olymmath

OMCPLP 2016 Problem 1

  • Day 1

Consider 1010 distinct positive integers that are all prime to each other (that is, there is no a prime factor common to all), but such that any two of them are not prime to each other. What is the smallest number of distinct prime factors that may appear in the product of 1010 numbers?

Dataset text AI-MO AoPS. Quoted with source.

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