Number Theory


An Interval Unifying Theorem About Primes

Authors: Juan Moreno Borrallo

In this paper it is proved the existence of a prime number in the interval between the square of any natural number greater than one, and the number resulting from adding or subtracting this natural number to its square (Oppermann’s Conjecture). As corollaries of this proof, they are proved three classical prime number’s conjectures: Legendre’s, Brocard’s, and Andrica’s. It is also defined a new maximum interval between any natural number and the nearest prime number. Finally, it is stated as corollary the existence of infinite prime numbers equal to the square of a natural number, plus a natural number inferior to that natural number, and minus a natural number inferior to that natural number.

Comments: 13 Pages.

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Submission history

[v1] 2017-07-03 02:59:01 (removed)
[v2] 2017-07-04 11:23:12 (removed)
[v3] 2017-07-05 03:11:26
[v4] 2017-07-11 07:05:28
[v5] 2017-07-18 03:50:04

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