2018-09-30 22:01:58 +00:00
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---
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id: 5900f3761000cf542c50fe89
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challengeType: 5
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title: 'Problem 10: Summation of primes'
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---
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## Description
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<section id='description'>
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The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
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Find the sum of all the primes below n.
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</section>
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## Instructions
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<section id='instructions'>
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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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2018-10-04 13:37:37 +00:00
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tests:
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- text: <code>primeSummation(17)</code> should return 41.
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2018-10-20 18:02:47 +00:00
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testString: assert.strictEqual(primeSummation(17), 41, '<code>primeSummation(17)</code> should return 41.');
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2018-10-04 13:37:37 +00:00
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- text: <code>primeSummation(2001)</code> should return 277050.
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2018-10-20 18:02:47 +00:00
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testString: assert.strictEqual(primeSummation(2001), 277050, '<code>primeSummation(2001)</code> should return 277050.');
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2018-10-04 13:37:37 +00:00
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- text: <code>primeSummation(140759)</code> should return 873608362.
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2018-10-20 18:02:47 +00:00
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testString: assert.strictEqual(primeSummation(140759), 873608362, '<code>primeSummation(140759)</code> should return 873608362.');
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2018-10-04 13:37:37 +00:00
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- text: <code>primeSummation(2000000)</code> should return 142913828922.
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2018-10-20 18:02:47 +00:00
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testString: assert.strictEqual(primeSummation(2000000), 142913828922, '<code>primeSummation(2000000)</code> should return 142913828922.');
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2018-09-30 22:01:58 +00:00
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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 primeSummation(n) {
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// Good luck!
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return true;
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}
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primeSummation(2000000);
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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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//noprotect
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function primeSummation(n) {
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// Initialise an array containing only prime numbers
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let primes = [2];
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let result = 2;
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function isPrime(y, primes) {
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// Find sqrt(y)
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const sqrt = Math.floor(Math.sqrt(y));
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// Divide y by each applicable prime, return false if any of them divide y
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for (let i = 0; i < primes.length && primes[i] <= sqrt; i++) {
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if (y % primes[i] === 0) {
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return false;
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}
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}
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// At this point x must be prime
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return true;
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}
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// For every odd integer, add it to the array if it is prime
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for (let x = 3; x < n; x += 2) {
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if (isPrime(x, primes)) {
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if (x > n) {
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return result;
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} else {
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result += x;
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primes.push(x);
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}
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}
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}
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return result;
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}
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```
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</section>
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