A076680 Numbers k such that 4*k! + 1 is prime.

0, 1, 4, 7, 8, 9, 13, 16, 28, 54, 86, 129, 190, 351, 466, 697, 938, 1510, 2748, 2878, 3396, 4057, 4384, 5534, 7069, 10364

Offset: 1

Author

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

Keywords

• nonn
• more

Comments

a(25) > 6311. - Jinyuan Wang, Feb 06 2020

Examples

			k = 7 is a term because 4*7! + 1 = 20161 is prime.
		

Links

• Factor Database, Factors of the numbers 4z!+1

Crossrefs

Cf. m*n!-1 is a prime: A076133, A076134, A099350, A099351, A180627-A180631.

Cf. m*n!+1 is a prime: A051915, A076679-A076683, A178488, A180626, A126896.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205.

Cf. n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.

Programs

Mathematica

Select[Range[5000],PrimeQ[4#!+1]&] (* Harvey P. Dale, Mar 23 2011 *)

PARI

is(k) = ispseudoprime(4*k!+1); \\ Jinyuan Wang, Feb 06 2020

Extensions

Corrected (added missed terms 2748, 2878) by Serge Batalov, Feb 24 2015

a(24) from Jinyuan Wang, Feb 06 2020

a(25)-a(26) from Michael S. Branicky, Jul 04 2024