I came across the EXPLICIT abc-conjecture which states the following :
Let $a,b,c\ge 1$ be coprime integers with $a+b=c$ (The condition $a+b=c$ implies that "pairwise coprime" and "coprime" are equivalent conditions).
Denote $n=rad(abc)$ , where $rad(m)$ is the product of the distinct prime factors of $m$ and $\omega=\omega(n)$ the number of distinct prime factors of $n$.
Then, the inequality $$c<\frac{6}{5}\cdot n \cdot\frac{\ln(n)^{\omega}}{\omega!} $$
holds
Questions :
I verified the conjecture for $a,b\le 10^4$ and noticed that it is false for the pair $(a,b)=(1,1)$. I assume this pair is ruled out and $a<b$ is assumed WLOG. Is this correct ?
Upto which $c$ has this conjecture be verified ?