A simple, step-by-step breakdown of two “perfect” math proofs. But which prime number is p? It must be on our list of primes, because our list is complete. But it also can’t be on our list of primes, ...

Prime numbers just got less lonely. A proof announced this week claims to show that the number of primes with a near-neighbour that is also a prime number is infinite – although the “near-neighbour” ...

Sixty-five million sound like a big deal by any standard. That’s the size of the improvement that an online army of collaborating mathematicians has already made to a groundbreaking proof involving ...

Mathematicians have taken a step forward in understanding patterns within the primes, numbers divisible only by 1 and themselves. According to the new work, the population of prime numbers contains an ...