Definition
A Fortunate number is the smallest integer m > 1 such that for a given positive integer n, primorial(n) + m is a prime number, where primorial(n) is the product of the first n prime numbers.

For example the first fortunate number is 3 because primorial(1) is 2 and 2 + 3 = 5 which is prime whereas 2 + 2 = 4 is composite.



Task
After sorting and removal of any duplicates, compute and show on this page the first 8 Fortunate numbers or, if your language supports big integers, the first 50 Fortunate numbers.



Related task
 Primorial numbers


See also
 oeis:A005235 Fortunate numbers 
 oeis:A046066 Fortunate numbers, sorted with duplicates removed


ClearAll[primorials]
primorials[n_] := Times @@ Prime[Range[n]]
vals = Table[
   primor = primorials[i];
   s = NextPrime[primor];
   t = NextPrime[s];
   Min[DeleteCases[{s - primor, t - primor}, 1]]
   ,
   {i, 100}
   ];
TakeSmallest[DeleteDuplicates[vals], 50]