A New Approximation of Prime Counting Function Based on Modified Logarithmic Integral
Marko V. Jankovic · HAL (Le Centre pour la Communication Scientifique Directe) · 2021
In this paper, a novel approximation of the prime counting function, based on modified Eulerian logarithmic integral, is going to be presented. Proposed approximation reduces the approximation error without increase of computational complexity when it is compared to approximation based on Eulerian logarithmic integral. Experimental results were used to support the claim. Combining proposed method with |Riemannian approximation of prime counting function it is possible to design the new approximation function that outperforms Riemannian approximation for all values that were analyzed.