89 lines
2.2 KiB
Markdown
89 lines
2.2 KiB
Markdown
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---
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id: 5900f3ce1000cf542c50fee0
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title: 'Problem 97: Large non-Mersenne prime'
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challengeType: 5
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forumTopicId: 302214
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dashedName: problem-97-large-non-mersenne-prime
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---
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# --description--
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The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form $2^{6972593} − 1$; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form $2^p − 1$, have been found which contain more digits.
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However, in 2004 there was found a massive non-Mersenne prime which contains 2,357,207 digits: $28433 × 2^{7830457} + 1$.
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Find the last ten digits of that non-Mersenne prime in the form $multiplier × 2^{power} + 1$.
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# --hints--
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`largeNonMersennePrime(19, 6833086)` should return a string.
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```js
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assert(typeof largeNonMersennePrime(19, 6833086) === 'string');
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```
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`largeNonMersennePrime(19, 6833086)` should return the string `3637590017`.
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```js
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assert.strictEqual(largeNonMersennePrime(19, 6833086), '3637590017');
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```
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`largeNonMersennePrime(27, 7046834)` should return the string `0130771969`.
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```js
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assert.strictEqual(largeNonMersennePrime(27, 7046834), '0130771969');
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```
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`largeNonMersennePrime(6679881, 6679881)` should return the string `4455386113`.
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```js
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assert.strictEqual(largeNonMersennePrime(6679881, 6679881), '4455386113');
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```
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`largeNonMersennePrime(28433, 7830457)` should return the string `8739992577`.
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```js
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assert.strictEqual(largeNonMersennePrime(28433, 7830457), '8739992577');
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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 largeNonMersennePrime(multiplier, power) {
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return true;
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}
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largeNonMersennePrime(19, 6833086);
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```
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# --solutions--
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```js
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function largeNonMersennePrime(multiplier, power) {
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function modStepsResults(number, other, mod, startValue, step) {
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let result = startValue;
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for (let i = 0; i < other; i++) {
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result = step(number, result) % mod;
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}
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return result;
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}
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const numOfDigits = 10;
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const mod = 10 ** numOfDigits;
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const digitsAfterPower = modStepsResults(2, power, mod, 1, (a, b) => a * b);
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const digitsAfterMultiply = modStepsResults(
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digitsAfterPower,
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multiplier,
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mod,
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0,
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(a, b) => a + b
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);
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const lastDigits = (digitsAfterMultiply + 1) % mod;
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return lastDigits.toString().padStart(10, '0');
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}
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```
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