r/mathriddles • u/kgndgn • 1h ago
Hard Prime number game
I'm going to teach you a game. Your goal is to find how far you can get.
You start with the numbers 1, 2, and 3. Using each number at most once, you may add or subtract any combination of them to obtain the next prime number.
Whenever you successfully obtain the next prime, that prime is added to your set of available numbers. You then repeat the process, always trying to generate the next prime number using each available number at most once.
How far can you go? What is the first prime number that you can no longer obtain?