2.0 KiB
2.0 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f3a61000cf542c50feb9 | 5 | Problem 58: Spiral primes | 302169 |
Description
Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
37 36 35 34 33 32 31
38 17 16 15 14 13 30
39 18 5 4 3 12 29
40 19 6 1 2 11 28
41 20 7 8 9 10 27
42 21 22 23 24 25 26
43 44 45 46 47 48 49
38 17 16 15 14 13 30
39 18 5 4 3 12 29
40 19 6 1 2 11 28
41 20 7 8 9 10 27
42 21 22 23 24 25 26
43 44 45 46 47 48 49
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%.
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%?
Instructions
Tests
tests:
- text: <code>spiralPrimes()</code> should return a number.
testString: assert(typeof spiralPrimes() === 'number');
- text: <code>spiralPrimes()</code> should return 26241.
testString: assert.strictEqual(spiralPrimes(), 26241);
Challenge Seed
function spiralPrimes() {
return true;
}
spiralPrimes();
Solution
// solution required