A051130 Indices of prime Bell numbers A000110.

2, 3, 7, 13, 42, 55, 2841

Offset: 1

Author

Ignacio Larrosa Cañestro

Keywords

• hard
• nonn
• nice

Comments

Bell(2841) has been certified to be a prime using Primo. This took 17 months on a P3-800, a P4-2400 and finally a P4-2800. There are no other terms below 6000. - Ignacio Larrosa Cañestro, Feb 13 2004

The next term, if it exists, is > 50000. - Vaclav Kotesovec, May 18 2021

No other terms < 100000. - Mathieu Gouttenoire, Oct 31 2021

Examples

			The Bell numbers Bell(2)=2, Bell(3)=5, Bell(7)=877 etc. are primes.
		

Links

• E. T. Bell, Exponential numbers, Amer. Math. Monthly, 41 (1934), 411-419.
• The Prime Database, 93074010508593618333...(6499 other digits)...83885253703080601131
• Eric Weisstein's World of Mathematics, Bell Number
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A000110, A051131.

Programs

Magma

[n: n in [0..1000]|IsPrime(Bell(n))]; // Vincenzo Librandi, Jan 30 2016

Mathematica

Reap[For[n = 1, n <= 3000, n++, If[PrimeQ[BellB[n]], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jun 05 2012 *)
Select[Range[2900],PrimeQ[BellB[#]]&] (* Harvey P. Dale, Nov 08 2012 *)