Becker–Stigler Conjecture

The Becker–Stigler Conjecture suggests that the only polynomial functions that satisfy a specific mathematical property involving the distribution of prime numbers are the simple squared functions, like \( n^2 \). In essence, it predicts that certain functions that preserve structures related to prime numbers are limited to these quadratic forms, implying a deep connection between polynomial structures and prime distribution. The conjecture has implications in number theory and the understanding of how primes are arranged, but it remains unproven and is a subject of ongoing mathematical research.