As far as I know, the most common RSA vulnerability found in the wild tends to be predictable random number generators that aren't actually random generating th

As far as I know, the most common RSA vulnerability found in the wild tends to be predictable random number generators that aren't actually random generating the same factors over and over for host keys on servers. Once one of p or q is shared between multiple hosts, you can factor using Euclid's algorithm for finding a GCD, which is over 2,300 years old. See, for instance, https://esj.com/articles/2012/02/27/rsa-key-kerfuffle.aspx https://esj.com/articles/2012/02/27/rsa-key-kerfuffle.aspx and http://www.loyalty.org/~schoen/rsa/ http://www.loyalty.org/~schoen/rsa/.