Andrew Granville: The Patterns in the Primes

source: Yale University    2015年8月20日
Math Mornings is a series of public lectures aimed at bringing the joy and variety of mathematics to students and their families. Speakers from Yale and elsewhere talk about aspects of mathematics that they find fascinating or useful. The talks will usually be accessible to students from 7th grade and up, although occasionally some familiarity with high-school subjects will be helpful. Math Mornings lectures will take place on three Sundays each semester, at Davies Auditorium, 10 Hillhouse Avenue.

Math Mornings is partially funded by grants from the National Science Foundation. It is part of Yale's Science Outreach program. To find out more see http://yale.edu/scienceoutreach

On Sunday, March 30, Andrew Granville gave his talk, "The Patterns in the Primes." A whole number, greater than 1, is a prime number if, and only if, it is not the product of two smaller whole numbers. The sequence of primes begins 2, 3, 5, 7, 11, 13, ... Are there any predictable patterns in the prime numbers? Is there are a formula for primes? Perhaps the main difficulty in answering these questions is that primes are defined in terms of what they are not (that is, they are not the product of two smaller whole numbers), rather than what they are, which makes them surprisingly difficult to understand. In this talk, Andrew Granville reviews what is known to be true, what we believe to be true but cannot prove, as well as discusses some wild speculations. He explores some of the latest most exciting discoveries in the theory of prime numbers, and see how we can apply those discoveries.