Prime number theorem - RSA I am having trouble understanding the prime number theorem.

As part of some revision for an exam, I am trying to answer the following questions (but seeing as I don't understand the concept of the prime number theorem, I'm not doing too well):

Question 1:

What is the proportion of numbers that are prime up to 1,000,000?

Question 2:

If we use prime numbers of size 1536 bits to generate an RSA modulus of 3072 bits, what is the proportion of numbers of size 1536 bits that are prime numbers?

I understand that using 1536 bits means that is it pretty much computationally infeasible to stage a brute force attack on an RSA key, but I don't understand why. In our lectures, we are given an example of $ln (2^{512}) = 355$ which means that 1 in every 355 numbers of size 512 bits is a prime. But I'm not really sure how to translate that to help with the two aforementioned questions. 

Can anyone please shed some light and explain the answers to those questions?
Apply your formula, perhaps simplified as $\ln(2^x)={x} \ln(2)$, so for 1536-bit numbers about one in $1536 \ln(2)$ are prime. In the case of $1{,}000{,}000=2^{20}$ (approx.) the number of primes is about one in $20 \ln(2)$.