prime number

In this excellent talk the mathematician Vicky Neale gives a fascinating and easy-to-follow introduction to the prime numbers.

Fermat's little theorem and fake primes.

There's been progress on one of the biggest open problems in maths: the twin prime conjecture.

Look for hidden gems in the gaps between known prime numbers.

This year has seen a flurry of results as mathematicians hunt down the elusive proof of the twin prime conjecture. Will they get their wish for Christmas this year?

Number theory is famous for problems that everyone can understand and that are easy to express, but that are fiendishly difficult to prove. Here are some of our favourites.

Agreeing to pay £50,000 for something worth £2 wouldn't win you any haggling competitions. In mathematics, however, a similar result can bring you international acclaim. This is the case with recent progress towards the famous twin prime conjecture.

This year's Abel Prize has been awarded to the Belgian mathematician Pierre Deligne for "seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields".

They've done it again! GIMPS has discovered the largest known prime number: 257,885,161-1. This massive 17,425,170 digit number was discovered thanks to clever distributed computing software that uses idle computer time donated by volunteers.

The prime numbers are the atoms amongst the integers, and while we know that there are infinitely many of them, there's no general formula that generates them all. Julian Havil looks at a little-known algorithm that sieves out all primes up to a given number, and which is astonishing in its simplicity.
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