Proving the Formula for the n-th Prime Number using Number Theory

  • Thread starter eljose
  • Start date
  • Tags
    Formula
In summary, the conversation is about a formula used in number theory to evaluate the n-th prime. The formula is p_n =\sum_{k=2}^{2^{n}}[ |n/(1+ \pi (k))|^{1/n}] where []=floor function and |x| is the modulus of x. The conversation also includes a humorous comment about the formula and a correction on the value of the third prime according to the formula. The person is seeking help to prove the formula.
  • #1
eljose
492
0
Hello i need help to prove the formula:

[tex] p_n =\sum_{k=2}^{2^{n}}[ |n/(1+ \pi (k))|^{1/n}] [/tex]

where []=floor function and |x| the modulus of x...this appear in number theory to evaluate the n-th prime however i am not able to prove it...:frown: :frown: :frown:
 
Last edited:
Physics news on Phys.org
  • #2
So according to this formula, with n= 3, 2 is the third prime? I did not know that!
 
  • #3
HallsofIvy said:
So according to this formula, with n= 3, 2 is the third prime? I did not know that!

:smile: Pure comedy!:smile:
 
  • #4
Though in fact, that's 2^n at the top of the summation. Even then, something's wrong, I get the third prime as being three according to the summation. Need to check again since I rushed thru it, but it doesn't look right.
 

FAQ: Proving the Formula for the n-th Prime Number using Number Theory

What is the purpose of proving a formula?

Proving a formula helps to establish its validity and ensures that it can be used confidently in future experiments or calculations. It also helps to understand the underlying principles and assumptions behind the formula.

How do you go about proving a formula?

To prove a formula, one must use logical reasoning and mathematical techniques such as algebra, calculus, or geometry. It is also important to follow a systematic approach and provide clear and concise steps to support the proof.

What is the significance of proving a formula?

Proving a formula is significant because it adds credibility and reliability to the formula. It also allows for the formula to be used in various applications and provides a deeper understanding of how it works.

Can a formula be proven wrong?

Yes, a formula can be proven wrong if there is evidence that contradicts its results or if it fails to accurately predict the expected outcome. In such cases, the formula may need to be revised or completely discarded.

How can I check if a formula has already been proven?

To check if a formula has already been proven, one can search for published research articles or scientific journals that cite the formula. It is also helpful to consult with experts in the field or reference textbooks that cover the topic.

Similar threads

Number of Die Throws until you get a repeated number
Replies
34
Views
3K
Use Euler's summation formula to prove the following....
Replies
17
Views
2K
Prove that a set of positive rational numbers is countable
Replies
24
Views
5K
Is ceil(n/k) equal to floor((n-1)/k) + 1 for positive integer values of n and k?
Replies
2
Views
3K
How to find z^n of a complex number
Replies
12
Views
2K
Prove that the product of 4 consecutive numbers cannot be a perfect square
Replies
14
Views
3K
Formula for Multiplying Two Elements in a Polynomial Ring
Replies
2
Views
2K
A Differential equation and Appell polynomials
Replies
1
Views
2K
Finding Prime numbers using Euler's formula
Replies
10
Views
8K
Compute sum (possibly using Parseval's formula)
Replies
1
Views
908

Hot Threads

Recent Insights

Back
Top