Improved of Approximating Function Li(x)

Israfil Okumus, Ercan Celik

Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for any positive number x and let the approximating function Li(x) denote the off set integral logarithm of x. This function is a good approximation to the number of prime numbers less than x. We propose a simple modification of Li(x) gauss prediction function for reduces of π(x)-Li(x).