You may not have met this remarkable palindromic number before.
is a prime. Because it contains , the Number of the Beast, this prime is nicknamed Belphegor's prime, after one of the Seven Princes of Hell. Here he is
This prime was discovered by Harvey Dubner, an expert in finding large unusual primes, and is one of a sequence which you can find on the Online Encyclopedia of Integer Sequences (OEIS) here. The next is
The OEIS seems to suggest this is only a 'probable' prime. A probable prime is a number that has passed a long series of tests from which we can conclude the probability it is not prime is very small. We also have exact tests but they are much slower, because they involve much longer calculations. In this case I found that according to SageMathCell, which I think uses an exact test, this is a definite prime, not just a probable one.
The next number after that would be a probable prime with more than ten times as many digits, so I won't try to display it here or prove it is a definite prime.
How did Dubner discover Belphegor's prime? Purely guessing but maybe he spotted the is prime and thought that was neat, so he then tried inserting more zeros and putting the numbers so formed to a probabilistic primality test until he struck gold with thirteen zeros each side of the evil .
I haven't really investigated but I thought interesting palindromic primes might not be all that rare. If there are seven demons in hell, what if we change to in recognition of the fact. Is
prime? Can we prove it? YES WE CAN! How spooky is that?
I hereby name it the Seven Demons Prime.
Picture credit http://en.wikipedia.org/wiki/File:Belphegor.gif, public domain.
