Belphegor's prime

There is something mysterious about prime numbers. And with the Halloween season approaching, it seems fitting to write an article about one of the most mysterious and maybe even scariest prime of them all.

Here is something mysterious about prime numbers. And with the Halloween season approaching, it seems fitting to write an article about one of the most mysterious and maybe even scariest prime of them all.

Here is the monstrosity that is Belphegor’s prime:
1000000000000066600000000000001

One, followed by 13 (unlucky) zeroes, 666, another 13 zeroes, and 1 again. It is 31 digits long (which is 13 backwards), and unbelievably, is only divisible by one and itself. This is a palindromic prime, meaning that it reads the same quantity right to left and left to right.

Discovered by mathematician Harvey Dubner, Belphegor’s prime is suitably named after the notorious demon of inventiveness.

Dubner also calculated the first few numbers of the form 1 0(n) 666 0(n) 1, where n represents the amount of times that 0 is repeated. It turns out that when n is 0, the resulting number is prime (16661). The next value of n where the result is prime, is 13, which outputs Belphegor’s infamous prime. And the succeeding value of n in this list is 42. The meaning of life, the universe, and everything. Very interesting.

We know from Euclid that there are an infinite number of prime numbers out there. But we are still unsure if there are an infinite number of palindromic ones. Maybe you will be the next to discover one.

Picture Source: factrepublic.com