How Evil Is Belphegor's Prime?

Mathematics for Simpletons

To guide you through the complex labyrinth of mathematics you need someone who is a complete klutz at the subject; Fortunately, this is one of my specialties and I am here to help.

That part of the human brain that is normally used for numerical computation is, in my case, occupied by a small piece of three-quarter inch plywood.

This article will explain the devilish Belphegor prime number in terms the writer cannot understand.

What Is a Prime Number?

A prime number can only be divided, with no remainder, by itself and 1. Starting at zero, which is not a prime number, the first non-prime number is four because it can be divided by two and by itself.

Do you want to learn more about prime numbers? Of course you don't, so here is some stuff that sciencenotes.org calls “interesting:”

• “There are an infinite number of prime numbers;
• “Two and three are the only consecutive prime numbers;
• “No prime number ends with 0; and,
• “No prime number greater than five ends in five.”

Then, there is Lemoine’s Conjecture, and it's superfluous to explain this to the kind of intellect attracted to HubPages but, just in case, it's “Any odd integer greater than five can be expressed as a sum of an odd prime (all primes other than two are odd) and an even semiprime” (geeksforgeeks.org). If you want to know what that means, or even what an integer is, you won't be able to found out here.

Mathematicians say that prime numbers are incredibly important. We'll have to take their word for it.

The Search for Prime Numbers

Some people spend time looking for prime numbers. As we've seen, there's an infinite quantity of them, so there's plenty of scope.

There's a thing out there called The Great Internet Mersenne Prime Search. Marin Mersenne (1588-1648) was a French monk; quite a bright chap by all accounts.

From The Stanford Encyclopedia of Philosophy we learn that “Mersenne himself undertook to establish a first list of what will eventually be called the 'Mersenne primes,' prime numbers that can be written in the form 2ⁿ− 1 (for some integer n), whose properties and determination are still topical questions in contemporary mathematics.” Obviously.

So now, we find ourselves in the company of a fellow called Luke Durant. It's October 2024, and Durant has discovered a new Mersenne prime number; it runs to more than 41 million digits. It's good to see he hasn't been wasting his time

“MORTY. HOLD THE FRONT PAGE.”

Recommended

Emily Dickinson's "There is a morn by men unseen"

Belphegor's Prime

But, enough of this frivolity, we are here to delve into that malicious little rascal, Belphegor's Prime.

This takes us back to 1984 and Harvey Dibner, an electrical engineer, amateur prime number searcher, and developer of the Dibner Cruncher. This is an indispensable gadget that employs a finite impulse response filter chip, it need scarcely be pointed out.

Using his gizmo, Dibner pulled this prime number out of the ether—1,000,000,000,000,066,600,000,000,000,001. That's one, followed by 13 zeroes, then 666 (in popular belief 666 signifies Satan), this is followed by 13 more zeroes and a trailing 1.

The number is palindromic and reads the same forwards as backwards. It also contains 31 digits, that is 13 backwards. Thirteen, of course, in Western culture is associated with bad luck.

It was Cliff Pickover, a man The New York Times says “Contemplates realms beyond our known reality,” who identified the sinister nature of Dibner's prime. He called it Belphegor's Prime, choosing the name of one of the seven princes of hell.

Belphegor was (is?) a nasty piece of work who is mentioned numerous times in the Bible as a troublemaker sent to Earth by the Devil.

Mythology.net tells us that “He is a shape shifter, delighting in using this ability to deceive mortals. His most common forms are polarized in their appearances. He will take the form of a beautiful woman, naked in all her glory, to seduce those who would fall for his wiles. He also appears as a terrible demon, with leathery flesh, huge horns, long sharp teeth and fingernails, and a gaping mouth.”

Belphegor is also known as the demon of inventiveness and one suspects there might be a bit of magical thinking going on in associating his prime number with evil.

The question in our title was, "How Evil Is Belphegor's Prime?" The answer is probably about as malevolent as a cocker spaniel puppy or a kitten playing with a ball of string.

Bonus Factoids

• There is said to be a relationship between prime numbers and perfect numbers. Geekesforgeeks.org tells us that “A perfect number is a positive integer equal to the total of its positive divisors, except the number itself in number theory.” Got it? No? Let's turn to Euclid for a clearer explanation: “If as many numbers as we please beginning from a unit be set out continuously in double proportion until the sum of all becomes a prime, and if the sum multiplied into the last make some number, the product will be perfect.” One suspects there might have been a slip up in the translation from Ancient Greek. For the rest of us a perfect number is the one on a winning lottery ticket.
• Scientific American confirms what most of us suspect: “Most real numbers are unknown—even to mathematicians.”
• How do you make seven even? Take away the “s.” Badum- tish. I'm here all week. Try the pi.
• The Piraha tribe in Amazonia is not troubled by numbers. Their culture has never developed the concept of numbers. These are my kind of people.

Sources

• “What Is a Prime Number? How to Tell If a Number Is Prime.” Anne Helmenstine, sciencenotes.org, May 5, 2023.
• “A 41-Million-Digit Prime Number Is the Biggest Ever Found – But Mathematicians’ Search for Perfection Will Continue.” John Voight, theconversation.com, November 13, 2024.
• “Belphegor.” Prof. Geller, mythology.net, April 8, 2017.
• “How a Mathematician Turned an Obscure Number Into a Scary Story.” Eric Grundhauser, Atlas Obscura, October 18, 2022
• “These Are the Most Bizarre Numbers in the Universe.” Manon Bischoff, Scientific American, May 23, 2023.

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This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2024 Rupert Taylor