Belphegor's Prime: 1000000000000066600000000000001

by Dr. Cliff Pickover

Gaze in awe at Belphegor's Prime:


is a palindromic prime number,
with 666 hiding among the zeros.

Please also note the ominous presence of 13 zeros.
Please don't stare at the number too long.
Look away for a few seconds, and take a deep breath.

The symbol of Belphegor's Prime resembles Pi,
only upside down.
It is derived from a bird glyph
first seen embedded in the Voynich Manuscript.

Der Hl. Augustinus und der Teufel

In demonology, Belphegor (or Beelphegor) is a demon.
The creature is one of the seven princes of Hell
and helps people make discoveries.
In John Milton's Paradise Lost,
Belphegor is one of the "Principalities of the Prime."
In hell, Belphegor is the demon of inventiveness.

← Interested in more mathematical weirdness through history?

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Prime of Belphegor Across Cultures

I gave the name to Belphegor's Prime, and now it is widley recognized as a mathematical and amusing oddity across different languages and cultures:
  1. See El primo de Belfegor.
  2. The Prime of Belphegor can be written concisely using the notation 1 0(13) 666 0(13) 1, where the number in parentheses denotes the number of consecutive zeros. Harvey Dubner determined that the first 7 numbers of this type have subscripts 0, 13, 42, 506, 608, 2472, and 2623 [see J. Rec. Math, 26(4)]. When will humanity discover the next in this series?
  3. Belphegor's Prime at Neatorama.
  4. Belphegor's Prime at Pat's Math Teacher blog
  5. Belphegor's Prime YouTube
  6. Belphegor's Prime at Deskarati
  7. Belphegor's Prime: 1000000000000066600000000000001 on a shirt.
  8. Belphegor's Prime on a poster.
  9. Belphegor's Prime at BBC News and Simon Singh and Homer Simpson
  10. Belphegor's Prime at Wikipedia
  11. Belphegor's Prime at another Wikipedia
  12. Belphegor's Prime article
  13. Belphegor's Prime Reddit

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