A109993 Numbers n such that 65537 * 2^n - 1 is prime.

2, 14, 16, 18, 26, 30, 36, 42, 62, 132, 242, 294, 302, 666, 816, 824, 998, 1218, 1472, 2522, 3098, 4148, 6404, 8102, 25656, 26490, 56702, 76442

Offset

1,1

Comments

Note that 65537 = 2^16 + 1 is the largest known Fermat prime. All terms have been proved prime. Proof for the largest: PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 65537*2^76442-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 99.98% 65537*2^76442-1 is prime! (101.6260s+0.0044s)

No more terms up to 92000.

Links

Table of n, a(n) for n=1..28.

Mathematica

Select[Range[1, 1000], PrimeQ[65537*2^# - 1] &] (* Julien Kluge, Jul 08 2016 *)

Prog

(PARI) is(n)=ispseudoprime(65537*2^n-1) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A112245.

Sequence in context: A276553 A032933 A194230 * A075041 A105453 A199368

Adjacent sequences: A109990 A109991 A109992 * A109994 A109995 A109996

Keyword

more,nonn

Author

Jason Earls, Sep 01 2005

Status

approved