A103319 -id:A103319 - cp's OEIS frontend

A139159 a(n) = prime(n)! + 1.

3, 7, 121, 5041, 39916801, 6227020801, 355687428096001, 121645100408832001, 25852016738884976640001, 8841761993739701954543616000001, 8222838654177922817725562880000001, 13763753091226345046315979581580902400000001, 33452526613163807108170062053440751665152000000001

Offset: 1

Artur Jasinski, Apr 11 2008

Cf. A039716.
Cf. A093804, A103319.
Cf. A139160, A139161, A139162, A139163, A139164, A139165, A139166, A139089, A139168.

Prime[Range[12]]!+1 (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

a(n)=prime(n)!+1 \\ Charles R Greathouse IV, Apr 29 2015

a(n) = A039716(n) + 1. - Michel Marcus, Nov 08 2013

More terms from Michel Marcus, Aug 10 2025

A093804 Primes p such that p! + 1 is also prime.

Original entry on oeis.org

2, 3, 11, 37, 41, 73, 26951, 110059, 150209

Offset: 1

Jason Earls, May 19 2004

Or, numbers n such that Sum_{d|n} d! is prime.
The prime 26951 from A002981 (n!+1 is prime) is a member since Sum_{d|n} d! = n!+1 if n is prime. - Jonathan Sondow, Jan 30 2005
a(n) are the primes in A002981[n] = {0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951, ...} Numbers n such that n! + 1 is prime. Corresponding primes of the form p! + 1 are listed in A103319[n] = {3, 7, 39916801, 13763753091226345046315979581580902400000001, 33452526613163807108170062053440751665152000000001, ...}. - Alexander Adamchuk, Sep 23 2006

			Sum_{d|3} d! = 1! + 3! = 7 is prime, so 3 is a member.

Chris K. Caldwell, The List of Largest Known Primes, 110059! + 1
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv:1202.3670 [math.HO], 2012. - From N. J. A. Sloane, Jun 13 2012
Apoloniusz Tyszka, A common approach to the problem of the infinitude of twin primes, primes of the form n! + 1, and primes of the form n! - 1, 2018.
Apoloniusz Tyszka, A new approach to solving number theoretic problems, 2018.

Cf. A062363, A002981, A038507, A088332, A103317, A103319.

seq(`if`(isprime(ithprime(n)!+1), ithprime(n), NULL),n=1..25); # Nathaniel Johnston, Jun 28 2011

Select[Prime[Range[5! ]],PrimeQ[ #!+1]&] (* Vladimir Joseph Stephan Orlovsky, Nov 17 2009 *)

isok(n) = ispseudoprime(n) && ispseudoprime(n!+1); \\ Jinyuan Wang, Jan 20 2020

One more term from Alexander Adamchuk, Sep 23 2006
a(8)=110059 (found on Jun 11 2011, by PrimeGrid), added by Arkadiusz Wesolowski, Jun 28 2011
a(9)=150209 (found on Jun 09 2012, by Rene Dohmen), added by Jinyuan Wang, Jan 20 2020

A163081 Primes of the form p$ + 1 where p is prime, where '$' denotes the swinging factorial (A056040).

Original entry on oeis.org

3, 7, 31, 4808643121, 483701705079089804581, 3283733939424401442167506310317720418331001

Offset: 1

Peter Luschny, Jul 21 2009

nonn

The values of p are 2, 3, 5, 31, 67, 139 which is A163079. Subsequence of A163075 (primes of the form k$ + 1).

			3 and 3$ + 1 = 7 are prime, so 7 is a member.

Jinyuan Wang, Table of n, a(n) for n = 1..7
Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
Peter Luschny, Swinging Primes.

Cf. A056040, A103319, A163074-A163083.

a := proc(n) select(isprime,[$2..n]); select(isprime, map(x -> A056040(x)+1,%)) end:

cp's OEIS Frontend

A139159 a(n) = prime(n)! + 1.

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A093804 Primes p such that p! + 1 is also prime.

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Author

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Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

A163081 Primes of the form p$ + 1 where p is prime, where '$' denotes the swinging factorial (A056040).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple