Oftentimes, numbers are just cold indicators, incapable of expressing menace or guile. Still, there’s Belphegor’s Prime, a supposedly sinister numeric palindrome with several strange properties. At least, that’s what one mathematical con artist would have you believe. But what is the Belphegor’s Prime?
The Belphegor’s Prime, known as the “evil” number: 1000000000000066600000000000001 is a palindromic prime with the number 666 in the middle and 13 zeros on each side, and horn-like 1s. It’s named after a Prince of Hell who made brilliant discoveries, and its symbol is the upside-down Greek letter pi.
The Evil Number
The first thing you should know about Belphegor’s Prime is that it is a literal prime number, which means it is divisible only by itself and one. Being a prime number isn’t exactly a claim to fame in and of itself. Still, given the ridiculous enormity of Belphegor’s Prime, its primality isn’t immediately obvious but can be proven using a primality algorithm. Furthermore, it is part of a calculable system of prime numbers.
According to Cliff Pickover, author, mathematician, and father of Belphegor’s Prime, the infernal number was discovered by prime number hunter Harvey Dubner, who determined that it was part of a sequence. The set of primes could be obtained by increasing or decreasing the number of zeroes on either side of the 666.
This means that the number 16,661, which contains no zeroes, is also a prime number. The next time a similar palindromic number becomes prime, it has 13 zeros, 42 zeros, and so on.
Harvey Dubner determined that the first seven numbers of this type have subscripts 0, 13, 42, 506, 608, 2472, and 2623.
Cliff Pickover, Mathematician, and Father of Belphegor’s Prime
While natural prime numbers are as rare as any other number, that is to say, they are not rare at all, given that an infinite number of digits exist theoretically, Belphegor’s Prime stands out for its poetic symmetry. (Source: Atlas Obscura)
Is There Another Way to Express This Number?
Another way to express the infernal number is 10(13)666(13), which truncates the 13 zeroes into parentheses, joining the Number of the Beast in the center of the string with a pair of traditionally bad luck numbers on either side. Furthermore, as some have pointed out, the number has 31 digits, which is simply a backward 13! There are circles within circles.
Despite these notable characteristics and the abstract connotation to Western concepts of “evil” numbers, the number known as Belphegor’s Prime is simply another number. It was not until Pickover obtained it that it became the cursed number that it is today.
Pickover appears modest about developing the concept of Belphegor’s Prime, but his ability to give a large number of characters made it famous.
I am not actually the ‘creator’ of the number, in the sense that people have known about beastly palindromic primes before I gave a name to a very eye-catching number with 13 zeros, to help focus broad attention on it.
Cliff Pickover, Mathematician, and Father of Belphegor’s Prime
(Source: Atlas Obscura)
Image from Curioustem