Question about filters (sieve of Eratosthenes)
- The following is interpretable as a question about filters, indexed by
the set of primes in the interval I define as [1,y], in the sieve of
Eratosthenes, and how they can be arranged.
Let x and y be integers such that 0<x<y.
Let G(x,y) be the number of composites in an interval of length
(y-x+1) that contain no factor in [2,y].
If p is a prime in the set of primes in [1,y], is there a standard
proof (or disproof) that, for all intervals [1+k,y+k] for which, for
all p, there are floor(n/p) integers i for which p|i, G(1+k,y+k) plus
the number of primes in [1,y] /\ [1+k,y+k] is maximal if k=0
With thanks in advance.