# Number of Primes between two integers

1. Nov 10, 2013

### Cheung

Is there a formula to calculate the EXACT number of primes between two integers? There are many very good ways of ESTIMATING the number but I have found very few that give the EXACT number, and those that do essentially require the knowledge of primes before hand (Legendre and Miessel.) While those are all nice I am looking for a formula (not an algorithm) that will spit out the EXACT number of primes by knowing only the two boundaries. Has it been done?

2. Nov 10, 2013

### goldust

Exact? No. But as the numbers in question approach infinity, they behave more accordingly to the Prime Number Theorem.

3. Nov 12, 2013

### jbriggs444

With the use of pi(n) you could easily construct a forumula for the number of primes between two integers i and j. However, I imagine that you would classify pi(n) as being an "algorithm" rather than a "formula".

http://mathworld.wolfram.com/PrimeCountingFunction.html

4. Nov 13, 2013

### Cheung

Thank you both for your reply's and to jbriggs444 I would consider using the logarithmic pi(x) an algorithm. I am looking for a formula/ function that would shed more light on the distribution of primes by solving for the number of primes using only the two integer limits.