T. Cochrane and R. E. Dressler [CD] proved that the abc-conjecture implies that, for every > 0, the gap between two consecutive numbers A with two exceptions given in Table 2.
@article{bwmeta1.element.bwnjournal-article-cmv82i1p79bwm,
author = {Jerzy Browkin},
title = {A consequence of an effective form of the abc-conjecture},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {79-84},
zbl = {0959.11041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p79bwm}
}
Browkin, Jerzy. A consequence of an effective form of the abc-conjecture. Colloquium Mathematicae, Tome 79 (1999) pp. 79-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p79bwm/
[000] [B] J. Browkin, The abc-conjecture, to appear. | Zbl 0971.11010
[001] [CD] T. Cochrane and R. E. Dressler, Gaps between integers with the same prime factors, Math. Comp. 68 (1999), 395-401. | Zbl 0929.11031