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

In summary, a method has been discovered to find a close approximate to the number of primes between 1 and a certain limit. This method involves using the limit (n) and the natural log of n to calculate the number of primes, with the formula n/(natural log of n). The actual number of primes can vary slightly from the calculated approximation. This method was previously discovered by mathematician Gauss and was also found by the speaker through experimenting with numbers.
  • #1
jobsism
117
0
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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  • #2


April fool to you, too!
 
  • #3


?
 
  • #4


jobsism said:
?

http://mathworld.wolfram.com/PrimeNumberTheorem.html"
 
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  • #5


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?
 
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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.
 

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

1. What is the definition of a prime number?

A prime number is a positive integer that is only divisible by 1 and itself.

2. How many prime numbers are there between 1 and a given limit?

The number of prime numbers between 1 and a given limit is infinite. However, as the limit increases, the density of prime numbers decreases.

3. What is the largest known prime number?

The largest known prime number as of 2021 is 2^82,589,933 − 1, which has over 24 million digits.

4. Are there any patterns or rules for identifying prime numbers?

There are some patterns and rules that can help identify prime numbers, but there is no known formula for generating all prime numbers. Prime numbers are often characterized by their lack of divisibility by other numbers.

5. What is the significance of prime numbers in mathematics and science?

Prime numbers have many applications in mathematics and science, particularly in number theory, cryptography, and computer science. They also play a crucial role in the distribution of prime numbers, which is important for studying the distribution of natural numbers.

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