Conjecture on the value of Pi(10^26), the number of primes less than 10^26

TL;DR

This paper proposes a conjecture for the number of primes less than 10^26 by interpolating known values of Pi(10^n) and using corrective functions, aligning with classical prime counting functions.

Contribution

It introduces a novel polynomial interpolation method with corrective functions to estimate Pi(10^26), extending known prime counts.

Findings

Conjectured range for Pi(10^26) aligns with Eulerian logarithmic integral.

Interpolation method shows consistency with Riemann functions.

Provides a new approach to estimating large prime counts.

Abstract

Based on the first 25 known values of Pi(10^n), the number of primes less than 10^n, with n integer between 1 and 25, we propose a conjectured value range of Pi(10^26) calculated by using polynomial interpolations with two corrective functions obtained by Thiele interpolations on relative differences of exact and interpolated values of Pi(10^n). The conjectured range value is in agreement with values obtained by the Eulerian logarithmic integral and with the Riemann functions.