Number Theory

    

Existing a Prime in Interval[n^2,n^2+n/2]

Authors: Hashem Sazegar

Oppermann’s conjecture states that for every positive integer n, there exists at least one prime number between n 2 and n 2 + n. Priorto this, Legendre had conjectured that there is always at least one prime number between n2 and (n + 1)2 . In this paper, we not onlyclaim to prove Oppermann’s conjecture but also propose a smaller interval, asserting that there exists at least one prime between n 2 andn 2 + n/2.

Comments: 7 Pages.

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Submission history

[v1] 2025-10-10 20:20:23
[v2] 2025-11-15 03:41:26

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