[belovedeagle]

> 2 more waiting to be identified among the running product

I don't know anything about this factoring project; does this mean that keys are somehow "tested" in batches, and if the batch comes out "dirty" then you know you can easily factor something in that batch (for some value of "easy")?

EDIT: Ah, nevermind, just figured it out. For those coming after, there's a running product of all public moduli in the tested set; you can test one key against all of them simultaneously. When you find a GCD /= 1, you've found a factor, and you know the key you just tested has it, but there's an older key which has that factor too, and you don't know which one. Presumably you either go and test them one by one or store "snapshots" of the running product to test.