Question

How many three-digit positive integers have at least one prime digit?

Answer 1

210

Explanation:

`512=2^9 \\` has 9 prime factors

Now, if you want to maximize the number of different prime factor, apply the following method: let
`p(n)` be the nth prime number, in increasing order. Let
`v` define as follow :
`v(0)=1,v(n+1)=v(n)p(n+1)` , and find n such that
`v(n) < 1000,v(n+1) > 1000`. n will be the number of factors and v(n) your integer.

`v(1)=2v(0)=2v(2)=3v(1)=6v(3)=5v(2)=30v(4)=7v(3)=210v(5)=11v(4)=2310`

There you are, 210 , with only 4 different prime factors.

→Credits: Xavier Dectot←