110 lines
1.9 KiB
Markdown
110 lines
1.9 KiB
Markdown
---
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id: 5e6dee7749a0b85a3f1fc7d5
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title: Lucas-Lehmer test
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challengeType: 5
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forumTopicId: 385281
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dashedName: lucas-lehmer-test
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---
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# --description--
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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 $S(1)=4$.
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# --instructions--
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Write a function that returns whether the given Mersenne number is prime or not.
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# --hints--
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`lucasLehmer` should be a function.
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```js
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assert(typeof lucasLehmer == 'function');
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```
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`lucasLehmer(11)` should return a boolean.
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```js
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assert(typeof lucasLehmer(11) == 'boolean');
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```
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`lucasLehmer(11)` should return `false`.
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```js
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assert.equal(lucasLehmer(11), false);
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```
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`lucasLehmer(15)` should return `false`.
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```js
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assert.equal(lucasLehmer(15), false);
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```
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`lucasLehmer(13)` should return `true`.
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```js
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assert.equal(lucasLehmer(13), true);
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```
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`lucasLehmer(17)` should return `true`.
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```js
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assert.equal(lucasLehmer(17), true);
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```
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`lucasLehmer(19)` should return `true`.
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```js
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assert.equal(lucasLehmer(19), true);
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```
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`lucasLehmer(21)` should return `false`.
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```js
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assert.equal(lucasLehmer(21), false);
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```
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# --seed--
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## --seed-contents--
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```js
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function lucasLehmer(p) {
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}
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```
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# --solutions--
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```js
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function lucasLehmer(p) {
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function isPrime(p) {
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if (p == 2)
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return true;
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else if (p <= 1 || p % 2 == 0)
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return false;
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else {
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var to = Math.sqrt(p);
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for (var i = 3; i <= to; i += 2)
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if (p % i == 0)
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return false;
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return true;
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}
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}
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function isMersennePrime(p) {
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if (p == 2)
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return true;
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else {
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var m_p = Math.pow(2, p) - 1
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var s = 4;
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for (var i = 3; i <= p; i++)
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s = (s * s - 2) % m_p
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return s == 0;
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}
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}
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return isPrime(p) && isMersennePrime(p)
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}
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```
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