A093437 -id:A093437 - cp's OEIS frontend

A093621 Smallest k>0 such that n!/k!+1 is prime.

1, 1, 1, 1, 2, 2, 4, 2, 2, 4, 3, 1, 5, 2, 3, 4, 2, 3, 5, 19, 10, 3, 5, 4, 5, 7, 5, 1, 6, 21, 2, 9, 15, 15, 13, 10, 27, 1, 4, 37, 14, 1, 4, 2, 34, 5, 8, 18, 24, 2, 13, 5, 11, 35, 48, 11, 7, 48, 27, 21, 30, 5, 43, 7, 4, 46, 13, 24, 16, 60, 12, 34, 5, 1, 38, 14, 28, 1, 10, 24, 50, 5, 3, 42, 40, 28

Offset: 0

Hugo Pfoertner, Apr 06 2004

nonn

The results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

			a(39) =37 because 39!/k!+1 is composite for all k=1..36; 39!/37!+1=39*38+1=1483 is prime.

Cf. A093437 largest prime of the form n!/k!+1, A002981 n!+1 is prime, A093623 Smallest k>0 such that n!/k!-1 is prime.

a(A002981(n)) = 1.

A093622 Largest prime of the form n!/k!-1.

Original entry on oeis.org

5, 23, 59, 719, 5039, 6719, 181439, 5039, 6652799, 479001599, 154439, 87178291199, 54486431999, 3487131647999, 59281238015999, 1067062284287999, 1013709170073599, 405483668029439999, 39070079, 180503769599

Offset: 3

Hugo Pfoertner, Apr 06 2004

nonn

			a(5) =59 because 5!/1!-1=119=7*17 is composite, whereas 5!/2!-1=59 is prime.

Dario Alpern, Factorization using the Elliptic Curve Method.

Cf. A093623 smallest k>0 such that n!/k!-1 is prime, A055490 primes of form n!-1, A093437 largest prime of the form n!/k!+1.

cp's OEIS Frontend

A093621 Smallest k>0 such that n!/k!+1 is prime.

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