A large integer is a sum of two prime avoiding numbers

Abstract

Let $f(n)={\min }_p|n-p|$, where $p$ is a prime. We show that there is a positive constant $\delta$ such that for any large integer $N$ there exist two positive integers $n_1$ and $n_2$ such that $N=n_1+n_2$ and $f(n_i)\gg \ln N(\ln \ln N{)}^{\delta }$, $i=1,2$.

The same result was obtained by M. R. Gabdullin. This version will not be published in this form. It will appear in a joint manuscript by M. R. Gabdullin and A. O. Radomskii

References in corpus (1)

• Long gaps in sieved sets