Thread: Inequality with the prime-counting function

Hi there guys, I hope I've posted this in the right section;

I'm going through a paper, and there is one statement which is:

for sufficiently large , where is the prime-counting function defined as the function counting the number of prime numbers less than or equal to . I'm having real difficulty justifying this claim, and I'd be really grateful if someone could help me out.

Thanks in advance,
HTale

Originally Posted by HTale

I'm going through a paper, and there is one statement which is:

for sufficiently large , where is the prime-counting function defined as the function counting the number of prime numbers less than or equal to .

Take logs, and it says . But ln(3)>1, so the result will follow from the prime number theorem.