Every year the University of Southampton runs the National Cipher Challenge.
Pit your wits against the brightest in the nation (and perhaps win some prizes)!
Our understanding of the prime numbers is progressing very slowly.
In the 3rd century before Christ, Eratosthenes developed a method for finding all primes up to a given integer. It is known as The Sieve of Eratosthenes. Other early historical developments are detailed here.
But, although slow, knowledge is progressing! Here‘s an interesting article dealing with recent developments, including research which proves that there are an infinite number of primes which contain the digit 7.
On a more simple level, this is a beautiful graphical representation of prime factorisation. Enjoy!