Primes having numbers with 4 and 2 prime factors (counting multiplicity) before and after them.

37, 61, 157, 277, 733, 877, 997, 1213, 1237, 2797, 3253, 3517, 3733, 6037, 7213, 7933, 9013, 9133, 9277, 10357, 12157, 12757, 13093, 16333, 16573, 17077, 18133, 18637, 23173, 23677, 23917, 25933, 26437, 27997, 30517, 32533, 33037, 33493, 34213, 37957, 40693

1

There are probably an infinite number of these primes. All these primes are of the form 6k+1; more specifically 24k+13.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

MathOverflow, Are there infinitely many primes p such that both p-1 and p+1 have at most 3 prime factors, counted with multiplicity?

(Mma) Select[Prime[Range[2, 1000000]], Plus @@ Transpose[FactorInteger[# - 1]][[2]] == 4 && Plus @@ Transpose[FactorInteger[# + 1]][[2]] == 2 &, 100]

Cf. A079153, A106639, S000328-S000330.

nonn

T. D. Noe, Nov 12 2014