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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-58-spiral-primes.md

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+---
+id: 5900f3a61000cf542c50feb9
+title: 'Problem 58: Spiral primes'
+challengeType: 5
+forumTopicId: 302169
+dashedName: problem-58-spiral-primes
+---
+
+# --description--
+
+Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
+
+<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>
+
+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.
+
+```js
+assert(typeof spiralPrimes(50) === 'number');
+```
+
+`spiralPrimes(50)` should return `11`.
+
+```js
+assert.strictEqual(spiralPrimes(50), 11);
+```
+
+`spiralPrimes(15)` should return `981`.
+
+```js
+assert.strictEqual(spiralPrimes(15), 981);
+```
+
+`spiralPrimes(10)` should return `26241`.
+
+```js
+assert.strictEqual(spiralPrimes(10), 26241);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function spiralPrimes(percent) {
+
+  return true;
+}
+
+spiralPrimes(50);
+```
+
+# --solutions--
+
+```js
+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;
+}
+```