A384298 Primes p such that p + 4, p + 12 and p + 16 are also primes.

7, 67, 97, 487, 757, 1567, 1597, 2377, 3907, 7687, 8677, 12097, 12907, 13147, 14407, 14767, 15667, 16057, 19417, 21487, 31177, 38317, 43777, 52567, 57637, 58897, 65167, 65827, 67477, 67927, 74857, 81547, 90007, 90187, 93967, 94777, 95467, 95617, 102547, 111427, 112237, 114757, 123817, 129277

Offset: 1

Author

Alexander Yutkin, May 25 2025

Keywords

• nonn

Comments

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

Examples

			p=97: 97+4=101, 97+12=109, 97+16=113 —> prime quartet: (97, 101, 109, 113).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

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), [0,1,3,4]):
select(q, [7+30*i$i=0..4309])[];  # Alois P. Heinz, May 29 2025

Mathematica

Select[Prime[Range[12099]],AllTrue[#+{4,12,16},PrimeQ]&] (* James C. McMahon, May 29 2025 *)

Formula

a(n) == 7 (mod 30).