The Computing Formula of Number of Primes No More than Any Given Positive Integer

Abstract

In this paper, we give out the formula of number of primes no more than any given n ( n ∈ Z + , n > 2). At the same time, we also show the principle, derivation process of the formula and application examples, it is usually marked with π ( n ), which is: that is: where “[ ]” denotes taking integer. r = 1,2,3,4,5,6; s x = s 1 , s 2 ,..., s j , s h ; s 1 , s 2 ,..., s j ,, s h = 0,1,2,3,.... As i ≥ 2 , 2 ≤ s x ≤ i -1 ( x =1,2,..., j , h ).