Counting function for powers of primes

robnybod · Feb 15, 2012

removed

epsi00 · Feb 15, 2012

at this point it is more important for you to show that your method works. I suggest you write a program and test your method using the formulas you posted. If the test works for large numbers, then you have something serious. By the way, this problem is an open problem in number theory so you may just have come up with a solution.

Norwegian · Feb 15, 2012

"Method" is correct and works, in the sense that it will give correct numbers in general. Unfortunately you will not be able to condense your expressions significantly. You would then, among other things, likely need a formula for the nth prime, and btw the exact same set up of inclusion/exclusion and floors can be used to express the prime counting function, for which there is very likely no short and elementary formula.

lostcauses10x · Feb 15, 2012

Sorry to see you remove this. Was Interesting.

Counting function for powers of primes

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Counting function for powers of primes

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