Suppose I have a set of 200-digit numbers that were created from the product of two randomly chosen 100 digit primes, P and Q. Considering that these 200-digit moduli have withstood a continued fraction attack (https://sagi.io/2016/04/crypto-classics-wieners-rsa-attack/), and Q is slightly larger than 2P, what is the best attack to use to factor the moduli?
p − 1 and q − 1 each have at least has at least one large prime factor
The paper at https://www.nku.edu/~christensen/Mathematical%20attack%20on%20RSA.pdf lists some of the factoring methods I have tried.
I am aware of cado-nfs (https://github.com/kurhula/cado-nfs) and yafu (https://github.com/DarkenCode/yafu/blob/master/README), and have used them to factor 100-digit moduli easily, but do not know how to tune the parameters to look for only 100-digit prime factors