Cash for Math: The Erdős Prizes Live On

There is (was? site doesn't seem to load for me..) a "bitcoins for formal proofs" site called Proof Market https://slawekk.wordpress.com/2014/01/11/proof-market

Theorems and proofs can be given in Coq or Agda format. If they pass the language's checker, bitcoins are dispensed.

From the article, I think the "remaining money" may be entirely notional. It talks about Ron Graham chipping in $5k to help cover a $10K bounty.

Besides, these days the money is mostly beside the point. It is like those Knuth reward checks, https://en.wikipedia.org/wiki/Knuth_reward_check. In most cases, certainly the most recent $500 "happy ending" problem, the bragging rights are worth more than the money.

One thing I've noticed is that some of the great problems, such as Fermat's Last Theorem, spawned entire fields of math, from which applications may have developed. It wouldn't shock me if some advances in cryptography were spinoffs of progress in pure math.

Then there's the prize for progress towards understanding the Navier-Stokes equation of fluid dynamics.

The answer to both is quite possibly, but we don't know. History has seen many mathematical curiosities gaining important practical applications, sometimes hundreds of years later. Indeed, much of computer science is based upon mathematics which was at one time impractical. A good example is strong encryption, the foundations for which were built long before we had machines that were able to implement it.