A384526 Primes p such that p + 6, p + 14 and p + 20 are also primes.

17, 23, 47, 53, 83, 257, 263, 353, 443, 557, 587, 593, 977, 1103, 1217, 1277, 1283, 1433, 1607, 1973, 1997, 2267, 2657, 2693, 2837, 3527, 3617, 4007, 4637, 4643, 4937, 5393, 5807, 6197, 6257, 6323, 6353, 6977, 8693, 10253, 10847, 10973, 11483, 11807, 12143, 12497, 12953, 13613, 14537

Offset: 1

Author

Alexander Yutkin, Jun 01 2025

Keywords

• nonn

Comments

Initial members of prime quartets that correspond to the difference pattern [6, 8, 6].

Examples

			p=47: 47+6=53, 47+14=61, 47+20=67 —> prime quartet: (47, 53, 61, 67).
		

Crossrefs

Cf. A000040, A001223.

Cf. A140565 [6, 2, 6], A382810 [6, 4, 6].

Programs

Maple

select(p -> andmap(isprime,[p, p + 6, p + 14, p + 20]), [seq(i,i=5 .. 20000, 6)]); # Robert Israel, Jun 01 2025

Mathematica

Select[Prime[Range[1700]], PrimeQ[#+6]&&PrimeQ[#+14]&&PrimeQ[#+20] &] (* Stefano Spezia, Jun 01 2025 *)

Formula

a(n) == 5 (mod 6). - Hugo Pfoertner, Jun 01 2025