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A134056 Least positive integer k such that (n!)! + k is prime. 0
1, 1, 7, 131, 131, 2897, 21997 (list; graph; refs; listen; history; internal format)
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.

EXAMPLE

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

CROSSREFS

Sequence in context: A002614 A187237 A095885 * A123036 A142011 A074224

Adjacent sequences:  A134053 A134054 A134055 * A134057 A134058 A134059

KEYWORD

hard,more,nonn

AUTHOR

Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 04 2007

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Last modified February 15 14:33 EST 2012. Contains 205817 sequences.