Here's what wikipedia has on it:
The Riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function ζ(s). The Riemann zeta function is defined for all complex numbers s * 1. It has certain so-called "trivial" zeros for s = −2, s = −4, s = −6, ... The Riemann hypothesis is concerned with the non-trivial zeros, and states that:
The real part of any non-trivial zero of the Riemann zeta function is ½.
The Riemann zeta function ζ(s) is defined for any complex number s with real part > 1 by the Dirichlet series:
ζ(s) = Sigma (n=1 to infinity) 1 / n^s
OK, so it is known that ζ(2) = 1/1^2 + 1/2^2 + 1/3^2... = pi/6
Then, it goes on to have much more complex stuff, properties etc. However, I do know that it is somehow related to prime numbers and related to 'predicting' the distribution of prime numbers (I think). I've also read somewhere that if the Riemann hypothesis is proven true, it will mean that a lot of our encryption (RSA, prime number factoring) will become obsolete.
I just wonder, why do we need to prove it, for it to be used in breaking encyryption. OK, so say we do prove it, then what? Is it any different from assuming it's true and then trying to use it in real world applications?
Plus, further info about the Riemann hypothesis would be helpful (i.e. understandable by us high school students)
The Riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function ζ(s). The Riemann zeta function is defined for all complex numbers s * 1. It has certain so-called "trivial" zeros for s = −2, s = −4, s = −6, ... The Riemann hypothesis is concerned with the non-trivial zeros, and states that:
The real part of any non-trivial zero of the Riemann zeta function is ½.
The Riemann zeta function ζ(s) is defined for any complex number s with real part > 1 by the Dirichlet series:
ζ(s) = Sigma (n=1 to infinity) 1 / n^s
OK, so it is known that ζ(2) = 1/1^2 + 1/2^2 + 1/3^2... = pi/6
Then, it goes on to have much more complex stuff, properties etc. However, I do know that it is somehow related to prime numbers and related to 'predicting' the distribution of prime numbers (I think). I've also read somewhere that if the Riemann hypothesis is proven true, it will mean that a lot of our encryption (RSA, prime number factoring) will become obsolete.
I just wonder, why do we need to prove it, for it to be used in breaking encyryption. OK, so say we do prove it, then what? Is it any different from assuming it's true and then trying to use it in real world applications?
Plus, further info about the Riemann hypothesis would be helpful (i.e. understandable by us high school students)
