Hypothetical Question about the Riemann Hypothesis

[DarkDarkly]

I don't understand this any more than any other 11th grade student who spends their time researching math problems on YouTube, but it is my understanding that the Zeros of the extended Riemann Zeta Function encode the distribution of prime numbers in some way. If we already HAD the distribution of prime numbers, would it be possible to reverse the process and solve for the zeros of the the function that way? If so, roughly how would you go about doing that?

 

[JeffM]

It is sometimes the case that if you know how to go

[MATH]A \rightarrow B[/MATH]
that you can figure out how to go

[MATH]B \rightarrow A.[/MATH]
But there is no logical necessity for that to happen. All biological mothers are women, but not all biological women are mothers.

Of course, in the case that you are discussing, we do not know how to go in either direction so the problem is what the lawyers call moot.

 

[DarkDarkly]

It is sometimes the case that if you know how to go

[MATH]A \rightarrow B[/MATH]
that you can figure out how to go

[MATH]B \rightarrow A.[/MATH]
But there is no logical necessity for that to happen. All biological mothers are women, but not all biological women are mothers.

Of course, in the case that you are discussing, we do not know how to go in either direction so the problem is what the lawyers call moot.

I see. I mostly wanted to know because I've been looking into the distribution of primes recently and have found some interesting patterns that APPEAR to not be a coincidence. though there is obviously still little outliers I'm working through, they aren't in the same places where it occurs in most patterns (like 25, and 49, which tend to appear alongside primes in some partial-solutions I've seen)