A396453 Primes p such that p^2 - 2 is a prime and p^2 + 2 is a semiprime.

2, 7, 29, 37, 43, 191, 233, 359, 541, 677, 719, 863, 881, 1223, 1297, 1307, 1429, 1447, 1549, 1619, 1783, 1997, 2053, 2239, 2287, 2297, 2393, 2707, 2729, 3089, 3221, 3527, 3709, 3943, 4229, 4349, 4723, 5857, 7127, 7229, 7237, 7247, 8741, 9403, 9511, 9521, 9533, 9907, 10009, 11681, 11783, 12347

Offset

1,1

Comments

2, and primes p such that p^2 - 2 and (p^2 + 2)/3 are primes.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 29 is a term because 29 is a prime, 29^2 - 2 = 839 is a prime, and 29^2 + 2 = 3 * 281 where 3 and 281 are primes.

Maple

filter:= t -> isprime(t) and isprime((t^2+2)/3):
filter(2):= true:
select(filter, [2, seq(op([6*i+1, 6*i+5]), i=1..1000)]);

Crossrefs

Intersection of A062326 and A109953.

Sequence in context: A059803 A076043 A180448 * A116968 A162172 A274682

Adjacent sequences: A396450 A396451 A396452 * A396454 A396455 A396456

Keyword

nonn

Author

Robert Israel, May 26 2026

Status

approved