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

Author

K. D. Bajpai, Apr 15 2015

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A241120, A253941, A253976, A253940.

Programs

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

Mathematica

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

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