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]