The problem with that is knowing that you have the minimum. The good thing about the question as asked is that it's asking for something specific and not a proof of impossibility. Your question is legitimate and interesting, but requires a proof of minimality.
A different question would be "who can come up with the smallest c in 6 months", which probably wouldn't yield the true answer, but for a $1M prize it might come quite close (and could lead to some interesting theoretical advancements).
