A362056 Prime numbers of the form prime(k)! - prime(k!).

3, 107, 4951, 39916141, 355687428046967

Offset: 1

Author

Michael S. Branicky, Apr 06 2023

Keywords

• nonn
• hard
• more

Comments

No other terms < prime(22)! - prime(22!) (using A062439).

Problem suggested by Carlos Rivera as a follow-on to Puzzle 1127 (see links).

Examples

			prime(2)! - prime(2!) = 3 is prime.
prime(3)! - prime(3!) = 107 is prime.
prime(4)! - prime(4!) = 4951 is prime.
prime(5)! - prime(5!) = 39916141 is prime.
prime(7)! - prime(7!) = 355687428046967 is prime.
		

Links

• Carlos Rivera, Puzzle 1127. Prime(11!)+Prime(11)!, The Prime Puzzles and Problems Connection.
• Carlos Rivera, Puzzle 1128. Prime(n)!-Prime(n!), The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A000040, A000142, A062439.

Prime terms in A261997.

Formula

A261997(k) = A000142(A000040(k)) - A000040(A000142(k)) is in A000040.