A252042 Primes p such that 2*p^3 + 1 and 2*p^3 + 3 are also primes.

2, 29, 1709, 5849, 6857, 6959, 8999, 10139, 11909, 13127, 13877, 15077, 15749, 17657, 19457, 23357, 23399, 26729, 27407, 27479, 28349, 30047, 31907, 32957, 39569, 46559, 46589, 46817, 50417, 58757, 59219, 60737, 62207, 62687, 62819, 66947, 70589, 71237, 74699

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..11485

Example

a(2) = 29 is prime: 2*29^3 + 1 = 48779 and 2*29^3 + 3 = 48781 are both primes.
a(3) = 1709 is prime: 2*1709^3 + 1 = 9982887659 and 2*1709^3 + 3 = 9982887661 are both primes.

Mathematica

Select[Prime[Range[10000]], And[PrimeQ[2*#^3 + 1], PrimeQ[2*#^3 + 3]] &]
Select[Prime[Range[7500]], AllTrue[2#^3+{1, 3}, PrimeQ]&] (* Harvey P. Dale, Apr 03 2023 *)

Prog

(PARI)  s=[]; forprime(p=2, 10^5, if(isprime(2*p^3 + 1) && isprime(2*p^3 + 3), s=concat(s, p))); s

Crossrefs

Cf. A000040, A153507, A174363, A247101.

Sequence in context: A077282 A059725 A112784 * A295426 A055559 A350858

Adjacent sequences: A252039 A252040 A252041 * A252043 A252044 A252045

Keyword

nonn

Author

K. D. Bajpai, Dec 13 2014

Status

approved