Number Theory


The Prime Counting Function and the Sum of Prime Numbers

Authors: Juan Moreno Borrallo

In this paper it is proved that the sum of consecutive prime numbers up to the square root of a given natural number is asymptotically equivalent to the prime counting function. Also, they are found some solutions such that both series are equal. Finally, they are listed the prime numbers at which both series are equal, and exposed some conjectures regarding this type of prime numbers.

Comments: 6 Pages.

Download: PDF

Submission history

[v1] 2019-11-18 11:12:58

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