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?:

π(x)\pi(x)

@Akshaj Gopalakrishnan

Yajat Shamji - 2 months, 1 week ago

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That's exactly what I needed! Thanks!

Akshaj Gopalakrishnan - 2 months, 1 week ago

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No problem!

Here is an example:

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

Yajat Shamji - 2 months, 1 week ago

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@Yajat Shamji What is that?

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) The prime-counting function?

Yajat Shamji - 2 months, 1 week ago

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@Yajat Shamji I don't know what is that

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) Go to Wikipedia and search prime-counting function.

Yajat Shamji - 2 months, 1 week ago

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lmgtfy lol

Percy Jackson - 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.

Akshaj Gopalakrishnan - 2 months, 1 week ago

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lmgtfy always doesn't help

Páll Márton (no activity) - 2 months, 1 week ago

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It did now :)

Percy Jackson - 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 :)

Percy Jackson - 2 months, 1 week ago

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

Akshaj Gopalakrishnan - 2 months, 1 week ago

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No prob :)

Percy Jackson - 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

Páll Márton (no activity) - 2 months, 1 week ago

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

Percy Jackson - 2 months, 1 week ago

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formula and not fomrula

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) Yeah. But brute force is faster

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) Really??? What is the 345th prime number Mr.@Páll Márton ???

Percy Jackson - 2 months, 1 week ago

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

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) 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

@Páll Márton

Percy Jackson - 2 months, 1 week ago

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@Percy Jackson lmao

Akshaj Gopalakrishnan - 2 months, 1 week ago

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@Páll Márton (no activity) Ok, its 2333 :) @Páll Márton

Percy Jackson - 2 months, 1 week ago

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@Percy Jackson 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)

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) Yes, very complex. Only a great mind such as mine can calculate that, but fail to understand why 1+1 = 2 lol :)

Percy Jackson - 2 months, 1 week ago

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@Percy Jackson nth prime=1+m=12n[[n1+π(m)]1n]\large \text{nth prime}=1+\displaystyle\sum_{m=1}^{2^n}[[\cfrac{n}{1+\pi(m)}]^{\frac{1}{n}}]

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) Copycat Páll lol

Percy Jackson - 2 months, 1 week ago

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

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) Ok, whatever..................

Percy Jackson - 2 months, 1 week ago

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@Páll Márton (no activity) Congratulation!!!

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) So if n=345, then mmax=2325m_{max}=2^{325}?

Páll Márton (no activity) - 2 months, 1 week ago

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@Páll Márton (no activity) ??? wdymn

Percy Jackson - 2 months, 1 week ago

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@Percy Jackson What does it mean?

Páll Márton (no activity) - 2 months, 1 week ago

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