Primes in the form $[αp+β]$

Details Primes in the form $[αp+β]$ Primes in the form $[αp+β]$

2008-03-12

arxiv.org/abs/0803.1740v3

Mathematics

Number Theory

Scientific paper

Let \beta be a real number. Then for almost all irrational \alpha>0 (in the
sense of Lebesgue measure)
\limsup_{x\to\infty}\pi_{\alpha,\beta}^*(x)(\log x)^2/x>=1, where
\pi_{\alpha,\beta}^*(x)={p<=x: both p and [\alpha p+\beta] are primes}.

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