What is the largest integer less than 9,000,000 whose smallest prime divisor is 3163?
Let n be the number we’re looking for.
Then 3163x = n < 9,000,000.
Now, x has to be smaller than 3163, because (3163)(3163) = 10,004,569.
If x is a prime number, than 3163 isn’t the smallest prime factor of this number n, and if x is composite, then n has even smaller prime factors than x.
So there is no such number n < 9,000,000 having 3163 as its smallest prime factor.