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I have moved this question to math.stackexchange.com. People who are interested in this question can discuss at :http://math.stackexchange.com/questions/1272431/distribution-of-composite-numbers

I have moved this question to math.stackexchange.com. People who are interested in this question can discuss at :https://math.stackexchange.com/questions/1272431/distribution-of-composite-numbers

Motivation: I want to give an abstract formulation of Eratosthenes's Sieve and try to conject a property of Eratosthenes's Sieve. If this property are right, then I can use it to find a low bound of numbers of primes between any segment $[N, M+N]$ in the set of natural numbers, so this problem is connected to distribution of primes.

Motivation: I want to give an abstract formulation of Eratosthenes's Sieve and try to conject a property of Eratosthenes's Sieve. If this property are right, then I can use it to find a low bound of numbers of primes between any segment $[1,N]$ in the set of natural numbers, so this problem is connected to distribution of primes.