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
5 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 - 5 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

A Former Brilliant Member - 5 months, 1 week ago

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formula and not fomrula

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member ??? wdymn

Percy Jackson - 5 months, 1 week ago

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@Percy Jackson What does it mean?

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member Yeah. But brute force is faster

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member Really??? What is the 345th prime number Mr.@Páll Márton ???

Percy Jackson - 5 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

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member Ok, its 2333 :) @Páll Márton

Percy Jackson - 5 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)

A Former Brilliant Member - 5 months, 1 week ago

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

Percy Jackson - 5 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}}]

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member Congratulation!!!

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member So if n=345, then mmax=2325m_{max}=2^{325}?

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member Copycat Páll lol

Percy Jackson - 5 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

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member Ok, whatever..................

Percy Jackson - 5 months, 1 week ago

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@A Former Brilliant Member 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 - 5 months, 1 week ago

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@Percy Jackson lmao

Akshaj Gopalakrishnan - 5 months, 1 week ago

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

Percy Jackson - 5 months, 1 week ago

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

Akshaj Gopalakrishnan - 5 months, 1 week ago

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No prob :)

Percy Jackson - 5 months, 1 week ago

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lmgtfy lol

Percy Jackson - 5 months, 1 week ago

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lmgtfy always doesn't help

A Former Brilliant Member - 5 months, 1 week ago

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It did now :)

Percy Jackson - 5 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 - 5 months, 1 week ago

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Have you tried the prime-counting function?:

π(x)\pi(x)

@Akshaj Gopalakrishnan

Yajat Shamji - 5 months, 1 week ago

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That's exactly what I needed! Thanks!

Akshaj Gopalakrishnan - 5 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 - 5 months, 1 week ago

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@Yajat Shamji What is that?

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member The prime-counting function?

Yajat Shamji - 5 months, 1 week ago

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@Yajat Shamji I don't know what is that

A Former Brilliant Member - 5 months, 1 week ago

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@A Former Brilliant Member Go to Wikipedia and search prime-counting function.

Yajat Shamji - 5 months, 1 week ago

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