ABSTRACT. A prime number is a whole number larger than 1, which is divisible only by itself and 1. Prime numbers are used in daily life in many ways, including encryption of sensitive data entered online. Euclid has shown that there are infinitely many prime numbers. Two primes which differ by 2 are called twin primes, like (3,5), (5,7), (11,13). The famous twin prime conjecture claims that there are infinitely many twin primes. This question has been unanswered for centuries. Professor Zhang achieved the first significant breakthrough in this area in the last many years. The methods developed by Professor Zhang will be applicable to a wide range of number theory problems. In this lecture, Professor Zhang will give an elementary survey of the problems and discuss his methods.

The Rockwell Lecture will be accessible to the public, including high school students and non‐mathematicians.