In [Nature Vol 580](https://www.nature.com/articles/d41586-020-00998-2), in an article about Shinichi Mochizuki's proposed proof of the abc-conjecture, there is a formulation saying:



> 
> The conjecture roughly states that if a lot of small primes divide two numbers $a$ and $b$, then only a few, large ones divide their sum, $c$.
> 
> 
> 


Is that a relevant description, and if so, how to see the connection?



A soft question on the ABC conjecture
If you are interested in the largest prime factor of $ab(a+b)$,
there is [xyz conjecture](https://arxiv.org/abs/0911.4147).


Smooth solutions to the abc equation: the xyz Conjecture


This paper studies integer solutions to the ABC equation A+B+C=0 in which none of A, B, C has a large prime factor. Set H(A,B, C)= max(|A|,|B|,|C|) and set the smoothness S(A, B, C) to be the largest prime factor of ABC. We consider primitive solutions (gcd(A, B, C)=1) having smoothness no larger than a fixed power p of log H. Assuming the abc Conjecture we show that there are finitely many solutions if p<1.


