NPR1(n) =number of primes below 10n
NPR2(n)= number of primes with at most n digits
NPR3(n)= number of distinct prime divisors below (10n
For a given n, which of the above is the biggest?
Rationalize your conclusion.
According to WolframAlpha, (10^3)! has 2877 prime factors, of which 168 are distinct.
168 is also the number of primes below 10^3, as well as the number of the number of primes with at most 3 digits.
It is true that there are numbers much smaller than (10^3)! with prime factors much larger than 10^3, but such numbers by definition will not appear in the factorial sequence until much later.
My impression is that these definitions are much the same.
Posted by broll
on 2017-01-02 22:16:44