A Belphegor prime (also known as a Beelphegor prime) is a prime Belphegor number, i.e., a palindromic prime of the form . The first few Belphegor primes are the Belphegor numbers
with , 13, 42, 506, 608, 2472, 2623, 28291, 181298, ... (OEIS A232448). Shifting this sequence by one gives 1, 14, 43, 507, 609, ... (OEIS A156166).
The above definition generalizes the original definition due to Pickover, who named
"the" Belphegor prime after one of the Seven Princes of Hell who is the demon of inventiveness. This prime has a number of numerological properties, including a central beast number 666 which is surrounded on each side by 13 (a number traditionally associated with bad luck) zeros and an overall decimal number length of 31-which is 13 backwards.