Geodesic
Prime avoiding numbers form a~basis of order~$2$
Sbornik. Mathematics, Tome 215 (2024) no. 5, pp. 612-633

Voir la notice de l'article provenant de la source Math-Net.Ru

For a positive integer $n$ we denote by $F(n)$ the distance of $n$ to the nearest prime number. Using the technique from the recent paper “Long gaps in sieved sets” by Ford, Konyagin, Maynard, Pomerance and Tao (J. Eur. Math. Soc., 23:2 (2021), 667–700) we prove that every sufficiently large positive integer $N$ can be represented as a sum $N=n_1+n_2$, where $F(n_i) \geq (\log N)(\log\log N)^{1/325565}$ for $i=1,2$. This improves the corresponding ‘trivial’ statement where only the inequality $F(n_i)\gg \log N$ is assumed. Bibliography: 17 titles.
Keywords: prime numbers, basis, sieving. 
@article{SM_2024_215_5_a1,
     author = {M. R. Gabdullin and A. O. Radomskii},
     title = {Prime avoiding numbers form a~basis of order~$2$},
     journal = {Sbornik. Mathematics},
     pages = {612--633},
     publisher = {mathdoc},
     volume = {215},
     number = {5},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_5_a1/}
}
TY  - JOUR
AU  - M. R. Gabdullin
AU  - A. O. Radomskii
TI  - Prime avoiding numbers form a~basis of order~$2$
JO  - Sbornik. Mathematics
PY  - 2024
SP  - 612
EP  - 633
VL  - 215
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2024_215_5_a1/
LA  - en
ID  - SM_2024_215_5_a1
ER  - 
%0 Journal Article
%A M. R. Gabdullin
%A A. O. Radomskii
%T Prime avoiding numbers form a~basis of order~$2$
%J Sbornik. Mathematics
%D 2024
%P 612-633
%V 215
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2024_215_5_a1/
%G en
%F SM_2024_215_5_a1
M. R. Gabdullin; A. O. Radomskii. Prime avoiding numbers form a~basis of order~$2$. Sbornik. Mathematics, Tome 215 (2024) no. 5, pp. 612-633. http://geodesic.mathdoc.fr/item/SM_2024_215_5_a1/