Register to reply

Counting function for powers of primes

by robnybod
Tags: prime counting
Share this thread:
Feb15-12, 01:56 PM
P: 3
Phys.Org News Partner Science news on
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief
Feb15-12, 03:42 PM
P: 84
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.
Feb15-12, 05:11 PM
P: 144
"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.

Feb15-12, 05:37 PM
P: 94
Counting function for powers of primes

Sorry to see you remove this. Was Interesting.

Register to reply

Related Discussions
Difference in Powers of Odd Primes Linear & Abstract Algebra 3
Question about shifting the indexes [nth powers] and counting numbers of series? Calculus & Beyond Homework 3
Primes and their powers Calculus & Beyond Homework 1
Divisibility of powers of primes Linear & Abstract Algebra 5
The sum over primes involving powers of 10 Linear & Abstract Algebra 2