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:
“And this must be the prime of life . . . I blink,
As if at pain; for it is pain, to think
This pantomime
Of compensating act and counter-act,
Defeat and counterfeit, makes up, in fact,
My ablest time.”
—Philip Larkin (1922–1986)
“Where the bee sucks, there suck I,
In a cowslip’s bell I lie;
There I couch when owls do cry.
On the bat’s back I do fly
After summer merrily.
Merrily, merrily shall I live now,
Under the blossom that hangs on the bough.”
—William Shakespeare (1564–1616)
“The barriers of conventionality have been raised so high, and so strangely cemented by long existence, that the only hope of overthrowing them exists in the union of numbers linked together by common opinion and effort ... the united watchword of thousands would strike at the foundation of the false system and annihilate it.”
—Mme. Ellen Louise Demorest 1824–1898, U.S. women’s magazine editor and woman’s club movement pioneer. Demorest’s Illustrated Monthly and Mirror of Fashions, p. 203 (January 1870)