Alice and Bob play a game in which they take turns
removing stones from a heap that initially has n stones.
The number of stones removed at each turn must be one
less than a prime number. Alice goes first.
The winner is the player who
takes the last stone.
Prove that there
are infinitely many values of n such that Bob has a winning strategy.
(In reply to Mapping out a bit
Well, one reason you could not follow my proof is because I misapplied the Prime Number Theorem. The number of primes through 10^M is not roughly M/Log(M), it is roughly 10^M/log(10^M) = 10^M/M. I am fixing my proof up now.