The relationship between the values of the error of calculation, and the space between primes

I understand the formula algorithm sieve of Eratosthenes

 This is the formula of the state, and not as a process, and hence all the problems.
But. There is a formula status, the recurrent formula, then you can consider in the opposite direction. Have the ending value of the

 we calculate the average value of

 Can definition (average value) and not very successful. But as long as you can, and so.

 

if we take N=m, where

 We have the formula for calculating the number of Prime numbers in the interval (0, m) when using the (average value).

Error of calculation depends on size of the space between the neighbouring Prime numbers.

 

This is the first formula, where the calculation magnitude of the error depends on the size of the gap between Prime numbers. For example:

 For example, a small table, values of the errors and the values of the gaps between primes. Number of Prime numbers from n=113 to n=127

The dependence of the error of the space, clear, and this is already a movement in the right direction.

Need to temporarily deviate from the General problem of determining the amount of errors in the computation of the number of Prime numbers in an interval. And go to a small private problems, for example in the simple number of and according to the formula algorithm sieve of Eratosthenes, find the next Prime number.

592,3888178679213	2	113
-472,4512455464308	12
-216,9030068656899	10
707,1021386805979	2
461,2867642163871	4
228,6685971646266	6
237,9450576627286	6
675,4368512268981	2
-463,1180393514804	12
500,3946198714099	4
272,201770363307	6
68,97173636254943	8
-146,0691796973624	10
130,73115586565	8
-73,30016050211227	10	127