Number Theory

    

Prime Numbers Estimation in A Special Palindromic Number

Authors: Zhi Li, Hua Li

The repunit number refers to the natural number composed of all the numbers 1, which is a special palindromic number. Whether the number of prime numbers in the repunit number is infinite, and how to calculate the number of prime numbers less than a certain integer have not been determined. This paper proves that the number of prime numbers of this kind is infinite by using the method of probability and statistics, and derives the calculation formula of it. On this basis, two conjectures are further proposed, that is, the ratio of the number of prime numbers in this palindromic number to the number of prime numbers in Mersenne number is 16ln (2)/(15ln (10)), and the number of prime numbers less than 24862048 digits is close to 15.

Comments: 3 Pages.

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Submission history

[v1] 2022-11-05 02:02:35

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