After 2000 years of searching we only know of 51 perfect numbers and they're all even. What else do and don't we know about these rare and precious jewels of maths?

A new prime number with nearly 25 million digits was discovered just in time for Christmas.

Prime number enthusiasts discover new largest prime with 22,338,618 digits.

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

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.