Belphegor's prime is thepalindromic prime number1000000000000066600000000000001 (1030 + 666 × 1014 + 1), a number which reads the same both backwards and forwards and is only divisible by itself and one.
Belphegor's prime was first discovered byHarvey Dubner,[1] a mathematician known for his discoveries of many large prime numbers and prime number forms. For Belphegor's prime in particular, he discovered the prime while determining a sequence of primes it belongs to.
The name "Belphegor's prime" was coined by authorClifford A. Pickover in 2012.[2]Belphegor is one of theSeven Princes of Hell; specifically, "the demon of inventiveness".[2] The number itself containssuperstitious elements that have given it its name: the number666 at the heart of Belphegor's prime is widely associated as being thenumber of the beast, used in symbolism to represent one of the creatures in theapocalypse or, more commonly, the devil. This number is surrounded on either side by thirteen zeroes and is 31 digits in length (thirteen reversed), withthirteen itself longregarded superstitiously as an unlucky number in Western culture.
ABelphegor number is a palindromic number in the form of. The sequence of the first four Belphegor numbers is:
Dubner noticed that 16661 is a prime number. By adding zeroes directly on both sides of the 666, Dubner found more palindromic prime numbers, including the Belphegor prime, which is second in the sequence. This sequence eventually became theBelphegor primes, named after the number.[1] The number of zeroes on each side of the 666 in the first few Belphegor primes is:[3][1]
Belphegor's prime contains 13 zeroes on either side of the central 666, and thus corresponds to the second number in this sequence.
In theshort scale, this number would be named "one nonillion, sixty-six quadrillion, six hundred trillion one." In thelong scale, this number's name would be "one quintillion, sixty-six billiard, six hundred billion one."