
#1
Nov1013, 09:02 PM

P: 3

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
Nov1013, 09:11 PM

P: 85

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




#3
Nov1213, 09:11 AM

P: 748

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
Nov1313, 09:15 PM

P: 3

Number of Primes between two integers
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.



Register to reply 
Related Discussions  
Consecutive integers divisible by a set of Primes  Linear & Abstract Algebra  4  
Sum the three primes, get number  Brain Teasers  0  
Sequence of ratios of primes and integers  Linear & Abstract Algebra  24  
Primes vs. integers  General Math  7  
Primes in ring of Gauss integers  help!!  Linear & Abstract Algebra  7 