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A139075 Primes p arising in A139074.

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%I A139075 #17 Jun 29 2025 22:17:26
%S A139075 3,2,3,31,1009,2,5702401,631
%N A139075 Primes p arising in A139074.
%C A139075 a(23) = (23+1579!)/23. - _Andrew V. Sutherland_, Apr 11 2008.
%C A139075 Smallest mother factorial prime p of order n, i.e. smallest prime of the form (p!+n)/n where p is prime.
%C A139075 For smallest daughter factorial prime p of order n see A139074.
%C A139075 For smallest father factorial prime p of order n see A139207.
%C A139075 For smallest son factorial prime p of order n see A139206.
%C A139075 a(9)=26737!/9+1 is a 106758 digit (probable) prime.  Easily calculated but too large to enter here a(10)=13, a(11)=566092801, a(12)=11. [Robert Price, Jan 19 2011]
%t A139075 a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! + n)/n], k++ ]; AppendTo[a, Prime[(Prime[k]! + n)/n]], {n, 1, 8}]; a
%Y A139075 Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A136019, A136020, A136026, A136027.
%K A139075 nonn
%O A139075 1,1
%A A139075 _Artur Jasinski_, Apr 08 2008, Apr 21 2008