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# Prime numbers

## Latest Articles

### Mathematicians Find a New Class of Digitally Delicate Primes

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.

### The Mysterious Math of Perfection

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

### Mathematicians Open a New Front on an Ancient Number Problem

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.

### Mathematicians Will Never Stop Proving the Prime Number Theorem

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

### A Number Theorist Who Solves the Hardest Easy Problems

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.

### The Map of Mathematics

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

### Mathematicians Catch a Pattern by Figuring Out How to Avoid It

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

### Big Question About Primes Proved in Small Number Systems

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.

### New Proof Settles How to Approximate Numbers Like Pi

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.