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.

Both arithmetic aficionados and the mathematically challenged will be equally captivated by new research that upends hundreds of years of popular belief about prime numbers.

In the years that followed, Sloane's catalog of number sequences got bigger. In 1995 the mathematician, together with his colleague Simon Plouffe, published The Encyclopedia of Integer Sequences ...

2. 3. 5. 7. 11. 13. 17. And so on. This is far from a comprehensive list of prime numbers—if we were to compile and write out an exhaustive list of all known prime numbers, this would be a truly ...

All the numbers from 501 to 1,000—half of the set—form a primitive set, as no number is divisible by any other. In this way, primitive sets might comprise a hefty chunk of the number line.

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 ...

However, rather than proving pi is irrational directly, it's also possible to confirm irrationality using a different property of the number.