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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');
}

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