Primes having numbers with a total of 6 prime factors (counting multiplicity) before or after them.
19, 23, 29, 37, 43, 59, 61, 67, 83, 157, 173, 227, 277, 283, 317, 347, 563, 653, 733, 787, 877, 907, 997, 1213, 1237, 1283, 1307, 1523, 1867, 2083, 2693, 2797, 2803, 3253, 3413, 3517, 3643, 3677, 3733, 3803, 4253, 4363, 4547, 4723, 5387, 5443, 5483, 5717
1
There are probably an infinite number of these primes.
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]] + Plus @@ Transpose[FactorInteger[# + 1]][[2]] == 6 &, 100]
Cf. A079153, A106639, S000327-S000329.
nonn
T. D. Noe, Nov 12 2014