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.
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Famous quotes containing the words prime, bell and/or numbers:
“In time, after a dozen years of centering their lives around the games boys play with one another, the boys’ bodies change and that changes everything else. But the memories are not erased of that safest time in the lives of men, when their prime concern was playing games with guys who just wanted to be their friendly competitors. Life never again gets so simple.”
—Frank Pittman (20th century)
“Its quick silver bell beating, beating
And down the dark one ruby flare
Pulsing out red light like an artery,”
—Karl Shapiro (b. 1913)
“Green grow the rushes-O
What is your one-O?”
—Unknown. Carol of the Numbers (l. 2–3)