Prime numbers

The proof creates stricter limits on potential exceptions to the famous Riemann hypothesis.

Terence Tao, who has been called the “Mozart of Mathematics,” wrote an essay in 2007 about the common ingredients in “good” mathematical research. In this episode, the Fields Medalist joins Steven Strogatz to revisit the topic.

How Fermat’s less famous "little theorem" got mathematicians young and old to play with prime-like Carmichael numbers.

Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.

New work attacks a long-standing barrier to understanding how prime numbers are distributed.

A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

Unpredictability can help computer scientists solve otherwise intractable problems.

In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes.