Prime numbers are like the atoms of mathematics: they are the indivisible building blocks from which all other numbers are composed. For millennia, these numbers, divisible only by 1 and by themselves, have fascinated humanity.
They keep many secrets, including how they are distributed on the digital right and the efforts made to protect them. further identify and other bounties have occupied generations of scholars.
Euclid proved about 2,300 years ago that there are infinitely many prime numbers. And yet, a few first it seems more interesting than others. I’ve compiled my personal short list of three extraordinary prime numbers and their stories.
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Sheldon the First
In episode 73 of the sitcom The Big Bang Theory, Physicist Sheldon Cooper asks his friends for the best number. Cooper then shares his choice of 73. His reasons: 73 is the 21st prime number; its inverse, 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 of what is now Morningside University (then Morningside College) wondered if there were other “Sheldon primes” sharing these properties. In 2015, he worked with two of his then-students, Jessie Byrnes and Alyssa Turnquist, to search for the first 10 million prime numbers; they found no other First Sheldon among them. The trio shared their findings in an article in Mathematical horizons called “Sheldon’s conjecture”.
Three years later, in 2019, Spicer and Carl Pomerance, a number theorist at Dartmouth College, showed conclusive proof that Sheldon’s prime number was unique. First, researchers showed that there cannot be a Sheldon prime greater than 10⁴⁵. Although 10⁴⁵ is unimaginably large, it is nevertheless a finite value, which means, in principle, that a computer can systematically search all prime numbers between 2 and 10⁴⁵ for other Sheldon primes. Of course, current computers are not powerful enough to handle this task directly. Mathematicians have continually narrowed down possible Sheldon candidates, approximating extremely large primes using integrals and thus gradually eliminating all Sheldon candidates. Ultimately, only number 73 remained.
When David Saltzberg, a physicist at the University of California, Los Angeles and scientific advisor to The Big Bang Theory, Having learned of the evidence, he and the sitcom’s writers paid homage to the effort by including portions of the evidence on a whiteboard in the background of an episode that aired in April 2019.
“6-7”
Anyone online in 2025 inevitably came across the “6-7” phenomenon. Social media and comment sections were flooded with 6-7s and no one really knew why. The meme, pronounced “six-seven,” has no deeper meaning; this is not code for sharing a message or expressing joy or annoyance. Instead, 6-7 is simply 6-7.
The precise origin of the meme is also unclear. Sometimes it’s attributed to a boy celebrate a basketball score; sometimes it’s the rap song “Doot Doot (6 7)”, by Skrilla. Sometimes people point out basketball player LaMelo Ball’s height: six feet seven inches.
The number 67 is certainly interesting from a mathematical point of view. It’s not just prime but super prime: it’s the 19th prime number, and 19 itself is also prime. Additionally, 67 is one of two consecutive pairs of “sexy primes,” or pairs of primes spaced six whole numbers apart. With 61 and the Sheldon prime, 73, 67 creates a sexy triplet.
And 67 is part of what mathematicians call the “lazy caterer sequence“, which indicates the maximum number of pieces into which a pancake, pizza or other disk can be divided with n cuts. One cut produces a maximum of two pieces; two cuts produce four. But if the third cut is done intelligently, the disc can be cut into seven pieces instead of just six. With 11 cuts, a crepe 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 the First
Forget 13 or 666. There is one number that truly represents the epitome of evil: Belphegor’s Prime, 1,000,000,000,000,066,600,000,000,000,001. The late mathematician and avid prime number hunter Harvey Dubner discovered this first (and many others).
During his research, he came across the prime number 16,661: a palindrome with the “devil’s number” 666 in the middle. You can easily add 0s between the 1 and the three 6s to this number to get more beastly palindromes, such as 1,066,601, 100,666,001, 10,006,660,001, etc. However, none of these palindromes are prime. All have divisors other than 1 and themselves.
Only when there are 13 0s between every 1 and 666 do we arrive at a prime number again. In shorter notation, this prime number of Belphegor, which bears the name of a demon, can be written as 10.30 +666 × 1014 +1.
It turns out that there are other palindromic primes of this form other than 16,661 and the Belphegor prime with 13 0. But none are as fiendishly difficult as 1030 +666 × 1014 + 1, unless the version with 666 666 0 is also a prime number. This remains to be determined.
This article was originally published in spectrum of science and has been reproduced with permission.
