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---
id: 5900f3a61000cf542c50feb9
title: 'Problem 58: Spiral primes'
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challengeType: 5
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forumTopicId: 302169
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---
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# --description--
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Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
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< div style = 'text-align: center;' >
< strong > < span style = 'color: red;' > 37< / span > < / strong > 36 35 34 33 32 < strong > < span style = 'color: red;' > 31< / span > < / strong > < br >
38 < strong > < span style = 'color: red;' > 17< / span > < / strong > 16 15 14 < strong > < span style = 'color: red;' > 13< / span > < / strong > 30< br >
39 18 < strong > < span style = 'color: red;' > 5< / span > < / strong > 4 < strong > < span style = 'color: red;' > 3< / span > < / strong > 12 29< br >
40 19 6 1 2 11 28< br >
41 20 < strong > < span style = 'color: red;' > 7< / span > < / strong > 8 9 10 27< br >
42 21 22 23 24 25 26< br >
< strong > < span style = 'color: red;' > 43< / span > < / strong > 44 45 46 47 48 49< br >
< / div >
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It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.
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If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?
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# --hints--
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`spiralPrimes()` should return a number.
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```js
assert(typeof spiralPrimes() === 'number');
```
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`spiralPrimes()` should return 26241.
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```js
assert.strictEqual(spiralPrimes(), 26241);
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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 spiralPrimes() {
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return true;
}
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spiralPrimes();
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```
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# --solutions--
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```js
// solution required
```