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# prime numbers

## Latest Articles

### How Can Infinitely Many Primes Be Infinitely Far Apart?

Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be.

### 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.

### Graduate Student’s Side Project Proves Prime Number Conjecture

Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

### Mathematicians Clear Hurdle in Quest to Decode Primes

Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.

### 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.

### What Hot Dogs Can Teach Us About Number Theory

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

### 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.