Nope. A session key is normally not created by one party and sent to another, it's generated by something like Diffie-Hellman in which the long-living RSA keys

Nope. A session key is normally not created by one party and sent to another, it's generated by something like Diffie-Hellman in which the long-living RSA keys are only used for authenticity verification. Diffie-Hellman requires discrete logarithms rather than factorization (and then there are more modern methods).