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A067365 a(n) = p-n!^5, where p is the smallest prime > n!^5+1.

%I A067365 #15 Dec 09 2016 11:36:22
%S A067365 2,5,13,13,7,7,11,71,23,19,197,17,101,53,17,47,73,97,53,433,251,251,
%T A067365 47,263,281,353,53,61,179,41,53,401,449,79,89,1283,367,2011,139,227,
%U A067365 1597,1657,1123,397,131,727,137,167,89,379,421,653,223,373,2221,1447
%N A067365 a(n) = p-n!^5, where p is the smallest prime > n!^5+1.
%C A067365 The first 60 terms are primes. Are all terms prime? For n!^i, with 0<i<6, it looks like the terms are prime, too (see references). But for n!^6: a(28)=1189=29*41.
%C A067365 The first 1592 terms are primes. - _Dana Jacobsen_, May 13 2015
%H A067365 Dana Jacobsen, <a href="/A067365/b067365.txt">Table of n, a(n) for n = 1..1592</a>
%H A067365 Cyril Banderier, <a href="http://algo.inria.fr/banderier/Computations/prime_factorial.html">Fortunate Numbers</a>
%t A067365 a[n_] := For[i=2, True, i++, If[PrimeQ[n!^5+i], Return[i]]]
%t A067365 spf[n_]:=Module[{c=(n!)^5},NextPrime[c+1]-c]; Array[spf,60] (* _Harvey P. Dale_, Feb 24 2015 *)
%o A067365 (MuPAD) for n from 1 to 50 do f := n!^5:a := nextprime(f+2)-f:print(a) end_for
%o A067365 (PARI) for(n=1, 100, f=n!^5; print1(nextprime(f+2)-f, ", ")) \\ _Dana Jacobsen_, May 13 2015
%o A067365 (Perl) use ntheory ":all"; use Math::GMP qw/:constant/; for my $n (1..500) { my $f=factorial($n)**5; say "$n ", next_prime($f+1)-$f; } # _Dana Jacobsen_, May 13 2015
%Y A067365 Cf. A037153, A037153, A005235, A067362, A067363, A067364.
%K A067365 nonn
%O A067365 1,1
%A A067365 Frank Buss (fb(AT)frank-buss.de), Jan 19 2002
%E A067365 Edited by _Dean Hickerson_, Mar 02 2002