A Modified Formula of Function Li (X) For Prime Number Counting

Abstract

Zhi Li and Hua Li

To calculate the number of prime numbers, the prime number theorem function x/ln (x) and Gaussian function Li (x) are most commonly used. However, the former is always less than and the latter is always greater than the actual number of prime numbers, and the deviation increases with the increase of the order of magnitude. The function p (x) has been proposed to improve x/ln (x). Now the Gaussian function Li (x) is dynamically modified, and a more ideal prime number estimation function q (x) is obtained. Numerical experiments show that the modified q (x) calculation is simple and accurate compared with the calculation results of p (x) and Riemann function R (x). 

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