The largest prime factor of X3+2

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2014 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Acta Arithmetica, volume 171, pages 67-80 (issn: 0065-1036, eissn: 1730-6264,

Copyright policy )

Authors: Irving, A. J.;

doi: 10.4064/aa171-1-5 , 10.48550/arxiv.1412.0024

arXiv: 1412.0024

The largest prime factor of X3+2

- Summary
- Subjects
- Metrics

Abstract

Improving on a theorem of Heath-Brown, we show that if $X$ is sufficiently large then a positive proportion of the values $\{n^3+2:n\in (X,2X]\}$ have a prime factor larger than $X^{1+10^{-52}}$.

15 pages

Related Organizations

University of Montreal
Canada

Keywords

Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT)

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	1
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

1

Average

Green

Fields of Science (3) View all

Fields of Science