2.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3ce1000cf542c50fee0 | Problem 97: Large non-Mersenne prime | 5 | 302214 | 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.
assert(typeof largeNonMersennePrime(19, 6833086) === 'string');
largeNonMersennePrime(19, 6833086)
should return the string 3637590017
.
assert.strictEqual(largeNonMersennePrime(19, 6833086), '3637590017');
largeNonMersennePrime(27, 7046834)
should return the string 0130771969
.
assert.strictEqual(largeNonMersennePrime(27, 7046834), '0130771969');
largeNonMersennePrime(6679881, 6679881)
should return the string 4455386113
.
assert.strictEqual(largeNonMersennePrime(6679881, 6679881), '4455386113');
largeNonMersennePrime(28433, 7830457)
should return the string 8739992577
.
assert.strictEqual(largeNonMersennePrime(28433, 7830457), '8739992577');
--seed--
--seed-contents--
function largeNonMersennePrime(multiplier, power) {
return true;
}
largeNonMersennePrime(19, 6833086);
--solutions--
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');
}