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%I #15 Jun 24 2018 19:56:11
%S 1,2,5,4,1,9,6,1,0,1,5,7,8,0,1,1,9,3,6,2,7,7,6,7,9,5,5,4,9,1,4,2,1,3,
%T 4,2,3,7,7,9,8,6,9,2,1,8,0,4,2,6,2,2,1,9,5,8,3,2,7,2,2,5,5,4,6,0,8,8,
%U 6,4,6,9,9,4,2,8,7,5,1,4,4,7,5,1,3,2,3
%N Decimal expansion of constant C such that floor(p# * C) is always a prime number (for p >= 2), where p# is the primorial function, i.e., the product of prime numbers up to and including p.
%C This constant is similar to Mills's constant (where floor(x^(3^n)) is always prime). I've calculated it all by myself and I never heard of it before. I can't even prove that it exists, but after my calculations, it is most likely. It definitely starts with these 43 decimal digits. Does anybody know if anyone calculated this before?
%C There should be infinitely many constants such that floor(p# * C) is always prime, but the range in which these numbers appear is extremely narrow and every such constant would start with these 74 decimal digits.
%e If the constant 1.2541961... is continuously multiplied by the prime numbers 2, 3, 5, 7, 11 ..., then floor(x) is always prime (i.e., 2, 7, 37, 263, 2897, ...).
%K nonn,cons
%O 1,2
%A _Martin Raab_, Mar 24 2006; extended Apr 22 2006 and again Jun 28 2007
%E a(76)-a(87) from _Jon E. Schoenfield_, Jul 23 2017
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