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Which is the biggest? (Posted on 2017-01-02) Difficulty: 2 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts Another approach Comment 2 of 2 |
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
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