are playing a game with the following rules:
- The game starts with a parameter N which is a positive integer.
- Ivan always plays first.
- In each turn, the player can either choose to add or subtract the largest prime smaller than N, to N.
- The loser is the person who cannot continue. The other person wins by default.
Ivan: N -> N + 7 = 17
Jake: N -> N - 13 = 4
Ivan: N -> 4 - 3 = 1
Ivan wins because Jake cannot continue the game.
Now, suppose that Ivan and Jake know how to play optimally. For how many starting values of \(N < 10^4\) does Jake win?