Prime numbers are like the atoms of mathematics: they are the indivisible building blocks from which all other numbers are made. For millennia, these numbers, which are divisible only by 1 and themselves, have fascinated mankind.
They guard many mysteries, including how they are distributed on the number line, and efforts to identify more and more prime numbers have occupied generations of scholars.
Euclid proved about 2,300 years ago that there are infinitely many prime numbers. And yet, some odd primes seem more interesting than others. I have compiled my personal short list of three extraordinary prime numbers and their stories.
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Sheldon Prime
In episode 73 of the sitcom big bang theory, Physicist Sheldon Cooper asks his friends for the best grades. Cooper then shared his selection of 73. Their reasons: 73 is the 21st prime number; Its opposite, 37, is the 12th prime number; And the product of 7 and 3 is 21.
A few years after the episode aired in 2010, mathematician Christopher Spicer, now of Morningside University (then Morningside College), wondered whether there were other “Sheldon primes” sharing these properties. In 2015 he worked with two of his then-students, Jesse Byrnes and Alyssa Turnquist, to discover the first 10 million prime numbers; They did not find any other Sheldon chief among them. The three shared their findings in an article math horizon Called the “Sheldon Conjecture”.
Three years later, in 2019, number theorists Spicer and Carl Pomerance of Dartmouth College showed conclusive evidence that the Sheldon prime was unique. First, researchers showed that there could be no Sheldon prime larger than 10⁴⁵. While 10⁴⁵ is unimaginably large, it is still a finite value, meaning that, in theory, a computer could systematically search all primes between 2 and 10⁴⁵ for other Sheldon primes. Of course, today’s computers are not powerful enough to tackle that task directly. Mathematicians continually limited the possible Sheldon candidates, using integrals to approximate very large primes and thus gradually eliminated all Sheldon contenders. Ultimately the number remained only 73.
When David Saltzberg, physicist and scientific advisor at the University of California, Los Angeles big bang theory, Upon learning of the evidence, he and the sitcom’s writers paid tribute to the effort by including parts of the evidence on a whiteboard in the background of an episode that aired in April 2019.
“6-7”
Anyone who was online in 2025 was inevitably faced with the “6-7” event. Social media and comment sections were flooded with 6-7s and no one really knew why. Meem, pronounced “six-seven”, has no deep meaning; This is not a code to share a message or express happiness or irritation. Instead 6-7 is just 6-7.
The exact origin of the meme is also unclear. Sometimes it is attributed to a boy Celebrating basketball scores; sometimes it is Rap song “Messenger (6 7),” By Scrilla. Sometimes people point to basketball player LaMelo Ball’s height: six feet, seven inches.
The number 67 is certainly interesting from a mathematical point of view. It is not only prime but super-prime: it is the 19th prime number, and 19 itself is prime. Additionally, 67 is part of two consecutive pairs of “sexy primes”, or pairs of primes that are six integers apart. Together with 61 and Sheldon Prime, 73, 67 makes a sexy prime triple.
And 67 is part of what mathematicians call “”Lazy Caterer’s Orderwhich indicates the maximum number of pieces a pancake, pizza or other disc can be divided into n cut. One cut produces a maximum of two pieces; Two cuts make four. But if the third cut is done deftly, the disc can be cut into seven pieces instead of six. With 11 cuts, one pancake can be divided into up to 67 pieces. The corresponding sequence is 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79,…
Belphegor Prime
Forget 13 or 666. There is one number that truly represents the epitome of evil: Belphegor Prime, 1,000,000,000,000,066,600,000,000,000,001. The late mathematician and avid prime number hunter Harvey Dubner discovered this prime (and many others).
During his research, he found the prime number 16,661: a palindrome with the “devil’s number” 666 in the middle. You can easily add 0 between the 1 and three 6’s in this number, such as 1,066,601, 100,666,001, 10,006,660,001, etc. Yet none of these palindromes is major. All have divisors other than 1 and themselves.
Only when there are 13 0s between every 1 and 666 do you reach a prime number again. In short notation, this Belphegor prime number, which was named after a demon, can be written as 1030 +666×1014 +1.
As it turns out, there are even more palindromic primes of this form besides the Belphegor prime with 16,661 and 13 0. But none are as devilishly difficult as 1030 +666×1014 + 1, unless the version with 666,666 0 is also a prime number. This is yet to be decided.
This article was originally published in spectrum der wissenschaft And was reproduced with permission.
