[bostik]

You know that in RSA the modulus n is effectively your public key, right? And that n = p * q, where p and q are essential parts of your private key?

So if you can factor n into the corresponding primes, you have just cracked the person's private key.

Implications? You can decrypt all RSA encrypted messages for that private key. You can IMPERSONATE the person whose private key you have cracked. (Signature = data encrypted with private key that can be verified with the public key.)

All encrypted messages sent to the compromised keys must be treated as leaked. All signatures made by the compromised keys are suspect.

It's as bad as it gets for the individuals in question.