What is Belphegor's Prime?

Discovered by Harvey Dubner, a mathematician and engineer hailing from New Jersey, Belphegor’s Prime is a fascinating example of a large palindromic prime number. Throughout the early 1990s, Dubner was instrumental in identifying a significant portion of the known prime numbers exceeding two thousand digits.

Dubner found that certain numbers, featuring 666 at their core, flanked by a specific count of zeros and encapsulated by the digit one at both ends, are indeed palindromic primes. This means they read identically forwards and backwards and lack non-trivial divisors—making them exceedingly rare.

The smallest example is 16,661, with no zeros. Following this are numbers like 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, which has 13 zeros, and the subsequent palindromic primes grow to enormous sizes, including those with up to 181,298 zeros.

Cliff Pickover, a noted author, remarked on the superstitious attributes of the second prime, dubbing it Belphegor’s Prime after one of the seven princes of hell associated with invention and discovery.

What Makes Belphegor’s Prime So Frightening?

Belphegor’s Prime translates to ‘one nonillion, sixty-six quadrillion, six hundred trillion and one’. Examining this number reveals its connections to various elements of superstition and the occult:

• It features 666 at its center—the infamous number of the beast from the Book of Revelation, often linked to malevolent forces.
• Flanked by 13 zeros on each side, a number frequently associated with bad luck and malevolence.
• The digit one at both ends creates an illusion of entrapment, as if the beast resides within the number itself.
• The total digit count of 31 is 13 reversed, further enhancing its ominous aura.

Pickover also associated Belphegor’s Prime with a mysterious symbol found in the Voynich manuscript, a cryptic document from the 1400s housed at Yale University, filled with enigmatic illustrations that many have attempted to decode. This symbol resembles an inverted Pi.

If Belphegor’s Prime gives you the chills this Halloween, take comfort in the fact that a similar technique can yield a ‘heavenly’ palindromic prime. In numerology, 666 is referred to as an ‘Angel number’ due to its three repeating digits, allowing for the interpretation that Belphegor’s Prime might not be as sinister as it appears. Alternatively, if that doesn’t provide enough comfort, simply replace the 666 in Belphegor’s Prime with 777, and you’ll create a new palindromic ‘angel’ prime to counter the ominous Belphegor Prime.

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