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Lucas-Lehmer test

curriculum/challenges/english/blocks/rosetta-code-challenges/5e6dee7749a0b85a3f1fc7d5.md

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--description--

Lucas-Lehmer Test: for $p$ an odd prime, the Mersenne number $2^p-1$ is prime if and only if $2^p-1$ divides $S(p-1)$ where $S(n+1)=(S(n))^2-2$, and $S(1)=4$.

--instructions--

Write a function that returns whether the given Mersenne number is prime or not.

--hints--

lucasLehmer should be a function.

js
assert(typeof lucasLehmer == 'function');

lucasLehmer(11) should return a boolean.

js
assert(typeof lucasLehmer(11) == 'boolean');

lucasLehmer(11) should return false.

js
assert.equal(lucasLehmer(11), false);

lucasLehmer(15) should return false.

js
assert.equal(lucasLehmer(15), false);

lucasLehmer(13) should return true.

js
assert.equal(lucasLehmer(13), true);

lucasLehmer(17) should return true.

js
assert.equal(lucasLehmer(17), true);

lucasLehmer(19) should return true.

js
assert.equal(lucasLehmer(19), true);

lucasLehmer(21) should return false.

js
assert.equal(lucasLehmer(21), false);

--seed--

--seed-contents--

js
function lucasLehmer(p) {

}

--solutions--

js
function lucasLehmer(p) {
    function isPrime(p) {
        if (p == 2)
            return true;
        else if (p <= 1 || p % 2 == 0)
            return false;
        else {
            var to = Math.sqrt(p);
            for (var i = 3; i <= to; i += 2)
                if (p % i == 0)
                    return false;
            return true;
        }
    }

    function isMersennePrime(p) {
        if (p == 2)
            return true;
        else {
            var m_p = Math.pow(2, p) - 1
            var s = 4;
            for (var i = 3; i <= p; i++)
                s = (s * s - 2) % m_p
            return s == 0;
        }
    }

    return isPrime(p) && isMersennePrime(p)
}