Belphegor's prime is the palindromic prime number corresponding to (10³⁰ + 666 × 10¹⁴ + 1). The number itself contains superstitious elements: it has 666 at its heart, it's surrounded on either side by 13 zeroes and is 31 digits in length (13 reversed).
Belphegor’s prime is a very special number that has many interesting properties and connections to mathematics, numerology, and mythology. Belphegor’s prime is a palindromic prime, which means it is a prime number that reads the same backwards and forwards. A prime number is a positive integer that has exactly two factors: itself and one. For example, 2, 3, 5, 7, 11, … are prime numbers. Belphegor’s prime can be expressed in scientific notation as shown in the image below.
Belphegor’s prime is named after Belphegor, one of the Seven Princes of Hell, who is the demon of inventiveness. He is often depicted as a horned beast or a beautiful woman, and he tempts people with wealth and power. He is also associated with the deadly sin of sloth. It contains many superstitious elements that have given it its name. The most obvious one is the number 666, which is widely regarded as the Number of the Beast, a symbol of the Antichrist or the Devil in Christian tradition.
Belphegor’s prime number is surrounded by 13 zeros on each side, and the whole number has 31 digits, which is 13 reversed. Both 13 and 31 are considered unlucky numbers in some cultures. Moreover, this number can be written as shown in below image which emphasizes the unluckiness built in with this netherly prime by literally placing a 13 on each side of the devil’s number.
Belphegor’s prime is also related to some mathematical concepts and puzzles. For instance, it can be seen as a special case of a repunit prime, which is a prime number that consists of only one repeated digit (such as 11, 111, 11111, …). Belphegor’s prime is a repunit prime in base 10¹⁴+666
It is also connected to the Fermat primes, which are primes of the form (such as 3, 5, 17, 257, …).
Belphegor’s prime can be obtained by multiplying two Fermat primes:
2¹⁶+1
&
2³²+1
Furthermore, Belphegor’s prime can be used to construct a magic square of order 4 with a magic constant of 10¹⁵+333×10⁷+(1/2)
I hope this gives you some insight into the fascinating nature of Belphegor’s prime. 🙏
