Author(s)

Wing K. Yu

Independent Researcher, Arlington, Washington State, USA.

In this paper, we prove Legendre’s conjecture: There is a prime number between n² and (n +1)² for every positive integer n. We also prove three related conjectures. The method that we use is to analyze binomial coefficients. It is developed by the author from the method of analyzing binomial central coefficients, that was used by Paul Erdős in his proof of Bertrand’s postulate - Chebyshev’s theorem.

Legendre’s Conjecture, Bertrand’s Postulate - Chebyshev’s Theorem, Oppermann’s Conjecture, Brocard’s Conjecture, Andrica’s Conjecture

Yu, W. (2023) The Proofs of Legendre’s Conjecture and Three Related Conjectures. Journal of Applied Mathematics and Physics, 11, 1319-1336. doi: 10.4236/jamp.2023.115085.