oh thanks for the edit - also found this https://www.youtube.com/watch?v=IuSnY_O8DqQ https://www.youtube.com/watch?v=IuSnY_O8DqQ and am watching now. and the a

oh thanks for the edit - also found this https://www.youtube.com/watch?v=IuSnY_O8DqQ https://www.youtube.com/watch?v=IuSnY_O8DqQ and am watching now. and the above tactic starts at 11m in. huh; and it's just euclid - a non-unity gcd means two keys (products) have a shared prime (and you get one of the primes). edit: also, "batch number field sieve" is the answer to my original question.