RNG - RSA - cryptography

[stijn0713]

For those who are familiar with random number generators and the RSA-encryption algorithm:

 

it is said that RNG is often used in for the purpose of key generation. If one looks at RSA, is it then used to randomly generate the

two distinct prime numbers p and q ? (in the context wikipedia uses: http://en.wikipedia.org/wiki/RSA_(algorithm)

 

If so, why should they be randomly generated? I know for example that Belgian eIDs are equipped with 2 RSA keys pairs which i guess are created by certificat holders (in casu Belgian Government). Do they use such RNG for those keys then? and what's the point of doing it ?

[cpd]

If a human were to think of two numbers they would 1) end up being limited to their knowledge of primes; 2) patterns would begin to emerge therefore a weakness present in the encryption and 3) could leave human error when choosing the primes where one of the conditions described in the wiki article aren't met. Whilst the Rng isn't responsible for ensuring such criteria are met it still plays a part.

 

The last sentence under the title "Importance of strong random number generation" sums up why its particularly important in public-key cryptography to have a strong Rng.

 

Not sure if that quite answers your question but never the less.