A386724 Twin primes p such that 6p+1, 6p-1 is a twin prime pair.

3, 5, 7, 17, 103, 107, 137, 283, 313, 347, 1033, 2027, 3257, 3673, 4217, 4547, 5023, 9433, 9767, 11833, 14593, 15137, 15733, 18253, 19423, 20717, 20983, 23537, 25847, 26113, 28753, 32057, 32323, 33073, 35053, 37307, 38327, 39163, 43607, 44623, 46183, 46273, 47743, 48407

Offset: 1

Author

Marc Morgenegg, Jul 31 2025

Keywords

• nonn

Comments

{3,5} and {5,7} are the only twin prime pairs occurring in this since (6p-1)*(6p+1)*(6p+11)*(6p+13) is always divisible by 5. Therefore the smallest possible gaps for p>7 is 4 (cousin primes).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002822, A001359, A014574, A176131 (subsequence), A182481, A294731. Subset of A060212.

Programs

Maple

q:= p-> isprime(p) and ormap(isprime, [p-2, p+2]) and andmap(isprime, [6*p-1, 6*p+1]):
select(q, [2*i+1$i=1..25000])[];  # Alois P. Heinz, Jul 31 2025

Mathematica

Select[Prime[Range[5000]], Or @@ PrimeQ[# + {-2, 2}] && And @@ PrimeQ[6*# + {-1, 1}] &] (* Amiram Eldar, Jul 31 2025 *)

Extensions

More terms from Pontus von Brömssen, Jul 31 2025