Green-Tao Theorem
The Green-Tao Theorem is a significant result in number theory that states there are infinitely many arithmetic progressions of prime numbers. An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. For example, the sequence 3, 7, 11, 15 consists of numbers that increase by 4.
This theorem was proven by mathematicians Ben Green and Terence Tao in 2004. Their work combined techniques from various areas of mathematics, including analytic number theory and combinatorics, to show that primes can be found in regular patterns, challenging the traditional view of their distribution.