leelguy wrote:I have looked at the prime counting function, however it doesnt seem to work. For instance if I wanted to find how many primes are less than 45,000 then I tried 45,000/ln(45,000) and that didnt come up with the right answer.
Part of the problem with counting primes is precisely that there is no formula that gives the answer. The function
is the actual count of the primes, but to find the value of
for any given
, you actually have to do the counting. This obviously can quickly become unreasonably time-consuming.
The other functions:. . . . .
...are approximations to
. They are useful in that they give approximate values in the form of general formulas
, rather than in the form of a laborious step-by-step counting.
leelguy wrote:If you could explain how to find the number of primes below a number in terms that someone in trig could understand then that would be awesome.
I'm sorry, but it is not reasonably feasible to attempt to teach classes within this environment.
But after you take calculus, some of the discussion of integrals, limits, etc, may make more sense.