Quote:
Originally Posted by goldbug
Thanks batalov and uau for the collision suggestion and to uau for running up to 1M^2?!?
This suggestion is going to help me greatly in extending the search to triplets, quadruplets of primes. Ideally it would be amazing to show that numbers of this form do not exist, or at least above some threshold. Can you see why? I will post here if I find any. Although, the triplets have a different form so the collision method becomes a little combinatoric as we generalize the problem upward.
2np1=p2^a*p3^b
2np2=p1^c*p3^d
2np3=p1^e*p2^f

my cases can be generalized to any number of prime powers...