Number Theory


An Approximation to the Prime Counting Function Through the Sum of Consecutive Prime Numbers

Authors: Juan Moreno Borrallo

In this paper it is proved that the sum of consecutive prime numbers under the square root of a given natural number is asymptotically equivalent to the prime counting function. Also, it is proved another asymptotic relationship between the sum of the first prime numbers up to the integer part of the square root of a given natural number and the prime counting function.

Comments: 6 Pages.

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Submission history

[v1] 2017-10-19 02:50:41

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