Number 6 on the unsolved problems list ("Is there an arithmetic progression of consecutive primes for any given (finite) length?") was solved affirmatively in 2004: https://en.wikipedia.org/wiki/Green%E2%80%93Tao_theorem

I once wrote a small python code that spat out a melody made from the difference between consecutive prime numbers. Probably not of significant import for mathematical research. But fun to listen to.