Somebody reblog with that one Sonic fandub meme of "what the FUCK are you talking about", because that is the EXACT emotion I'm experiencing here.
Alice and Bob are playing Magic: the Gathering. If Alice does nothing, Bob will win next turn.
Bob's current position allows him to respond to anything Alice does by doing a Stupid Card Trick that grants him an arbitrarily large number of hit points. By "arbitrarily large", we mean that Bob can pick any number he wants, but it has to be finite; i.e., he can't say "infinity plus one".
Alice's plan is to do something that will break the setup that permits Bob's Stupid Card Trick, thereby forcing him to pick a number of hit points for it to give him before he loses it. Alice will then follow up with her own Stupid Card Trick which allows her to deal an arbitrarily large amount of damage.
So all Alice needs to do is say a number that's larger than the number Bob said, and she wins, right?
Well, not quite. Unlike Bob's Stupid Card Trick, Alice's Stupid Card Trick only works if the number she picks is prime. If anything Bob does in response prevents her from picking a prime number, she does no damage, and Bob wins next turn.
It so happens that Bob does have the ability to respond in a way that reduces the number Alice picked by one. Any prime number minus one is non-prime, so this counters Alice's Stupid Card Trick.
But: Alice has the ability to counter Bob's counter by reducing the number she picked by a further one. This puts her back in business if and only if the prime number she picked in the first place is still prime after having two subtracted from it.
The question is, then: is it guaranteed that Alice can always pick a prime number that's larger than Bob's number and is still prime after having two subtracted from it, no matter what number Bob picks?
Answering that question requires proving the twin prime conjecture, one of the great unsolved problems of mathematics.
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