MathLabs

Problem 3

Let S={1,2,3,…,280}S=\{1,2,3,\ldots,280\}. Find the smallest integer n such that each n-element subset of S contains five numbers which are pairwise relatively prime.
Step 3 of 5: Select 60 isolated pairwise-coprime numbers
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P={1}∪{p<280:p prime},∣P∣=60P=\{1\}\cup\{p<280:p\text{ prime}\},\quad |P|=60
Detailed analysis

Let P consist of 1 and all primes below 280. It has 60 members, and all members of P are pairwise relatively prime.