2013 OIM Problems/Problem 5

Problem

Let $A$ and $B$ be two sets such that:

1. $A \cup B$ is the set of positive integers.

2. $A \cap B$ is empty.

3. If two positive integers have as difference a prime greater than 2013, then one of them is in $A$ and the other in $B$ .

Find all the possibilities for sets $A$ and $B$ .

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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