A134056 Least positive integer k such that (n!)! + k is prime.

1, 1, 7, 131, 131, 2897, 21997

Offset

1,3

Comments

The terms beyond a(3), found by PrimeForm, produce probable primes of lengths 24, 199, 1747 and 16474 digits. As both (8!)! and 2*((8!)!) each have the same number of digits, a(8) will correspond to a 168187-digit prime (by Bertrand's Postulate). For all n, if k > 1, then k >= nextprime(n!). As (8!)!+1 is composite, a(8) >= 40343.

Links

Table of n, a(n) for n=1..7.

Example

a(3) = 7 as (3!)! + 7 = 6! + 7 = 720 + 7 = 727 is the smallest prime larger than (3!)!.

Crossrefs

Sequence in context: A361369 A361367 A332050 * A123036 A142011 A074224

Adjacent sequences: A134053 A134054 A134055 * A134057 A134058 A134059

Keyword

hard,more,nonn

Author

Rick L. Shepherd, Oct 04 2007

Status

approved