Large Gaps between Consecutive Prime Numbers
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چکیده
Let G(X) denote the size of the largest gap between consecutive primes below X . Answering a question of Erdős, we show that G(X) > f(X) logX log logX log log log logX (log log logX) , where f(X) is a function tending to infinity with X . Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes. CONTENTS
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تاریخ انتشار 2014