A073828 Primes of the form 1 + 0!*1!*2!*...*n! (subsequence of A019515).

2, 2, 3, 13, 125411328001, 69113789582492712943486800506462734562847413501952000000000000001

Offset: 1

Author

Rick L. Shepherd, Aug 16 2002

Keywords

• nonn

Comments

a(4) = 125411328001 and the 65-digit a(5) have been certified prime with Primo. Any additional terms are too big to include here. a(3) = 13 and a(4) have twin primes, 11 and 125411327999 (also certified prime with Primo). No other primes of the form 0!*1!*2!*...*n! - 1 exist for n < 108.

Examples

			a(0) = 1 + 0! (0=A073827(0)) = 1 + 1 = 2. a(1) = 1 + 0!*1! (1=A073827(1)) = 1 + 1*1 = 2. a(4) = 1 + 0!*1!*2!*3!*4!*5!*6!*7! (7=A073827(4)) = 1 + 1*1*2*6*24*120*720*5040 = 125411328001
		

References

• Ryser, H. J. Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., p. 53, 1963.

Links

• M. Fleuren, Smarandache Factorial Products.

Crossrefs

Cf. A073827 (corresponding n), A000178 (superfactorials), A019515 (supersequence: superfactorials + 1), A000142 (factorials).

Programs

PARI

pr=1; for(n=0,115, pr=pr*n!; if(isprime(pr+1), print1(pr+1,",")))

Formula

a(k) = 1 + 0!*1!*2!*...*A073827(k)!.