A384299 Primes p such that p + 8, p + 12 and p + 20 are also primes.

11, 59, 89, 389, 479, 1439, 1559, 1601, 2531, 2699, 3209, 3449, 3911, 5639, 5849, 7529, 8081, 8669, 10091, 12269, 12401, 12899, 13151, 14411, 14759, 17021, 19421, 21011, 21851, 22271, 23189, 25931, 26099, 28649, 28859, 31139, 31469, 33191, 33569, 36551, 39659, 40751, 42689, 43391, 43781, 44111

Offset: 1

Author

Alexander Yutkin, May 25 2025

Keywords

• nonn

Comments

Initial members of prime quartets that correspond to the difference pattern [8, 4, 8].

Examples

			p=89: 89+8=97, 89+12=101, 89+20=109 —> prime quartet: (89, 97, 101, 109).
		

Crossrefs

Cf. A000040, A001223.

Cf. A136162 [2, 4, 2], A052378 [4, 2, 4], A382810 [6, 4, 6].

Programs

Maple

q:= n-> andmap(i-> isprime(n+4*i), [0,2,3,5]):
select(q, [5+6*i$i=1..7351])[];  # Alois P. Heinz, May 29 2025

Mathematica

Select[Prime[Range[4591]],AllTrue[#+{8,12,20},PrimeQ]&] (* James C. McMahon, May 29 2025 *)