2.6 KiB
2.6 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3a61000cf542c50feb9 | Problem 58: Spiral primes | 5 | 302169 | problem-58-spiral-primes |
--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 percent of primes along both diagonals first falls below percent
?
--hints--
spiralPrimes(50)
should return a number.
assert(typeof spiralPrimes(50) === 'number');
spiralPrimes(50)
should return 11
.
assert.strictEqual(spiralPrimes(50), 11);
spiralPrimes(15)
should return 981
.
assert.strictEqual(spiralPrimes(15), 981);
spiralPrimes(10)
should return 26241
.
assert.strictEqual(spiralPrimes(10), 26241);
--seed--
--seed-contents--
function spiralPrimes(percent) {
return true;
}
spiralPrimes(50);
--solutions--
function spiralPrimes(percent) {
function isPrime(n) {
if (n <= 3) {
return n > 1;
} else if (n % 2 === 0 || n % 3 === 0) {
return false;
}
for (let i = 5; i * i <= n; i += 6) {
if (n % i === 0 || n % (i + 2) === 0) {
return false;
}
}
return true;
}
let totalCount = 1;
let primesCount = 0;
let curNumber = 1;
let curSideLength = 1;
let ratio = 1;
const wantedRatio = percent / 100;
while (ratio >= wantedRatio) {
curSideLength += 2;
for (let i = 0; i < 4; i++) {
curNumber += curSideLength - 1;
totalCount++;
if (i !== 3 && isPrime(curNumber)) {
primesCount++;
}
}
ratio = primesCount / totalCount;
}
return curSideLength;
}