The Proofs of Legendre’s Conjecture and Three Related Conjectures  

作　　者：Wing K. Yu Wing K. Yu(Independent Researcher, Arlington, Washington State, USA)

机构地区：[1]Independent Researcher, Arlington, Washington State, USA

出　　处：《Journal of Applied Mathematics and Physics》2023年第5期1319-1336,共18页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Legendre’s Conjecture Bertrand’s Postulate - Chebyshev’s Theorem Oppermann’s Conjecture Brocard’s Conjecture Andrica’s Conjecture 

分 类 号：O17[理学—数学]