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# Prime numbers

## Latest Articles

### ‘Sensational’ Proof Delivers New Insights Into Prime Numbers

July 15, 2024

The proof creates stricter limits on potential exceptions to the famous Riemann hypothesis.

### What Makes for ‘Good’ Mathematics?

February 1, 2024

Terence Tao, who has been called the “Mozart of Mathematics,” wrote an essay in 2007 about the common ingredients in “good” mathematical research. In this episode, the Fields Medalist joins Steven Strogatz to revisit the topic.

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

November 22, 2023

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

November 1, 2023

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

October 26, 2023

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

### How to Build a Big Prime Number

July 13, 2023

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

April 26, 2023

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

April 3, 2023

Unpredictability can help computer scientists solve otherwise intractable problems.

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

October 13, 2022

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

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