--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--

engineersDreamComeTrue() should return 2039506520.

assert.strictEqual(engineersDreamComeTrue(), 2039506520);

--seed--

--seed-contents--

function engineersDreamComeTrue() {

  return true;
}

engineersDreamComeTrue();

--solutions--

// solution required