Problems & Puzzles: Conjectures

Conjecture 32. The ABC Conjecture

Here we deal with one computational consequence of the so called "ABC Conjecture": 


  • A + B = C

  • gcd(A, B) = 1

  • R = product of the distinct prime factors in (A*B*C)

  • Q=log(c)/log(R)

Find a value of Q larger than Q = 1.629911 produced by A = 2, B = 6436341 (*) or show that this is the largest value possible for Q.


* Found by Eric Reyssat according to


Frank Rubin wrote on Sept 07:

On the Conjecture 32 webpage you might like to add a link to Bart de Smit's webpage on this same problem. ...

The University of Leiden has a huge project going to try to find these ABC Triples.  They have a network of over 22,000 computers working on it.  I was very lucky to find 6 triples that they did not find, especially since they had about a 20 year lead.



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