# Plus Advent Calendar Door #23: Prime pleasures

23 is a prime number. Mathematicians love primes. But why? Find out with this prime collection of prime articles.

Mathematical mysteries: the Goldbach conjecture

There are lots of seemingly easy questions about primes that are nevertheless hard to answer. Here's the Goldbach conjecture.

Elusive twins

Primes tend to come in pairs: 5 and 7, 11 and 13, and so on. But do they really? That's the question posed by the twin prime conjecture.

Primes lie at the heart of one of the hardest open problems in maths. Find out more with The prime number lottery, The music of the primes and A whirlpool of numbers.

Safety in numbers

Primes are also what keeps your credit card details safe when you buy something over the internet. Find out how with Simon Singh.

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. Here are two ways of sieving out all primes up to a given number: Sundaram's sieve and a geometrical method.