94 lines
2.3 KiB
Markdown
94 lines
2.3 KiB
Markdown
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---
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id: 5e6dee7749a0b85a3f1fc7d5
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title: Lucas-Lehmer test
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challengeType: 5
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isHidden: false
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---
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## Description
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<section id='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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</section>
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## Instructions
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<section id='instructions'>
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Write a function that returns whether the given Mersenne number is prime or not.
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</section>
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## Tests
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<section id='tests'>
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``` yml
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tests:
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- text: <code>lucasLehmer</code> should be a function.
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testString: assert(typeof lucasLehmer == 'function');
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- text: <code>lucasLehmer(11)</code> should return a boolean.
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testString: assert(typeof lucasLehmer(11) == 'boolean');
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- text: <code>lucasLehmer(11)</code> should return <code>false</code>.
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testString: assert.equal(lucasLehmer(11), false);
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- text: <code>lucasLehmer(15)</code> should return <code>false</code>.
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testString: assert.equal(lucasLehmer(15), false);
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- text: <code>lucasLehmer(13)</code> should return <code>true</code>.
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testString: assert.equal(lucasLehmer(13), true);
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- text: <code>lucasLehmer(17)</code> should return <code>true</code>.
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testString: assert.equal(lucasLehmer(17), true);
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- text: <code>lucasLehmer(19)</code> should return <code>true</code>.
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testString: assert.equal(lucasLehmer(19), true);
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- text: <code>lucasLehmer(21)</code> should return <code>false</code>.
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testString: assert.equal(lucasLehmer(21), false);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function lucasLehmer(p) {
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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