# How Riemann hypothesis would break internet security?

1. Jul 18, 2013

### Avichal

I saw this in one of the episodes of Numb3rs - (a T.V. show that describes how math can be used to solve crimes)
It basically said that if Riemann hypothesis is true then it could break all the internet security. I want to know how.
I couldn't understand Riemann hypothesis from Wikipedia and other sources so don't throw all the math at me.

P.S. :- I don't know under which forum this thread belongs. I couldn't find a number theory forum

2. Jul 18, 2013

### FredericGos

It's a TV show. For all practical purposes, the Riemann hypothesis IS true. It just hasn't been proved to be. There are computers out there trying to falsify it 24/7, and they haven't succeeded yet.

So if it could break internet security, that would have been done a long time ago.

3. Jul 18, 2013

### Avichal

Ah, why would they show such a thing? I got so excited!
Yes if it was true then it would have been broken a long time ago ... didn't think of that

4. Jul 18, 2013

### FredericGos

Because it sounds cool. ;)

5. Jul 19, 2013

### jackmell

I believe this is a modern day math old-wives tale. It stems from the (beautiful) connection between prime numbers and the zeros of the zeta function:

$$\psi(x)=-\frac{1}{2\pi i} \mathop\int\limits_{\gamma-i\infty}^{\gamma+i\infty} \frac{\zeta'(s)}{\zeta(s)}\frac{x^s}{s} ds$$

That's primes on the left and zeros on the right. Riemann conjectured that the conjugate zeros of the zeta function all have real part equal to 1/2 (Re(z)=1/2).

Now, one of the most hack-proof security systems used today on computers relies on the RSA algorithm which involves factoring very large numbers: if you know the prime factors, you can compute the number but if you know only the number, very hard to find it's factors if it's a product of two very large primes.

So that if the Riemann hypothesis is proven, someone will have shown indeed the conjugate zeros are all on the line Re(z)=1/2. However, this information will do nothing towards finding the prime factors of an RSA number.

Last edited: Jul 19, 2013