Gödel numbers are typically associated with formal mathematical statements, and there isn’t a formal proof for 2+2=5 in standard arithmetic. However, if you’re referring to a non-standard or humorous context, please provide more details.

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Of course I don’t know enough about the actual proof for it to be anything but a joke but there are infinite numbers so there should be infinite proofs.

there are also meme proofs out there I assume could be given a Gödel number easily enough.

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