There are several conjectures in Mathematics that seem to be true but have not been proved. Of course, as computing power increased, folks have expanded their search for counterexamples ever and ever upwards.

Providing a counterexample to a conjecture with a very large number would be interesting, but I cannot think of any non-trivial examples where a really large number has been found to disprove a (non-trivial) conjecture. I've seen plenty of large numbers serving as bounds to some value, but usually this is something known to be bounded (i.e. finite) anyway.

Out of curiosity, what's the largest counterexample you've seen to disprove a conjecture?

  • $\begingroup$ An interesting link: [The phenomena of eventual counterexamples][1] [1]: mathoverflow.net/questions/15444/… $\endgroup$ – lsr314 Jul 23 '13 at 0:03
  • $\begingroup$ Ah, I figured someone would have asked this! My search-fu on this site is not very good. $\endgroup$ – Emily Jul 23 '13 at 0:06

Google about Polya's conjecture. I don't know if it is the largest, though. The smallest number that is a counterexample is $906.150.257$, yet it is quite large.

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