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Belphegor Prime


A Belphegor prime (also known as a Beelphegor prime or a beastly palindromic prime) is a prime Belphegor number, i.e., a palindromic prime of the decimal form 1(0...)666(0...)1, with an equal number of zeros on each side of 666 (Ondrejka 2001, p. 32). 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 original named prime is

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

which Pickover (n.d.) called "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

Numberphile. "The Most Evil Number (Belphegor's Prime)." Featuring T. Padilla. Oct. 31, 2018. https://www.youtube.com/watch?v=zk_Q9y_LNzg.Ondrejka, R. "The Top Ten Prime Numbers (a Catalogue of Primal Configurations)." May 5, 2001. https://t5k.org/lists/top_ten/topten.pdf.Pickover, C. "Belphegor's Prime: 1000000000000066600000000000001." n.d. https://sprott.physics.wisc.edu/pickover/pc/1000000000000066600000000000001.html.Sloane, N. J. A. Sequences A156166 and A232448 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Belphegor Prime

Cite this as:

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

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