Problem

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Tags: AMC, USA(J)MO, USAMO, inequalities, blogs, number theory unsolved, number theory



$(\text{a})$ Do there exist 14 consecutive positive integers each of which is divisible by one or more primes $p$ from the interval $2\le p \le 11$? $(\text{b})$ Do there exist 21 consecutive positive integers each of which is divisible by one or more primes $p$ from the interval $2\le p \le 13$?