## On Prime Numbers and Arithmetic Progressions |

**Professor Alan Taylor**

Union College

January 12, 2015

5:00 pm

Bailey Hall 207

Refreshments will be served in Bailey Hall 204 4:45pm

The number-theoretic study of the interplay between prime numbers and arithmetic progressions goes back to some early work of Lagrange and Waring in the 18th century. Questions that have since arisen include the following:The answer to the first (Dirichlet’s theorem) is one of the deepest results of the 19th century. The answer to the second (the Green-Tao theorem) is one of the deepest results of the 21st century. We’ll discuss these along with the original theorem (and proof) of Lagrange and Waring.

- Does every long arithmetic progression contain a large set of primes?
- Does every large set of primes contain a long arithmetic progression?

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Fri Apr 20 01:01:19 EDT 2018 |