# Tagged Questions

Prime numbers are natural numbers greater than 1 not divisible by any smaller number other than 1. This tag is intended for questions about, related to, or involving prime numbers.

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### Integration by parts of the Logarithmic Integral

I am doing work on analytic number theory, and I am currently looking at the Prime Number Theorem, that is $$\pi(x) \sim Li(x)$$ Some of my sources say that I can do integration by parts on the ...
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### For which primes $p$ does $px^2-2y^2=1$ have a solution?

Let $p$ be an odd prime. If $px^2-2y^2=1$ is solvable, we can get Jacobi symbol $(\frac{-2}{p})=1$, so $p=8k+1,8k+3$. But when $k=12$, $p=97$, the Pell equation $97x^2-2y^2=1$ is unsolvable. I think ...
### Primes and infinite primes of the form $29 + 72k$
can you give the validity or proof of the following statements of my observations on Primes? $(1)$ For a positive integer $k$, there exists infinitely many primes of the form $29 + 72k$. $(2)$ If the ...