Tony Feng, Steenrod operations in étale cohomology and applications to the Brauer group of a surface over a finite field is an interesting and well-written preprint. Even if you are not interested in the particular result, its introduction and appendix discuss the history of a closely related result which turned out to go through various stages of having false results and being misinterpreted for over 30 years!
13532385396179 doesn’t climb to a prime concerns a rather esoteric conjecture by Conway, for which a reasonably small counterexample was found. It's a fun story to read.
In case you enjoy watching talks, there are now videos available for the following conferences.