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# prime numbers

## Latest Articles

### 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.

### Mathematicians Seal Back Door to Breaking RSA Encryption

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

### In the Universe of Equations, Virtually All Are Prime

Equations, like numbers, cannot always be split into simpler elements.

### The Universal Pattern Popping Up in Math, Physics and Biology

Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.

### A Chemist Shines Light on a Surprising Prime Number Pattern

When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.

### The Infinite Primes and Museum Guard Proofs, Explained

A simple, step-by-step breakdown of two “perfect” math proofs.

### Robert Langlands, Mathematical Visionary, Wins the Abel Prize

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.