You should start with "odds this composite *has* a 35digit factor." Absent any knowledge of the number's special form, that's about 1/n, so 1/35 in this case.
Then, given there is such a factor to find, and *no* previous ECM attempts, you could calculate your odds of finding the factor after a certain number of curves. That's roughly (11/e^(z/y)), where z is the number of curves you plan to run and y is the expected number of curves required to discover a factor of that specific size. yvalues are freely available for each n divisible by 5; if you wish to run nonstandard B1 bounds, invoking gmpecm with "v" flag will print the expected curve counts.
I am not 100% certain about the above formula; I have used it in the past when z is of the same order of magnitude of y (say, 2000 curves when 4400 is the expected number of curves), but I believe it's an approximation when z is a few hundred or more that isn't quite accurate if you're running a very small number of curves.
EDIT: Note that previous ECM failures alter the first probability it is less likely a factor of the desired size exists when ECM has already been run. Calculating this probability is left as an exercise for the reader.
Last fiddled with by VBCurtis on 20161217 at 00:00
