## prime number

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.

**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.

**Abigail Kirk**investigates a method that does just that.

- Happy birthday Plus! — celebrating 10 years of bringing mathematics to life
- Plus 10 — what were the greatest mathematical advances in the last decade?