Prime numbers

Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.

Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.

Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

Why do mathematicians enjoy proving the same results in different ways?

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”