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%I #46 Feb 17 2022 00:35:47
%S 2,3,7,13,42,55,2841
%N Indices of prime Bell numbers A000110.
%C 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
%C The next term, if it exists, is > 50000. - _Vaclav Kotesovec_, May 18 2021
%C No other terms < 100000. - _Mathieu Gouttenoire_, Oct 31 2021
%H E. T. Bell, <a href="http://www.jstor.org/stable/2300300">Exponential numbers</a>, Amer. Math. Monthly, 41 (1934), 411-419.
%H The Prime Database, <a href="https://primes.utm.edu/primes/page.php?id=68825">93074010508593618333...(6499 other digits)...83885253703080601131</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BellNumber.html">Bell Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%e The Bell numbers Bell(2)=2, Bell(3)=5, Bell(7)=877 etc. are primes.
%t Reap[For[n = 1, n <= 3000, n++, If[PrimeQ[BellB[n]], Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Jun 05 2012 *)
%t Select[Range[2900],PrimeQ[BellB[#]]&] (* _Harvey P. Dale_, Nov 08 2012 *)
%o (Magma) [n: n in [0..1000]|IsPrime(Bell(n))]; // _Vincenzo Librandi_, Jan 30 2016
%Y Cf. A000110, A051131.
%K hard,nonn,nice
%O 1,1
%A _Ignacio Larrosa Cañestro_