Ridiculous counterfactual. The LLM started failing 100% of the time 60! orders of magnitude sooner than the point at which we have checked literally every number.

This is not even to mention the fact that asking a GPU to think about the problem will always be less efficient than just asking that GPU to directly compute the result for closed algorithms like this.

Correctness in software is the first rung of the ladder, optimizing before you have correct output is in almost all cases a complete waste of time. Yes, there are a some scenarios where having a ballpark figure quickly can be useful if you can produce the actual result as well and if you are not going to output complete nonsense the other times but something that approaches the final value. There are a lot of algorithms that do this (for instance: Newton's method for finding square roots).

99.7% of the time good and 0.3% of the time noise is not very useful, especially if there is no confidence indicating that the bad answers are probably incorrect.