58 lines
1.5 KiB
Markdown
58 lines
1.5 KiB
Markdown
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---
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id: 5900f4741000cf542c50ff86
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title: 'Problem 263: An engineers'' dream come true'
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challengeType: 5
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forumTopicId: 301912
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dashedName: problem-263-an-engineers-dream-come-true
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---
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# --description--
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Consider the number 6. The divisors of 6 are: 1,2,3 and 6.
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Every number from 1 up to and including 6 can be written as a sum of distinct divisors of 6:
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$1 = 1$, $2 = 2$, $3 = 1 + 2$, $4 = 1 + 3$, $5 = 2 + 3$, $6 = 6$.
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A number $n$ is called a practical number if every number from 1 up to and including $n$ can be expressed as a sum of distinct divisors of $n$.
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A pair of consecutive prime numbers with a difference of six is called a sexy pair (since "sex" is the Latin word for "six"). The first sexy pair is (23, 29).
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We may occasionally find a triple-pair, which means three consecutive sexy prime pairs, such that the second member of each pair is the first member of the next pair.
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We shall call a number $n$ such that:
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- ($n - 9$, $n - 3$), ($n - 3$, $n + 3$), ($n + 3$, $n + 9$) form a triple-pair, and
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- the numbers $n - 8$, $n - 4$, $n$, $n + 4$ and $n + 8$ are all practical,
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an engineers’ paradise.
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Find the sum of the first four engineers’ paradises.
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# --hints--
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`engineersDreamComeTrue()` should return `2039506520`.
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```js
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assert.strictEqual(engineersDreamComeTrue(), 2039506520);
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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 engineersDreamComeTrue() {
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return true;
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}
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engineersDreamComeTrue();
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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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