Abstract

In this paper we will present some inequality on some subsequence of the sequence of prime numbers such that ≡ 1(mod2k+1), where k is positive integer. We prove that for every positive integer k there exists a positive constant real number Kk, such that for every real number λ>Kk, there exists a natural number nλ, such that for every natural number n>nλ, it is true the inequality Π Pki/Pki-2k<λPkn/2k.n, where Pkn is the n-th prime number≡ 1(mod 2k-1) . The constant Kk is equal with e2k.M(2k+1,1)+22k.σk, where M(2k+1,1)is the Merten’s constant and σk is the sum of the convergent series ΣpΞ1(mod2k+1) 1/p(p-2k). We find approximate values of constant k1 and k2.

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References

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