Hi,

I want to know why is the Riemann hypothesis still unsolved? I really want to know the reasons due to which it is still unsolved.

It is a difficult problem. What are you thinking by asking "why"?

It is a difficult problem. What are you thinking by asking "why"?

How do we know it's difficult? Because so many people have been unable to solve it!

 

OP has a good question. What is it, exactly, that makes RH a difficult problem? Why have FLT and the Poincaré conjecture been solved, but not RH?

 

That's way above my pay grade. But at heart it's a very good question IMO.

Edited October 19, 20169 yr by wtf

Nobody can find a technique that can predict what the next prime will be, to infinity without going through the list and working it out. They are trying to find a bespoke formula that can predict them; a shortcut. The pattern of occurrence of primes appears to be random but I think they think otherwise and, I think, that's one of the reasons why it is so difficult. This article by Marcus Du Sautoy gives an easy, potted read to the problem and it's history..

 

https://plus.maths.org/content/prime-number-lottery

Edited October 19, 20169 yr by StringJunky

So now I get that.

Thanks for all your help.

Nobody can find a technique that can predict what the next prime will be, to infinity without going through the list and working it out. They are trying to find a bespoke formula that can predict them; a shortcut. The pattern of occurrence of primes appears to be random but I think they think otherwise and, I think, that's one of the reasons why it is so difficult. This article by Marcus Du Sautoy gives an easy, potted read to the problem and it's history..

 

https://plus.maths.org/content/prime-number-lottery

 

Actually we think that the primes behave essentially like a pseudo-random number sequence (with a few known differences that are already well-understood). The Riemann hypothesis would confirm some that (at least in parts). It would allow to make a lot of predictions about the behaviour of primes (because many methods used to study random number sequences could be used to tackle prime numbers).

It's a common misconception that the Riemann hypothesis would result in hidden patterns in the prime numbers. The opposite is true: The reason why there are so many unproven conjectures about primes is that we don't know if there are any fancy, hidden patterns.

Edited November 20, 20169 yr by renerpho

Actually we think that the primes behave essentially like a pseudo-random number sequence (with a few known differences that are already well-understood). The Riemann hypothesis would confirm some that (at least in parts). It would allow to make a lot of predictions about the behaviour of primes (because many methods used to study random number sequences could be used to tackle prime numbers).

It's a common misconception that the Riemann hypothesis would result in hidden patterns in the prime numbers. The opposite is true: The reason why there are so many unproven conjectures about primes is that we don't know if there are any fancy, hidden patterns.

Right. Thanks for the clarification.