, '2', primesMap, n)
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);
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}
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function doesReplacingMakeFamily(prime, digitToReplace, primesMap, family) {
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let count = 0;
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const replaceWith = '0123456789';
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for (let i = 0; i < replaceWith.length; i++) {
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const nextNumber = parseInt(
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prime.replace(new RegExp(digitToReplace, 'g'), replaceWith[i]),
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10
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);
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if (isPartOfFamily(nextNumber, prime, primesMap)) {
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count++;
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}
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}
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return count === family;
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}
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function isPartOfFamily(number, prime, primesMap) {
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return (
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isPrime(number, primesMap) && number.toString().length === prime.length
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);
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}
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function getSievePrimes(max) {
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const primesMap = new Array(max).fill(true);
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primesMap[0] = false;
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primesMap[1] = false;
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for (let i = 2; i < max; i++) {
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if (primesMap[i]) {
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let j = i * i;
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for (j; j < max; j += i) {
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primesMap[j] = false;
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}
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}
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}
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return primesMap;
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}
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function isPrime(num, primesMap) {
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return primesMap[num];
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}
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const primesMap = getSievePrimes(1000000);
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for (let number = 1; number < 300000; number++) {
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if (primesMap[number]) {
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if (isNFamily(number, primesMap, n)) {
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return number;
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}
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}
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}
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return -1;
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}
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```
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