Bell Number - Prime Bell Numbers

Prime Bell Numbers

The first few Bell numbers that are primes are:

2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837 (sequence A051131 in OEIS)

corresponding to the indices 2, 3, 7, 13, 42 and 55 (sequence A051130 in OEIS).

The next prime is B2841, which is approximately 9.30740105 × 106538. As of 2006, it is the largest known prime Bell number. Phil Carmody showed it was a probable prime in 2002. After 17 months of computation with Marcel Martin's ECPP program Primo, Ignacio Larrosa Cañestro proved it to be prime in 2004. He ruled out any other possible primes below B6000, later extended to B30447 by Eric Weisstein.

Read more about this topic:  Bell Number

Famous quotes containing the words prime, bell and/or numbers:

    “I did not know I was in my prime until afterwards.”
    —Mason Cooley (b. 1927)

    “When a nation’s young men are conservative, its funeral bell is already rung.”
    —Henry Ward Beecher (1813–1887)

    “The land cannot be cleansed of the blood that is shed therein, but by the blood of him that shed it.”
    —Bible: Hebrew Numbers 35:33.