**Title:** Patterns in the Primes

**Speaker:** Professor Andrew Granville

**Speaker Info:** University of Montreal

**Brief Description:**

**Special Note**: **Annual Undergraduate Prize Lecture & Awards Ceremony**

**Abstract:**

Primes are the building blocks from which the integers are made, and so it is of interest to understand how they are distributed. Questions abound:* How many primes are there? * How many primes are there up to a given point? * Is there a good formula that tells us what is a prime and what is not? * Is there a way to find out quickly whether a given integer is prime? * How many primes are there in certain patterns? * Do polynomials take on many prime values? How about consecutive prime values? * How are primes spaced?

Versions of some of these questions are considered to be among the most difficult open problems in mathematics. On the other hand there has been spectacular recent progress on several of these questions. We will discuss all this and more in this lecture.

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