A256811 Primes p such that (p^2+2)/3 and (p^4+2)/3 are prime.

37, 521, 881, 1619, 2053, 2213, 2341, 3527, 3637, 3727, 4157, 5147, 7019, 10009, 10891, 12277, 14741, 15913, 16273, 17747, 18757, 24499, 25307, 25577, 26209, 27073, 31481, 31517, 32833, 35083, 36739, 36791, 39079, 40231, 40949, 41039, 42013, 42461, 42767, 47917

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

a(1) = 37; (37^2 + 2)/3 = 457; (37^4 + 2)/3 = 624721; all three are prime.

Mathematica

Select[Prime[Range[10^4]], PrimeQ[(#^2 + 2)/3] && PrimeQ[(#^4 + 2)/3] &]

Prog

(PARI) forprime(p=1, 10^5, if(!((p^2+2)%3)&&!((p^4+2)%3)&&isprime((p^2+2)/3)&&isprime((p^4+2)/3), print1(p, ", "))) \\ Derek Orr, Apr 16 2015
(Magma) [p: p in PrimesUpTo(5*10^4) | IsPrime((p^2+2) div 3)  and IsPrime((p^4+2) div 3 )]; // Vincenzo Librandi, Apr 20 2015

Crossrefs

Cf. A241120, A253941, A253976, A253940.

Sequence in context: A197240 A220331 A142764 * A123035 A232033 A006303

Adjacent sequences: A256808 A256809 A256810 * A256812 A256813 A256814

Keyword

nonn,easy

Author

K. D. Bajpai, Apr 15 2015

Status

approved