Matlab Problem :

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 consecutive sexy pair (since "sex" is the Latin word for "six". This is a website for people of all ages. If you have a dirty mind read about number theory here). The first sexy pair is (5,11). The first consecutive 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 engineer paradise.

Your job is to find the first engineer paradise. Can you find the second engineer paradise? How about the third?