An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function
An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function
Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable. These methods also offer avenues for number-theoretic exploration through analytical manipulation. In this work, we introduce a novel approximation function, …