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IMAS 2021–2022 Junior Division, Round 2 Question 3

IMAS · IMAS 2021–2022 Junior Division, Round 2

Question 3

Using the set of integers from 1 to 2022 inclusive, at most how many integers can we choose such that the positive difference between any two chosen numbers is not a prime number?
  1. $253$
  2. $254$
  3. $504$
  4. $505$
  5. $506$