Largest n had been factored

Um, do you mean factored, or do you mean largest known n such that n=pq?

Not sure about the former. The latter probably grows by a couple of digits every week

 

So really, what you're asking for is the two largest known primes. I'm not sure if this is the best option, but it's certainly big:
[tex](2^{20996011}-1)(2^{13466917}-1)[/tex]
is the product of two primes and has about 10 million digits.

 

A site devoted to the largest known primes. The two Nate mentioned are the #39 (?) and #40 (?) Mersenne primes.

 

this is where this should have gone

no problem......

M^2 is the answer, where M is the largest known Prime.