login
Numbers k such that k! + prime(k) is prime.
7

%I #30 Sep 22 2024 15:21:04

%S 1,2,3,4,5,6,9,11,17,18,25,31,40,96,174,193,204,269,523,650,659,797,

%T 1437,1862,2515,4983,5557,11429

%N Numbers k such that k! + prime(k) is prime.

%C The numbers corresponding to 2515 and 4983 are probable primes. [_Farideh Firoozbakht_, Oct 15 2009]

%C a(28) > 10000. - _Giovanni Resta_, Mar 16 2014

%e n=5: 5! = 120 and prime(5) = 11, 120+11 = 131.

%e 6 is listed because 6!+prime(6) = 720+13 = 733 is prime.

%t Do[ If[ PrimeQ[ n! + Prime[ n ] ], Print[ n ] ], {n, 1, 700} ]

%t Select[Range[1000], PrimeQ[#! + Prime[#]] &] (* _Vincenzo Librandi_, Mar 05 2015 *)

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

%o (Magma) [n: n in [1..200] | IsPrime(Factorial(n)+ NthPrime(n))]; // _Vincenzo Librandi_, Mar 05 2015

%Y Cf. A063499 (Primes of form prime(n) + n!). [_Alexander R. Povolotsky_, Aug 13 2008]

%K nonn

%O 1,2

%A _Jason Earls_, Sep 24 2001

%E More terms from _Robert G. Wilson v_, Sep 28 2001

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

%E a(25)-a(26) from _Farideh Firoozbakht_, Oct 15 2009

%E a(27) from _Giovanni Resta_, Mar 16 2014

%E a(28) from _Michael S. Branicky_, Sep 22 2024