Honest question. I know treif needs 60 (even though min hatorah 2:1 suffices), so if there is a real concern of a treif egg – especially if one is later discovered, ALL the eggs plus the pot would be treif unless there was a ratio of 60:1 kosher.
Mei’kar hadin, we’re not choshesh for an egg coming from a treifa or having a blood spot. We go according to rov, and in fact we eat food made with unchecked b’dieved.
However, Yisroel kedoshim heim, and a minhag developed to boil three eggs so that in case one is no good, at least m’d’Oraisa it will be batel. (Davar sheb’minyan is also a d’rabbonon.)
The minhag was never to do 61 or to asser b’dieved. I don’t know is 61 would even help, because this is not a taam issue.