Zhang's theorem

Zhang's theorem is a significant result in number theory that relates to prime numbers, specifically in understanding how well certain prime-related functions approximate each other. It builds on the famous Goldbach conjecture, which suggests that every even number can be expressed as the sum of two primes. Zhang proved that there are infinitely many pairs of primes separated by a finite gap—meaning primes tend to appear close together infinitely often—implying that prime numbers can be "clustered" more closely than previously proved. This work advances our understanding of the distribution of primes and their pattern of occurrence along the number line.