I do have a question about one part of your disproof:
Spoiler for Question
The disproof stands.
I speculated, Bushindo's code could be something similar to the inductive step in my disproof.
This problem runs deeper than it appeared at the first glance. However, our tag team solution is practical. It must be exact for any intermediate sum past infinity. And 137, as it turns out, is a hefty step towards the infinity.
Edited by Prime, 15 January 2013 - 06:26 PM.