A108240 Numbers k such that (10^k)^2 + 5*(10^k) - 1 is prime.

0, 1, 2, 7, 45, 54, 60, 99, 195, 271, 476, 1491, 2713, 8155

Offset: 1

Author

Jason Earls, Jun 17 2005

Keywords

• more
• nonn

Comments

All of the primes for the terms <= 2713 have been certified. Primality proof for the largest: PFGW Version 20041001.Win_Stable (v1.2 RC1b) [FFT v23.8] Primality testing (10^2713)^2+5*(10^2713)-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 34.96% (10^2713)^2+5*(10^2713)-1 is prime! (216.4510s+10.6592s)

Crossrefs

Cf. A108195.

Programs

PARI

is(n)=ispseudoprime((10^n)^2+5*(10^n)-1) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(14) from Michael S. Branicky, Mar 27 2023