Sieving Very Thin Sets of Primes, and Pratt Trees with Missing Primes
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چکیده
Suppose P is a set of primes, such that for every p ∈ P , every prime factor of p − 1 is also in P . We apply a new sieve method to show that either P contains all of the primes or the counting function of P is O(x) for some c > 0, where c depends only on the smallest prime not in P . Our proof makes use of results connected with Artin’s primitive root conjecture.
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تاریخ انتشار 2013