A newer extreme abc-example due to Tim Dokchitser
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Tim Dokchitser just wrote a paper "LLL & ABC" in which he presents 
(apart from developing a new interesting method for abc-hunting)
a new record for the uniform abc-conjecture. 

Let r = (3+sqrt(13))/2. Then

   r^-5 (r-1) + r^5 (r-2) = 2^9
   
has quality 2.02922... 

My congratulations to Tim!

It's not hard to see that this example is related to 
2^16 - 13 71^2 = -3.

August 2003,
Benne de Weger