14 questions linked to/from The myth of no prime formula?
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### Is there a known mathematical equation to find the nth prime?

I've solved for it making a computer program, but was wondering there was a mathematical equation that you could use to solve for the nth prime?
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### Who discovered the first explicit formula for the n-th prime?

I just found out on Wolfram that there is a formula for the n-th prime in terms of elementary functions. I wonder who found it and if he was rewarded for this. The formula (here) is: Also shown at ...
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### What would be the immediate implications of a formula for prime numbers?

What would be the immediate implications for Math (or sciences as a general) if someone developed a formula capable of generating every prime number progressively and perfectly, also able to prove (or ...
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### Formula for the nth prime number. [closed]

I need to see how to make a certain development, and did not find any reference to do, the only quote I found, so is the following, I know (have shown) $$\pi(m)=-1+\sum_{j=1}^{m} F(j)$$ with F(j)=...
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### A Shorter Proof of Rosser's Theorem Without Using The Prime Number Theorem

While researching on the elementary proof of Bertrand's Postulate I came to know about a theorem of Rosser's which states that $p_n$ $>$ $n$ $\text{ln}$ $n$. I have seen Rosser's original proof and ...
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### a practical prime counting function

Looking at Prime counting functions on Wikipedia, I only found formulas with no hint on how people got there. So, to better understand, I've decided to build one from scratch, starting from a naive ...
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### A formula that counts exactly the twin prime averages occuring in an interval $[a,b]$ is surprisingly succinct!

Let $p_n$ denote the $n$th prime number. Let $p_n \lt a \lt b \lt p_{n+1}^2$ be any such integers. Their oddness or divisibility does not matter as in my previous posts, which makes this formula ...
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### Inquiry on prime counting function

One of my close friends and I have been working towards an exact prime counting function. The approach we have came up accurately produces the number of composite numbers that occur before a given ...
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