# How many numbers have more primes than half that number?

If I have a number $n$ and I count all the prime numbers below $n$, for how many numbers will there be more primes below $n$ than half of $n$?

Hint: Taking the fact that $1$ is not usually counted a prime, how many prime even numbers are there below $n$?
• Approximately $\frac{n}{\ln(n)}$ which is almost always smaller than $\frac{n}{2}$, but there are a few numbers for which the condition does hold (namely $3$, $5$ and $7$)... right? – barak manos Jun 13 '15 at 13:47
• @barakmanos approximately half of the numbers below $n$ are even. If $1$ is not counted as prime the number of primes below $3$ is $1$ and half of $3$ is $1.5$. – Mark Bennet Jun 13 '15 at 13:50