Mersenne: ECM better than O(sqrt(f)) ?

I've read on the list some time ago that ECM takes, like Pollard-Rho or P-1, O(sqrt(f)) operations mod N to find a factor f. But looking at the factors found so far I find that hard to believe; according to that formula, finding a 50-digit factor should be 10^15 times harder than finding a

RE: Mersenne: ECM better than O(sqrt(f)) ?

I've read on the list some time ago that ECM takes, like Pollard-Rho or P-1, O(sqrt(f)) operations mod N to find a factor f. But looking at the factors found so far I find that hard to believe; according to that And quite right too. It's just plain wrong. ECM runs in sub-exponential