Here is the Wiki on Bounded Gaps Between Primes that we looked at in
class. It shows the most recent value as mathematicians work trying to prove the Twin Primes Conjecture. (We would like to get down to H=2.) Pay particular attention
to all the mistakes that were made by mathematicians as they worked on this, and how many different people made contributions.
Here is a Book on Primes written for a general audience -- no advanced knowledge of math required!