Number Theory

    

On Prime Numbers Between kn And (k+1)n

Authors: Wing K. Yu

In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, if n ≥ (k −1), then there always exists at least a prime number p such that kn < p ≤ (k+1)n. The Bertrand-Chebyshev’s theorem is a special case of this theorem when k =1.

Comments: 18 Pages.

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Submission history

[v1] 2022-04-29 20:27:58
[v2] 2022-05-04 01:42:26
[v3] 2022-05-15 15:47:14
[v4] 2022-06-10 11:35:36
[v5] 2023-10-21 03:14:06

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