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# prime numbers

## Latest Articles

### Pierre de Fermat’s Link to a High School Student’s Prime Math Proof

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

### The Hidden Connection That Changed Number Theory

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

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

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

### How to Build a Big Prime Number

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

### Why Mathematicians Re-Prove What They Already Know

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.

### How Randomness Improves Algorithms

Unpredictability can help computer scientists solve otherwise intractable problems.

### 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.

### A Numerical Mystery From the 19th Century Finally Gets Solved

Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

### A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special

The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.