Large Prime Gaps

Large prime gaps refer to the stretches between consecutive prime numbers where the difference is unexpectedly wide. For example, after a prime number, the next prime might be quite far away, creating a large gap. Mathematically, as numbers grow larger, these gaps can become bigger, but they still follow certain patterns and conjectures. Researchers study these gaps to better understand the distribution of prime numbers, which are fundamental in mathematics and have applications in cryptography and computer security. Despite advances, understanding the precise behavior of these gaps remains an area of active mathematical exploration.