# Difference between revisions of "ABC conjecture"

The abc conjecture asserts, roughly speaking, that if a+b=c and a,b,c are coprime, then a,b,c cannot all be too smooth; in particular, the product of all the primes dividing a, b, or c has to exceed $c^{1-\varepsilon}$ for any fixed $\varepsilon \gt 0$ (if a,b,c are smooth).
This shows for instance that $(1-\varepsilon) \log N / 3$-smooth a,b,c of size N which are coprime cannot sum to form a+b=c. This unfortunately seems to be too weak to be of much use for the finding primes project.