Pi(x) - How many primes below x?
Forwarded message:
X-within-URL: http://www.utm.edu/research/primes/howmany.shtml#pi_def
Consequence Three: The chance of a random integer x being prime is about 1/log(x)
1.1. pi(x) is the number of primes less than or equal to x
[up] 2. The Prime Number Theorem: approximating pi(x)
Even though the distribution of primes seems random (there are (probably) infinitely many twin primes and there are (definitely) arbitrarily large gaps between primes), the function pi(x) is surprisingly well behaved: In fact, it has been proved (see the next section) that:
The Prime Number Theorem: The number of primes not exceeding x is asymptotic to x/log x.
In terms of pi(x) we would write:
The Prime Number Theorem: pi(x) ~ x/log x.
____________________________________________________________________ Technology cannot make us other than what we are. James P. Hogan The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage@ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------
participants (1)
-
Jim Choate