On the Number of Primes in the Interval (<i>x</i>, 2<i>x</i>) by an Elementary Method

Abstract

An elementary formula to know the number of primes in the interval ( x , 2 x ) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1, 2 x ]). An elementary method to know the number of primes in a given magnitude is suitably placed in the form of a general formula, and we have proved it. The general formula is applied to the terms of the equation , and a tactical simplification of the terms gives rise to an expressio n whose verification envisages scope for its further studies.