A064278 Numbers k such that k! + prime(k) is prime.

1, 2, 3, 4, 5, 6, 9, 11, 17, 18, 25, 31, 40, 96, 174, 193, 204, 269, 523, 650, 659, 797, 1437, 1862, 2515, 4983, 5557, 11429

Offset: 1

Author

Jason Earls, Sep 24 2001

Keywords

• nonn

Comments

The numbers corresponding to 2515 and 4983 are probable primes. [Farideh Firoozbakht, Oct 15 2009]

a(28) > 10000. - Giovanni Resta, Mar 16 2014

Examples

			n=5: 5! = 120 and prime(5) = 11, 120+11 = 131.
6 is listed because 6!+prime(6) = 720+13 = 733 is prime.
		

Crossrefs

Cf. A063499 (Primes of form prime(n) + n!). [Alexander R. Povolotsky, Aug 13 2008]

Programs

Magma

[n: n in [1..200] | IsPrime(Factorial(n)+ NthPrime(n))]; // Vincenzo Librandi, Mar 05 2015

Mathematica

Do[ If[ PrimeQ[ n! + Prime[ n ] ], Print[ n ] ], {n, 1, 700} ]
Select[Range[1000], PrimeQ[#! + Prime[#]] &] (* Vincenzo Librandi, Mar 05 2015 *)

PARI

for(n=1, 100, if (isprime(n!+prime(n)), print1(n, ", ")))

Extensions

More terms from Robert G. Wilson v, Sep 28 2001

More terms from John Sillcox (JMS21187(AT)aol.com), Apr 05 2003

a(25)-a(26) from Farideh Firoozbakht, Oct 15 2009

a(27) from Giovanni Resta, Mar 16 2014

a(28) from Michael S. Branicky, Sep 22 2024