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%I #9 Dec 15 2017 17:36:51
%S 0,1,2,11,17,25,38,53,107,245,255,367,719,1077,2189,2853,3236,3511,
%T 3633,4531,4858,5422
%N Numbers n such that (n!/n#) * 2^n + 1 is prime, where n# = primorial numbers (A034386).
%C n!/n# is known as n compositorial. All values have been proved prime. No more terms up to 6100. Primality proof for the largest, which has 17219 digits: PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (5422!/5422#)*(2^5422)+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2719 Calling Brillhart-Lehmer-Selfridge with factored part 36.34% (5422!/5422#)*(2^5422)+1 is prime! (66.5095s+0.0129s)
%t f[n_] := n!/Fold[Times, 1, Prime[ Range[ PrimePi[ n]]]]*2^n + 1; Do[ If[ PrimeQ[ f[n]], Print[n]], {n, 0, 1100}] (* _Robert G. Wilson v_, Jul 18 2005 *)
%Y Cf. A049420, A091421.
%K more,nonn
%O 1,3
%A _Jason Earls_, Jul 15 2005
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