@11011110 I've asked the same question a couple of years ago because it is related to the certificate complexity of being a prime. It got the answer 47867742232066880047611079, see
@11011110 This problem is quite closely related: https://mathoverflow.net/questions/52825/coloring-mathbb-zk
@jsiehler How about the chromatic number of the plane? Easy to state with finite unit-distance graphs (assuming ZFC). https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem
I made some Smullyan-style metapuzzles using this observation for Sudoku many years ago. They were of the type that suppose that some fields are missing from a Sudoku puzzle, fill out the rest of it.
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