A364076 Numbers k such that (12^k - 1)^2 - 2 is prime.

3, 29, 51, 7824, 15456, 22614, 28312, 47014, 68835

Offset: 1

Author

Jeppe Stig Nielsen, Jul 03 2023

Keywords

• nonn
• hard
• more

Comments

Such primes are sometimes called Carol primes of base 12.

Links

• Prime-Wiki, Carol-Kynea prime.
• Eric Weisstein's World of Mathematics, Near-Square Prime.

Crossrefs

Cf. A091515 (b=2), A100901 (b=6), A100903 (b=10), A100905 (b=14), A364078 (b=18), A364080 (b=20), A100907 (b=22).

Cf. A364077

Programs

Mathematica

Select[Range[1500],PrimeQ[(12^#-1)^2-2]&] (* James C. McMahon, Jan 04 2024 *)

PARI

for(k=1,1200,ispseudoprime((12^k-1)^2-2)&&print1(k,", "))