Belphegor's prime is the name for the number 10,000,000,000,000,66,600,000,000,000,001 = \(10^{30} + 666 \cdot 10^{14} + 1\).[1] It is a palindromic prime, notable for its curious decimal expansion containing the beast number. Clifford Pickover named the number after a demon from the Judeo-Christian mythos, playing on 666's association with the devil in numerology.

Using exponents to represent digit repetition, the number could be written \(10^{13}6660^{13}1\). (The presence of the number 13 — associated with bad luck in Western culture — further ties into the numerological theme.) Harvey Dubner calculated that the first few numbers of the form \(10^n6660^n1\) have \(n = 0,\,13,\,42,\,506,\,608,\,2472,\,2623\).

Sources Edit

  1. Clifford Pickover, Belphegor's Prime: 1000000000000066600000000000001!

See also Edit

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