A174363 Primes p such that 2*p^3 -+ 3 are also prime.

2, 13, 1223, 2357, 4013, 4027, 4507, 5903, 8713, 9623, 10663, 11717, 12757, 12983, 13883, 15877, 16103, 16787, 16823, 16883, 18097, 22697, 23357, 24677, 26107, 27953, 28603, 30313, 31327, 34147, 35617, 35933, 41183, 44893, 46687, 46817, 48247, 50417, 52963, 54083

Offset: 1

Author

Vincenzo Librandi, Mar 17 2010

Keywords

• nonn

Comments

Intersection of A153507 and A243630. - Felix Fröhlich, Nov 27 2019

Examples

			For p=2, 2*2^3 -+ 3 = (13, 19), both prime, so 2 is a term of the sequence.
For p=13, 2*13^3 -+ 3 = (4391, 4397), both prime, so 13 is a term of the sequence.
		

Links

• Harvey P. Dale and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A153507, A243630.

Programs

Magma

[p: p in PrimesUpTo(100000)|IsPrime(2*p^3-3) and IsPrime(2*p^3+3)]

Maple

select(p -> andmap(isprime, [p, 2*p^3+3, 2*p^3-3]), [seq(p, p=1.. 10^5)]); # K. D. Bajpai, Nov 28 2019

Mathematica

Select[Prime[Range[5000]],And@@PrimeQ[2 #^3+{3,-3}]&] (* Harvey P. Dale, Jan 25 2013 *)

PARI

forprime(p=1, 55000, if(ispseudoprime(2*p^3-3) && ispseudoprime(2*p^3+3), print1(p, ", "))) \\ Felix Fröhlich, Nov 27 2019