Proof of the existence and finding the minimum point of equilibrium.

Equilibrium point - at these points, margin of error in the calculation of the number of primes in the interval change periodically sign.

This result is pure computation error. This follows from the calculations for the derivation of the algorithm of the sieve of Eratosthenes. The first step, every prime number subtracted from the calculation error, the value is equal.

hence, the net error divided, on a one-time deductible amount.

and you get.

result, the number of prime numbers that are redeemed in whole error. What's next. At least on the same segment of composite numbers as prime and repay all the computation error. Each compound number adds to the uncertainty of the calculated values ​​equal

Hence the second step. At maturity, the entire error, a new computation error, which is equal

she was again divided by the value of a one-time deductible

and count the number of prime numbers and repay this new computation error

And so on.

 compare

 n>1

The limit of the sum of me not figure out (if it is), if and only if the number of terms in the series to limit the number (n)

 We prove the existence and find the minimum point of equilibrium