In 2014 Stijn Hanson, then our Academic Secretary, completed his studies at York by producing a very interesting dissertation on prime numbers, and moreover discovering some interesting results in this area. He has decided to let us host his dissertation on the website under a Attribution-Noncommercial-Sharealike 4.0 International License.
Without further ado, here is a brief description in the author's own words, and the actual document,
Since antiquity mathematicians have studied prime numbers. They are the building blocks of all numbers and yet mask some of the deepest mysteries in all of mathematics. This paper is a survey of some of the recent progress made towards the notorious twin prime conjecture, which asks whether there are an unlimited number of primes which are two apart, and contains some original results by the author.