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replace 2 numbers by least prime divisor of their sum

Source: 2011 Grand Duchy of Lithuania, Mathematical Contest p5 (Baltic Way TST)

October 3, 2020
number theorycombinatorics

Problem Statement

Positive integers 1,2,3,...,n1, 2, 3, ..., n are written on a blackboard (n>2n > 2). Every minute two numbers are erased and the least prime divisor of their sum is written. In the end only the number 9797 remains. Find the least nn for which it is possible.
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