The good news is that this will never see the inside of a courtroom, as publishing factorizations of numbers is legal. So is doing whatever you want to your own hardware.
But anyway, how hard does the math problem have to be before it becomes illegal to solve? If my signing key is 4, would it be illegal for someone to say "Gentlemen, it has come to my attention that the number 4 is the product of 2 and 2."? Why?
How is 4 different from
68575999143494039
77654744967172758
17990411426461294
73261271699761332
96980951450542789
80888450430107555
07864648023040197
95402754670660318
614966266413770127 ? (I need to know what the law is before I can try to avoid breaking it.)
Also, is the mere act of looking up the factorization of this number in a table illegal? If not, what about using a program that has the number stored in a table? If not, what if that program lazily computes the factorization. Is strict evaluation legal, but not lazy evaluation?
How about if I have a friend that randomly wants to know the factorization of a number and I compute it in my head? What if it's for breaking a cryptosystem, but I don't know that, I just think it's a problem he's challenging me with? Who broke the law? What law was broken?
Anyway, I don't think you've thought this through. You used the word "cute" dismissively, though, which was very cute...