  This is an extension and background to a talk I gave on 9 October 2013 to the
Brown Graduate Student Seminar, called `A friendly intro to sieves with a look
towards recent progress on the twin primes conjecture.' During the talk, I
mention several sieves, some with a lot of detail and some with very little
detail. I also discuss several results and built upon many sources. I'll
provide missing details and/or sources for additional reading here.

Number Theory