50 lines
1.2 KiB
Markdown
50 lines
1.2 KiB
Markdown
---
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id: 5900f4351000cf542c50ff47
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title: >-
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Problem 200: Find the 200th prime-proof sqube containing the contiguous
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sub-string "200"
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challengeType: 5
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forumTopicId: 301840
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dashedName: >-
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problem-200-find-the-200th-prime-proof-sqube-containing-the-contiguous-sub-string-200
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---
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# --description--
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We shall define a sqube to be a number of the form, ${p^2}{q^3}$, where $p$ and $q$ are distinct primes.
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For example, $200 = {5^2}{2^3}$ or $120072949 = {{23}^2}{{61}^3}$.
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The first five squbes are 72, 108, 200, 392, and 500.
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Interestingly, 200 is also the first number for which you cannot change any single digit to make a prime; we shall call such numbers, prime-proof. The next prime-proof sqube which contains the contiguous sub-string `200` is 1992008.
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Find the 200th prime-proof sqube containing the contiguous sub-string `200`.
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# --hints--
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`primeProofSqubeWithSubString()` should return `229161792008`.
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```js
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assert.strictEqual(primeProofSqubeWithSubString(), 229161792008);
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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 primeProofSqubeWithSubString() {
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return true;
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}
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primeProofSqubeWithSubString();
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```
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# --solutions--
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```js
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// solution required
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```
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