2006 Alabama ARML TST Problems/Problem 12

Problem

Yoda begins writing the positive integers starting from 1 and continuing consecutively as he writes. When he stops, he realizes that there is no set of 5 composite integers among the ones he wrote such that each pair of those 5 is relatively prime. What’s the largest possible number Yoda could have stopped on?

Solution

The least group of 5 positive consecutive integers with the property that each pair of those is relatively prime is the set . Therefore, the largest number he could have stopped on is .