Question

How many primes occur between 0 and 230,948,202? (Note: the answer is the number of primes, not the primes themselves!) Answer Check

Answer 1

Answer:

There are approximately 27,613,774 primes between 0 and 230,948,202

Step-by-step explanation:

The Prime Number Theorem states that between 0 and $x$, the number of primes in this interval can be approximated by the following formula.

$\pi(x) = \frac{x}{log x}$

So

How many primes occur between 0 and 230,948,202?

This is approximately $\pi(230,948,202)$

So

$\pi(230,948,202) = \frac{230,948,202}{\log{230,948,202}} = 27,613,774$

There are approximately 27,613,774 primes between 0 and 230,948,202