A384527 Primes p such that p + 6, p + 12, p + 14, p + 20 and p + 26 are also primes.

17, 47, 257, 587, 1277, 4637, 14537, 19457, 71327, 101267, 113147, 115757, 150197, 179807, 191447, 193367, 267887, 302567, 344237, 408197, 416387, 442817, 482387, 536267, 566537, 652727, 886967, 1043747, 1268777, 1300127, 1373147, 1464257, 1589657, 1616597, 1988237

Offset: 1

Author

Alexander Yutkin, Jun 01 2025

Keywords

• nonn

Comments

Initial members of prime sextuples that correspond to the difference pattern [6, 6, 2, 6, 6].

Examples

			p=257: 257+6=263, 257+12=269, 257+14=271, 257+20=277, 257+26=283 —> prime sextuple: (257, 263, 269, 271, 277, 283).
		

Crossrefs

Cf. A000040, A001223.

Cf. A023241 [6, 6], A140565 [6, 2, 6].

Programs

Mathematica

Select[Prime[Range[150000]],PrimeQ[#+6]&&PrimeQ[#+12]&&PrimeQ[#+14]&&PrimeQ[#+20]&&PrimeQ[#+26] &] (* Stefano Spezia, Jun 01 2025 *)

Formula

a(n) == 17 (mod 30). - Hugo Pfoertner, Jun 01 2025