Register to reply

Number of Primes between two integers

Share this thread:
Cheung
#1
Nov10-13, 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?
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
goldust
#2
Nov10-13, 09:11 PM
P: 85
Exact? No. But as the numbers in question approach infinity, they behave more accordingly to the Prime Number Theorem.
jbriggs444
#3
Nov12-13, 09:11 AM
P: 907
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

Cheung
#4
Nov13-13, 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 Fun, Photos & Games 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