Abstract: A 1938 result of Rankin shows that there are consecutive primes less than 
whose difference is (loglog{x})(loglogloglog{x})/(logloglog{x})^2)
. Over the past 75 years, improvements have only been in the implied constant. We will show how one can use recent progress on small gaps between primes to quantitatively improve this bound. A similar improvement was found independently by Ford, Green, Konyagin and Tao using different techniques.
