55 lines
1.3 KiB
Markdown
55 lines
1.3 KiB
Markdown
---
|
||
id: 5900f4741000cf542c50ff86
|
||
title: 'Problem 263: An engineers'' dream come true'
|
||
challengeType: 5
|
||
forumTopicId: 301912
|
||
dashedName: problem-263-an-engineers-dream-come-true
|
||
---
|
||
|
||
# --description--
|
||
|
||
Consider the number 6. The divisors of 6 are: 1,2,3 and 6.
|
||
|
||
Every number from 1 up to and including 6 can be written as a sum of distinct divisors of 6:
|
||
|
||
1=1, 2=2, 3=1+2, 4=1+3, 5=2+3, 6=6.
|
||
|
||
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.
|
||
|
||
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).
|
||
|
||
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.
|
||
|
||
We shall call a number n such that : (n-9, n-3), (n-3,n+3), (n+3, n+9) form a triple-pair, and the numbers n-8, n-4, n, n+4 and n+8 are all practical,
|
||
|
||
an engineers’ paradise.
|
||
|
||
Find the sum of the first four engineers’ paradises.
|
||
|
||
# --hints--
|
||
|
||
`euler263()` should return 2039506520.
|
||
|
||
```js
|
||
assert.strictEqual(euler263(), 2039506520);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function euler263() {
|
||
|
||
return true;
|
||
}
|
||
|
||
euler263();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|