Number Theory

    

Primality Test and Factorization Using Lambert Series Near Q=1

Authors: Jesus Sanchez

In this paper we will demonstrate that we can check if a number is prime, the number of factors it has and even information about these factors using the following integral: q=1/2π ∫_(-π)^π〖e^pjω (L_(〖(e〗^(-jω))) (s,2)-e^(-2jω)/(1-e^(-jω) )) 〗 dω (1) Where p is the number to be checked and L_(〖(e〗^(-jω))) (s,2) represents the Lambert series that will be studied in the paper. All the steps to arrive to that integral will be shown although they will be very similar to the already shown in [12][13]. In this paper to calculate the Lambert series apart from the summation that comes from its definition, it will be used the paper by Banerjee-Wilkerson [14] that provides closed solutions for different cases. In the conclusions, it will be shown if this exercise is computationally worth to make the primality test and calculate the factors of a number p.

Comments: 26 Pages.

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Submission history

[v1] 2022-06-18 09:41:47

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