the number of primes under x,pi(x)?

Question

What is known of the function related to prime numbers pi(x),the number of primes under number x.

i want to know as much as possible of function pi(x) the number of primes lower then x

Answer 1

pi(x) was calculated to ab out pi(4*10^22) [later 4e23], but was stopped after a dsscrepancy of 1 was discovered.

Answer 2

I happen to know that this function is asymptotic to the logarithmic integral of x. That function is defined as the integral of 1/ln(x) taken up to x, but the lefthand bound varies from definition to definition. It only introduces a small numerical difference. Anyway, the fact that pi(x) ~ Li(x) was proven by two people both around the beginning of the 1900s. The result is called the Prime Number Theorem.

Answer 3

ther ar etwo primes lower than x or pi the first one is 3 and the second one is 2 .

The first few primes numbers are below

2 , 3 , 5 , 7 , 11 , 13, 17 , 19 , 23 , 29 , 31 , 37 , .....

Answer 4

You're thinking of phi(n), the totient function. Everything you need to know about it can be found here:
http://mathworld.wolfram.com/TotientFunction.html

***

Sorry, I got confused. You can read about the prime counting function pi(x) here:
http://mathworld.wolfram.com/PrimeCountingFunction.html

Answer 5

There are lots of references you can check in the Online Encyclopedia of Integer Sequences:

http://www.research.att.com/~njas/sequences/A000720

A few of the links are given below...