where x \geq 2 and c is an absolute positive constant. (The proof involves a curious induction procedure which they call real type induction). They have also other results. For example if P is contained in [2,x1-\delta] then G(x,K) \geq c, \delta e-Kx, where \delta > 0 is arbitrary and c1 is an absolute positive constant. They also study max F(x,A) where A ranges over more general sets of integers.
Classif.: * 11N35 Sieves
11N05 Distribution of primes
Keywords: small sieve; sifting by primes; coprime sifting set
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