On properties of the numbers coprime with the primes up to p_n
Abstract
In this paper we investigate about the effective distribution of the numbers coprime with the primes up to p_n .More precisely we prove that these numbers form a periodically monotone sequence . Then we examine some properties of this sequence which, in a certain sense, are transferred to the sequence of primes. Moreover we study the distribution of twin and cousin terms within the above sequence . This study also makes furthermore strongly plausible that the set of twin primes as well as the set of cousin primes is infinite.
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