Sunday, October 31, 2021

Happy Halloween: Belphagor's Prime and Triple Digit Integers

 Happy Halloween: Belphagor's Prime and Triple Digit Integers

Greetings everyone.  And a very Happy Halloween to you, hopefully you are all celebrating, having a great time, staying safe and sane.   

Today, I'm going there, talking about a number with a very dark and evil repetition, better known to religions as the "number of the beast":  six hundred and sixty six.  And to try to balance things out, I'm also going to be talking about a holy number.  

A Prime Evil:  Belphegor's Prime - Starring the Triple Six 

Belphegor's Prime is a large palindrome number:


that has three sixes in the middle of 13 zeroes on other side enclosed by a 1.  A two for one deal, not only the number of the beast but also the presence of a number with a unlucky repetition, 13.  Engineer and mathematician Harvey Dubner determined this monster of a number to be a prime integer.   However, the number received its nefarious name from well-known mathematics and science author Cliff Pickover.   

Who is Belphegor?   In religion, Belphegor is a prince of Hell, whose purpose in demonhood was to trick people into discovery (with a heavy price attached).  

Other connections to the infamous triple six include:

* The sum of the integers 1 to 36.  

* Multiply 2/3 by 1000 and take the integer part (without rounding) to get this number.

*  The triple six can be written has every roman numeral less than 1,000.  

*  It make can property very valuable, such as 666 5th Ave in New York City selling for a then record $1.8 billion, only to be changed to 660 5th Ave sometime later.  


Triple Digit Integers - The Glory of Triple Seven

Triple sixes aren't the only number to receive a mythological, metaphysical, or religious repetition.   

For instance, triple sevens, 777, is said to be a very heavenly number.  In Christianity, 777 represents the perfection of Trinity, made up of the Father, Son (Jesus Christ), and the Holy Spirit.  

Maybe the prime factorization of 777, 3 × 7 × 37, is what lead Judaism to declare the numbers 3 and 7 to be "perfect".

Finally, 777 is what brings much happiness to slot players. If you have been a casino, you know why. 

In numerology, triple numbers are promoted to have significance in the new age religion.  111, 222, 333, and so on, are given various meanings depending on the new age writer.  111 and its four digit number "relative", 1111, are very popular in the new age industry, often suggesting completion, oneness with the universe, and positive attraction thoughts. 

Generating Triple Digit Palindrome Numbers

You can generate integers 1 [ n number of zeros ] ddd [ n number of zeroes ] 1, where d is the digit 0 through 9 through the following formula:

10^(2n+4) + d × 111 × 10^(n+1) + 1


n = 1, d = 9:   1099901

n = 2, d = 2:   100222001

n = 3, d = 3:   10003330001

No guarantees that the integer you get is prime.  Use at your own risk.  


Grundhauser, Eric.  "How a Mathematician Turned an Obscure Number Into a Scary Story"  Atlas Obscura.  August 23, 2016.   Accessed August 1, 2021.

"660 Fifth Avenue".  Wikipedia Last Edited. August 11, 2021.  Accessed August 11, 2021.

"666 (number)" Wikipedia.  Last Edited July 31, 2021.  Accessed August 9, 2021.

"777 (number)" Wikipedia.  Last Edited August 6, 2021.  Accessed August 9, 2021.

Three very infamous tarot cards: The Tower, The Devil, Death.  (Gilded Tarot Deck - Ciro Marchetti)

Happy Halloween,


All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

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