data/problems/293.yml
---
:id: 293
:name: Pseudo-Fortunate Numbers
:url: https://projecteuler.net/problem=293
:content: "An even positive integer N will be called admissible, if it is a power
of 2 or its distinct prime factors are consecutive primes. \nThe first twelve admissible
numbers are 2,4,6,8,12,16,18,24,30,32,36,48.\n\nIf N is admissible, the smallest
integer M \\> 1 such that N+M is prime, will be called the pseudo-Fortunate number
for N.\n\nFor example, N=630 is admissible since it is even and its distinct prime
factors are the consecutive primes 2,3,5 and 7. \n The next prime number after
631 is 641; hence, the pseudo-Fortunate number for 630 is M=11. \nIt can also be
seen that the pseudo-Fortunate number for 16 is 3.\n\nFind the sum of all distinct
pseudo-Fortunate numbers for admissible numbers N less than 10<sup>9</sup>.\n\n"