On Selberg's approximation to the twin prime problem

2015/04/16 by Balasubramanian, R., Srivastav, Priyamvad
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1504.04347

Abstract

In his Classical approximation to the Twin prime problem, Selberg proved that for x sufficiently large, there is an n ∈ (x,2x) such that 2^Ω(n)+2^Ω(n+2) ≤ λ with λ=14, where Ω(n) is the number of prime factors of n counted with multiplicity. This enabled him to show that for infinitely many n, n(n+2) has atmost 5 prime factors, with one having atmost 2 and the other having atmost 3 prime factors. By adopting Selberg's approach and using a refinement suggested by Selberg, we improve this value of λ to about λ=12.59.

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