Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-5, author = {A. J. Irving}, title = {The largest prime factor of X$^3$ + 2}, journal = {Acta Arithmetica}, volume = {168}, year = {2015}, pages = {67-80}, zbl = {06487226}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-5} }
A. J. Irving. The largest prime factor of X³ + 2. Acta Arithmetica, Tome 168 (2015) pp. 67-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-1-5/