What is the approximate number of primes between 1 and a given limit?

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Discussion Overview

The discussion revolves around the approximation of the number of prime numbers between 1 and a specified limit, with a focus on the formula n/(natural log of n). Participants explore the origins of this approximation and share personal experiences related to discovering mathematical concepts.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant proposes that the number of primes up to a limit n can be approximated using the formula n/(natural log of n), providing an example with n=10.
  • Another participant humorously questions the originality of the discovery, referencing Gauss as an earlier discoverer of the approximation.
  • A participant expresses surprise at the historical context, indicating a desire to have discovered it earlier.
  • There is a discussion about the process of discovering mathematical ideas, with one participant sharing their method of experimenting with numbers on calculators.
  • Another participant reflects on their own experience with the Sieve of Eratosthenes and encourages continued exploration of mathematics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the originality of the discovery, with some acknowledging Gauss's earlier work while others express personal pride in their own discoveries. The discussion remains unresolved regarding the implications of discovering known mathematical concepts.

Contextual Notes

There is an implicit assumption that the approximation method is well-known, but participants do not clarify the extent of its historical recognition or its acceptance in contemporary mathematics.

Who May Find This Useful

Individuals interested in number theory, mathematical approximations, and the history of mathematical discoveries may find this discussion relevant.

jobsism
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Primes between 1 and a limit!

I just discovered something cool! I found out a method to find a close approximate to the number of primes between 1 a certain limit. If n is the limit, then number of primes is approximately equal to n/(natural log of n). For example, number of primes between 1 and 10 is 10/ln(10) = 4.34, and the actual number of primes is 4! I'm just so happy on finding out something like this! :!) Tell me what you guys think of this. Also, please tell me if it was already found out earlier.
 
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April fool to you, too!
 


?
 


jobsism said:
?

http://mathworld.wolfram.com/PrimeNumberTheorem.html"
 
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jobsism said:
I just discovered something cool! I found out a method to find a close approximate to the number of primes between 1 a certain limit. If n is the limit, then number of primes is approximately equal to n/(natural log of n). For example, number of primes between 1 and 10 is 10/ln(10) = 4.34, and the actual number of primes is 4! I'm just so happy on finding out something like this! :!) Tell me what you guys think of this. Also, please tell me if it was already found out earlier.

Well, if you really found it entirely on your own, it indicates innate math ability. Gauss was 15 when he found it. How old are you? I found the Sieve of Eratosthenes when I was in high school. My teacher said "What took you so long?." The world doesn't give you much credit for being the nth person to discover or invent something. But keep trying. You just might come up with something original.
 
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How, exactly, did you discover this?
 


So it was already found earlier by Gauss? sheesh, if only i was born earlier.. :D

Robert1986 said:
How, exactly, did you discover this?

I have this habit of punching numbers into calculators, and trying things with them. It was pure coincidence that i found this one out.

SW VandeCarr said:
How old are you? I found the Sieve of Eratosthenes when I was in high school. My teacher said "What took you so long?." The world doesn't give you much credit for being the nth person to discover or invent something. But keep trying. You just might come up with something original.

Yeah, i guess you are right. Will keep trying though. I'm 16 by the way.
 

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