# Problem 293: Pseudo-Fortunate Numbers
An even positive integer N will be called admissible, if it is a power
of 2 or its distinct prime factors are consecutive primes. The first
twelve admissible numbers are 2,4,6,8,12,16,18,24,30,32,36,48. If N is
admissible, the smallest integer M > 1 such that N+M is prime, will
be called the pseudo-Fortunate number for N. For example, N=630 is
admissible since it is even and its distinct prime factors are the
consecutive primes 2,3,5 and 7. The next prime number after 631 is 641;
hence, the pseudo-Fortunate number for 630 is M=11. It can also be seen
that the pseudo-Fortunate number for 16 is 3. Find the sum of all
distinct pseudo-Fortunate numbers for admissible numbers N less than
109.