A383396 Primes p such that p + 6, p + 10, p + 12, p + 16 and p + 22 are also primes.

7, 31, 2677, 35521, 42451, 44257, 55807, 93481, 118891, 198817, 221707, 234181, 313981, 393571, 560227, 669847, 1107781, 1210387, 1596367, 1616611, 1738411, 2710921, 3194551, 3377587, 3441931, 3484561, 3586537, 3699181, 3887551, 3904897, 4095661, 4192261, 4239721

Offset: 1

Author

Alexander Yutkin, Apr 25 2025

Keywords

• nonn

Comments

Initial members of prime sextuples that correspond to the difference pattern [6, 4, 2, 4, 6].

Examples

			p = 2677: 2677 + 6 = 2683, 2677 + 10 = 2687, 2677 + 12 = 2689, 2677 + 16 = 2693, 2677 + 22 = 2699 -> prime sextuple: (2677, 2683, 2687, 2689, 2693, 2699).
		

Crossrefs

Cf. A000040, A001223.

Cf. A052378 [4, 2, 4], A022008 [4, 2, 4, 2, 4].

Programs

Mathematica

Select[Prime[Range[298900]], AllTrue[#+{6,10,12,16,22}, PrimeQ]&] (* James C. McMahon, May 02 2025 *)

Formula

a(n) == 1 (mod 6).