Prime number generation is typically done like this. Pick a random number, then add 2 until you get a prime.

So you can do something similar. Pick a deterministically generated bit string, and use as key the next prime number (you need to do it twice, for p and q).

You certainly get less security and I unfortunately don't have any reference to quantify that.

As I was saying in another post, I'm writing about deterministic password generation (i.e. not RSA keys). Draft here: https://medium.com/@0x0ece/how-i-manage-my-passwords-technic...

Even if there is, such a key would be much less safe (assuming the attacker knew the algorithm, which must be assumed, otherwise why keep the key in a safe?)