Numbering Primes

Is there any formula or function to express a prime as the nth prime?

For example, if I have "7", I can say it's the 4th prime number. (2,3,5,7)

If I have a large prime number, like 8161 or something, how can I find which numbered prime it is (without going through and counting all the primes)?

Note by Akshaj Gopalakrishnan
2 months, 1 week ago

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Have you tried the prime-counting function?:

$\pi(x)$

- 2 months, 1 week ago

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That's exactly what I needed! Thanks!

- 2 months, 1 week ago

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No problem!

Here is an example:

$\pi(4) = 1, 2, 3, 4 = 2, 3 = 2$

- 2 months, 1 week ago

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What is that?

- 2 months, 1 week ago

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The prime-counting function?

- 2 months, 1 week ago

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I don't know what is that

- 2 months, 1 week ago

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Go to Wikipedia and search prime-counting function.

- 2 months, 1 week ago

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lmgtfy lol

- 2 months, 1 week ago

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I wasn't sure what to ask google lol. I don't remember what exactly I googled, but I just got algorithms to find the nth prime.

- 2 months, 1 week ago

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lmgtfy always doesn't help

- 2 months, 1 week ago

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It did now :)

- 2 months, 1 week ago

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I know the answer but this comment section is too small for my proof.

Yours sincerely, Fermat or rather Percy(Perseus) Jackson

@Vinayak Srivastava, @Frisk Dreemurr, @Yajat Shamji @Páll Márton LOLOLOLOLOLOL

@Akshaj Gopalakrishnan - Don't mind my antics, here's a link :)

- 2 months, 1 week ago

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Oh wow that's complicated. Thanks! That helps!

- 2 months, 1 week ago

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No prob :)

- 2 months, 1 week ago

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There are some function to calculate approximately how many prime numbers are in a given intervall. But there is no fomrula to calculate the nth prime number. Maybe a good dream yet :) We are waiting for @Percy Jackson lol

- 2 months, 1 week ago

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I gave a link. Mr. Sir pinky(sierpinsky) has made a formula :) @Páll Márton

- 2 months, 1 week ago

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formula and not fomrula

- 2 months, 1 week ago

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Yeah. But brute force is faster

- 2 months, 1 week ago

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Really??? What is the 345th prime number Mr.@Páll Márton ???

- 2 months, 1 week ago

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I don't know. But if you are so clever use your formulas and tell us lol

- 2 months, 1 week ago

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but i can't prove it, because as I said -

I know the answer but this comment section is too small for my proof.

Yours sincerely, Perseus Jackson

- 2 months, 1 week ago

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lmao

- 2 months, 1 week ago

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Ok, its 2333 :) @Páll Márton

- 2 months, 1 week ago

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Ahmmm. To use these formulas is possible only with computers. You are right, it can be faster, but the complexity is still big. (I think)

- 2 months, 1 week ago

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Yes, very complex. Only a great mind such as mine can calculate that, but fail to understand why 1+1 = 2 lol :)

- 2 months, 1 week ago

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$\large \text{nth prime}=1+\displaystyle\sum_{m=1}^{2^n}[[\cfrac{n}{1+\pi(m)}]^{\frac{1}{n}}]$

- 2 months, 1 week ago

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Copycat Páll lol

- 2 months, 1 week ago

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I just wrote it in a more readable form to show you brute force is faster

- 2 months, 1 week ago

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Ok, whatever..................

- 2 months, 1 week ago

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Congratulation!!!

- 2 months, 1 week ago

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So if n=345, then $m_{max}=2^{325}$?

- 2 months, 1 week ago

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??? wdymn

- 2 months, 1 week ago

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What does it mean?

- 2 months, 1 week ago

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