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A109993 Numbers n such that 65537 * 2^n - 1 is prime. 0

%I

%S 2,14,16,18,26,30,36,42,62,132,242,294,302,666,816,824,998,1218,1472,

%T 2522,3098,4148,6404,8102,25656,26490,56702,76442

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

%C 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)

%C No more terms up to 92000.

%t Select[Range[1, 1000], PrimeQ[65537*2^# - 1] &] (* _Julien Kluge_, Jul 08 2016 *)

%o (PARI) is(n)=ispseudoprime(65537*2^n-1) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A112245.

%K more,nonn

%O 1,1

%A _Jason Earls_, Sep 01 2005

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Last modified September 28 06:57 EDT 2021. Contains 347703 sequences. (Running on oeis4.)