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 by Jer)

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. 

Posted by Steve Herman on 2016-02-05 09:53:48