A basic feature of number theory, prime numbers are also a fundamental building block of computer science, from hashtables to cryptography.

For instance, the largest known prime number, which is 2 136279841 − 1, is 41,024,320 digits long. At first, that number may seem mind-bogglingly large.

We have known for millennia that an infinite number of prime numbers, i.e., 2, 3, 5, 7, 11, etc., can be divided by themselves and the number 1 only.

In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper that any mathematician would be really ...