"is there a biggest prime, or can I always find a bigger one?"
A prime primer: Simon Singh gives an overview of what prime numbers are.

"a strange mathematical landscape whose contours held the secrets of how the primes were distributed"
Patterns and landscapes: Marcus du Sautoy takes us deeper into the patterns of prime numbers.

"they’re like the hydrogen and oxygen of the world of mathematics"
Talking primes: BBC Radio 4's Material World discusses what these numbers might mean.