10³⁰ + 666 × 10 + 1: the obscure number that has an evil reputation

This is the story of a hunter and a weaver of stories, but, above all, of a somewhat sinister number.

To be more precise, one of the prime numbers, those that are divisible only by 1 and themselves, and that have been a source of fascination since the dawn of civilization.

Or at least since about 3,570 years ago, when, during the reign of Apophis I, the Egyptian scribe Ahmes created the Rhind Mathematical Papyrus and recorded fractions whose denominators were prime numbers differently.

Mathematicians have spent millions of hours on them because, as well as being beautiful, seductive and very useful, they are also infuriating: these number theory atoms have no obvious pattern, so the more they are found, the more erratic they seem to be.

Not even the immense power of computers helps much.

But, on that long and tortuous road to reveal all its mysteries, they have come across curiosities that they share with those of us who don’t know so much to delight us.

They are like delicious tidbits of knowledge that remind us how cool the world of numbers is.

And from time to time they serve us when we are entertained with the most popular culture.

Fans of “The Big Bang Theory” series, for example, may remember Dr. Sheldon Cooper saying…

“The best number is 73. Why? 73 is the 21st prime.”

“Its mirror, 37, is 12° and its mirror, 21, is the product of multiplying 7 x 3”.

“In binary 73 is a palindrome, 1001001, which backwards is 1001001.”

Probably Sheldon would also like the number that summons us here today, because in addition to being a cousin, it shares that poetic symmetry of palindromes (it is the same read from left to right as from right to left),

However, it is more demonic.

The hunter

It was found by a cousin hunter (as those who are dedicated to looking for them are called… do you remember that they are very difficult to find?).

This is Harvey Dubner, an American electrical engineer and mathematician known for his contributions to the search for large prime numbers.

Dubner set out to trace a set of primes starting at 16661 and adding zeros to each side, between 1 and 6.

That is, it started with 16661 -which is a prime number-, and checked if 1066601 was also a prime number. It was not.

He did the same with 100666001, 10006660001… and neither was prime, but he didn’t give up.

It continued unsuccessfully until it reached 1000000000000066600000000000001 and… eureka! found the first of the numbers with those characteristics that was prime.

Dubner continued with his laborious task and found that those with 42, 506, 608, 2472 and 2623 zeros added were also prime numbers.


Another mathematician, Cliff Pickover -our story weaver- detected certain hellish traits in that first number.

From the beginning, Dubner’s experiment had 666 at its heart, the number of the Beast, according to the Apocalypse or Revelations, the last book of the New Testament and of the Christian Bible, where it says…

“Here is wisdom. Let him who has understanding count the number of the beast, for it is the number of man; and his number is six hundred and sixty-six.”

In addition, he noticed that this bestial number in that first prime “was surrounded by 13 zeros on both sides, long considered superstitious as an unlucky number in Western culture,” Pickover told BBC Mundo.

On top of that, “it had 31 digits in total, which is 13 backwards.”

The mathematician decided to give 1000000000000066600000000000001 a name: Belphegor’s cousin.

Belfegor is one of the 7 princes of hell, the demon of the deadly sin of sloth, but also, curiously, of excrement, hence the woodcut included in Jacques August Simon Collin de Plancy’s “Dictionnaire Infernal” (1818 and 1863), in which he appears elegantly portrayed in the toilet.

Although much attention was paid to him in ancient times, his role changed and he became the one in charge of tempting mortals with the gift of discovery and invention, which doesn’t sound bad at all, but who knows!

Belphegor’s cousin also has his symbol: it is a backwards π (pi), and is derived from a bird glyph that appears in the undeciphered 15th-century Voynich Manuscript.


Pickover is the author of 50 books on topics ranging from math and medicine to life after death and artificial intelligence.

Its stated goal is to “expose to a wide audience the wonders of science and mathematics”, and it does so by using playful yet complex concepts such as “vampire numbers” and “magical hypercubes”.

“Francis Bacon (artist 1909-1992) once said: ‘The artist’s job is always to delve into the mystery,’ and I use this approach for much of my creative output,” he told BBC Mundo.

“I’ve found that giving names to certain numbers or math concepts helps stimulate interest in people of all ages.”

“The name helps focus attention and discussion, and rejuvenates students’ interest in mathematics.”

“Mathematics is the hammer that breaks the ice of our unconscious”, he concluded.

Remember that you can receive notifications from BBC Mundo. Download the new version of our app and activate it so you don’t miss out on our best content.

BBC-NEWS-SRC: IMPORTING DATE: 2022-09-17 08:50:04

10³⁰ + 666 × 10 + 1: the obscure number that has an evil reputation