# Problem 263: An engineers' dream come true

![graphic](img263.gif)

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.