What's up in

# Twin primes conjecture

## Latest Articles

### A New Generation of Mathematicians Pushes Prime Number Barriers

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

### Teenager Solves Stubborn Riddle About Prime Number Look-Alikes

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

### How Do Mathematicians Know Their Proofs Are Correct?

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.

### A Solver of the Hardest Easy Problems About Prime Numbers

On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

### Mathematicians Outwit Hidden Number Conspiracy

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.

### 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.

### 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.

### Where Proof, Evidence and Imagination Intersect

In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?