2020-12-16 00:37:30 -07:00
---
id: 5e6dee7749a0b85a3f1fc7d5
title: Lucas-Lehmer test
challengeType: 5
forumTopicId: 385281
2021-01-13 03:31:00 +01:00
dashedName: lucas-lehmer-test
2020-12-16 00:37:30 -07:00
---
# --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)
}
```
