[Virginia-American]

The biggest problem with proving Riemann Hypothesis is that the world of electronic commerce and cryptology as we know it today, would vanish instantly

Huh?

How would showing that the relative error in the approximation

pi(x) = Li(x) + error

(where pi(x) is # primes <=x and Li (x) is the integral from 0 to x of dt / ln(t) )

is O(sqrt(x)ln (x)) rather than some larger function, break any codes?

To crack the RSA system, you need a way to factor numbers that are hundreds, if not thousands, of digits long. AFAIK, the RH does not provide a factoring algorithm.

[Boiler Plate]

I based my statement on this article.

http://www.finextra.com/fullstory.asp?id=12452