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Belphegor Prime


A Belphegor prime (also known as a Beelphegor prime) is a prime Belphegor number, i.e., a palindromic prime of the form 1(0...)666(0...)1. The first few Belphegor primes are the Belphegor numbers

 B_n=10^(2n+4)+666·10^(n+1)+1

with n=0, 13, 42, 506, 608, 2472, 2623, 28291, 181298, ... (OEIS A232448). Shifting this sequence by one gives 1, 14, 43, 507, 609, ... (OEIS A156166).

The above definition generalizes the original definition due to Pickover, who named

 B_(13)=10000000000000_()_(13)6660000000000000_()_(13)1

"the" Belphegor prime after one of the Seven Princes of Hell who is the demon of inventiveness. This prime has a number of numerological properties, including a central beast number 666 which is surrounded on each side by 13 (a number traditionally associated with bad luck) zeros and an overall decimal number length of 31-which is 13 backwards.


See also

13, Beast Number, Belphegor Number, Integer Sequence Primes, Palindromic Prime

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References

Pickover, C. "Belphegor's Prime: 1000000000000066600000000000001." http://sprott.physics.wisc.edu/pickover/pc/1000000000000066600000000000001.html.Sloane, N. J. A. Sequences A156166 and A232448 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Belphegor Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BelphegorPrime.html

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