The Bateman—Horn Conjecture, Part I: heuristic derivation (Stephan Garcia, Pomona)

The Bateman—Horn Conjecture is a far-reaching statement about the distribution of the prime numbers.  It implies many known results, such as the Green—Tao theorem, and a variety of famous conjectures, such as the Twin Prime Conjecture.  In this expository talk, we start from basic principles and provide a heuristic argument in favor of the conjecture.  This talk should be accessible to undergraduates with a background in modular arithmetic.