Files

89 lines
2.2 KiB
Markdown
Raw Permalink Normal View History

---
id: 5900f3ce1000cf542c50fee0
title: 'Problem 97: Large non-Mersenne prime'
challengeType: 5
forumTopicId: 302214
dashedName: problem-97-large-non-mersenne-prime
---
# --description--
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.
However, in 2004 there was found a massive non-Mersenne prime which contains 2,357,207 digits: $28433 × 2^{7830457} + 1$.
Find the last ten digits of that non-Mersenne prime in the form $multiplier × 2^{power} + 1$.
# --hints--
`largeNonMersennePrime(19, 6833086)` should return a string.
```js
assert(typeof largeNonMersennePrime(19, 6833086) === 'string');
```
`largeNonMersennePrime(19, 6833086)` should return the string `3637590017`.
```js
assert.strictEqual(largeNonMersennePrime(19, 6833086), '3637590017');
```
`largeNonMersennePrime(27, 7046834)` should return the string `0130771969`.
```js
assert.strictEqual(largeNonMersennePrime(27, 7046834), '0130771969');
```
`largeNonMersennePrime(6679881, 6679881)` should return the string `4455386113`.
```js
assert.strictEqual(largeNonMersennePrime(6679881, 6679881), '4455386113');
```
`largeNonMersennePrime(28433, 7830457)` should return the string `8739992577`.
```js
assert.strictEqual(largeNonMersennePrime(28433, 7830457), '8739992577');
```
# --seed--
## --seed-contents--
```js
function largeNonMersennePrime(multiplier, power) {
return true;
}
largeNonMersennePrime(19, 6833086);
```
# --solutions--
```js
function largeNonMersennePrime(multiplier, power) {
function modStepsResults(number, other, mod, startValue, step) {
let result = startValue;
for (let i = 0; i < other; i++) {
result = step(number, result) % mod;
}
return result;
}
const numOfDigits = 10;
const mod = 10 ** numOfDigits;
const digitsAfterPower = modStepsResults(2, power, mod, 1, (a, b) => a * b);
const digitsAfterMultiply = modStepsResults(
digitsAfterPower,
multiplier,
mod,
0,
(a, b) => a + b
);
const lastDigits = (digitsAfterMultiply + 1) % mod;
return lastDigits.toString().padStart(10, '0');
}
```