MathDB

Alice and Bob play the following game: starting with the number

2

written on a blackboard, each player in turn changes the current number

n

to a number

n + p

, where

p

is a prime divisor of

n

. Alice goes first and the players alternate in turn. The game is lost by the one who is forced to write a number greater than

\underbrace{22...2}_{2020}

. Assuming perfect play, who will win the game.

Problem Statement