Hardy-Littlewood Conjectures

The Hardy-Littlewood Conjectures are a set of mathematical predictions about prime numbers, which are numbers only divisible by 1 and themselves. They propose that certain patterns of prime numbers, such as twin primes (pairs like 11 and 13), occur infinitely often, and provide formulas to estimate how frequently these patterns appear as numbers grow larger. While proven for some cases, many of these conjectures remain unproven but are considered quite plausible by mathematicians, shaping much of the ongoing research in understanding the distribution of prime numbers across all natural numbers.