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.
伪幸运数
如果正偶数N是2的幂，或者其所有不同的质因数恰好是连续质数，就被称为是可接受的。
前十二个可接受数是2、4、6、8、12、16、18、24、30、32、36、48。
如果N是可接受数，使得N+M为质数的最小整数M > 1就被称为N的伪幸运数。
例如，N=630是可接受数，因为它是偶数，而且它所有不同的质因数为连续质数2、3、5、7。
在631之后的下一个素数是641；因此，630的伪幸运数是M=11。
同样可以看出，16的伪幸运数是3。
找出所有小于109的可接受数N，分别求出其伪幸运数，并求所有不同的伪幸运数的和。