A263174 Primes p such that p^2 +- 12 and p^3 +- 12 are also primes.

5, 75641, 249199, 294001, 378779, 438479, 535229, 897349, 918989, 933199, 1271069, 1393771, 1403569, 2270669, 2523991, 2752219, 3427751, 3966761, 4348489, 4496941, 4621619, 4731929, 4851719, 5721281, 7518869, 7606801, 8413411, 8649881, 8757691, 9068659, 9586999

Offset

1,1

Comments

Intersection of A153116 and A153322.

Links

Table of n, a(n) for n=1..31.

Example

a(1) = 5 (prime): 5^2 + 12 = 37; 5^2 - 12 = 13; 5^3 + 12 = 137; 5^3 - 12 = 113; are all prime.
a(2) = 75641(prime): 75641^2 + 12 = 5721560893; 75641^2 - 12 = 5721560869; 75641^3 + 12 = 432784586599733; 75641^3 - 12 = 432784586599709; are all prime.

Maple

select(p -> andmap(isprime, [p, p^2+12, p^2-12, p^3+12, p^3-12]), [seq(p, p=1.. 10^6)]);

Mathematica

k = 12; Select[Prime[Range[10^6]], PrimeQ[#^2 + k] && PrimeQ[#^2 - k] && PrimeQ[#^3 + k] && PrimeQ[#^3 - k] &]

Prog

(PARI) forprime(p = 1, 1000000, if(isprime(p^2+12) && isprime(p^2-12) && isprime(p^3+12) && isprime(p^3-12), print1(p, ", ")));
(Magma) [p: p in PrimesUpTo(1000000) | IsPrime(p^2+12) and IsPrime(p^2-12) IsPrime(p^3+12) and IsPrime(p^3-12)];

Crossrefs

Cf. A153116, A153322.

Sequence in context: A050816 A171981 A145232 * A123591 A133381 A366270

Adjacent sequences: A263171 A263172 A263173 * A263175 A263176 A263177

Keyword

nonn,less

Author

K. D. Bajpai, Oct 11 2015

Status

approved