A382810 Primes p such that p + 6, p + 10 and p + 16 are also primes.

7, 13, 31, 37, 73, 97, 157, 223, 373, 433, 1087, 1291, 1423, 1483, 1543, 1861, 1987, 2341, 2383, 2677, 2683, 3313, 3607, 4441, 4507, 4783, 4993, 5641, 5851, 6037, 6961, 7237, 7867, 8731, 9613, 9733, 10723, 13093, 13681, 14143, 14731, 16057, 16411, 16921, 17377

Offset: 1

Author

Alexander Yutkin, Apr 05 2025

Keywords

• nonn

Comments

The four primes need not be consecutive; otherwise we have the sequence A078856.

Examples

			p=37: 37+6=43, 37+10=47, 37+16=53 -> prime quartet: (37, 43, 47, 53).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A000040, A001223, A023200, A031924.

Cf. A078852 [4, 6, 6], A078856 [6, 4, 6], A078858 [6, 6, 4], A033451 [6, 6, 6].

Programs

Maple

q:= p-> andmap(i->isprime(p+i), [0, 6, 10, 16]):
select(q, [$2..20000])[];  # Alois P. Heinz, Apr 05 2025

Mathematica

Select[Prime[Range[2000]],AllTrue[#+{6,10,16},PrimeQ]&] (* James C. McMahon, Apr 13 2025 *)