Prime Sums of Exactly Three Distinct Factorials

[franktaw at netscape.net]

For *any* k > 1, the number of primes of the form n!+k is finite.  In 
particular, n!+k is divisible by k whenever n>=k.  More generally, when 
n >= any divisor of k > 1.

In this case, k = A! + 1.

In particular, 7!+1 = 5041 = 71^2, so 7! + n! + 1! cannot be prime for 
n >= 71.  Meaning Jonathan has probably found all of them.

Franklin T. Adams-Watters


-----Original Message-----
From: Jonathan Post <jvospost3 at gmail.com>
...
  It is the case in general, for fixed A distinct from B, that A! + B! + 
1! = prime has either no solutions, or several solutions after which 
all higher A gives the same common prime factor to A! + B! + 1!, and it 
is not clear under what circumstances "several" means infinite.
...
7! + n! + 1! is prime for n = {8, 12, 16, 23, 27, 33, 37, 42, 53, ?}.

...