Success again! The composite cofactor of 3,538+ was the product of 77-digit and 101-digit prime numbers:

77-digit prime factor:
36126580918649837686342401003279006682373340513695232649824622781879534478413

101-digit prime factor:
11719073511775047063331807610812599296908677959178977786661672364811977892269985241782059001063330309

The factors will be reported to the Cunningham project and will be recorded on Page 113. We should have the next factors in a few days!

Some think me an idiot as I ask questions when I don't understand things ... but, if I don't ask, how can I learn? :)

So, the first part of the post indicates we have "the" cofactor but the last line indicates that the search continues.

So, the question, are we looking only for any factor set for a particular prime? Or all the possible factors?

Not that it will make any difference in my participation ... but curiosity overwhelms ... :)

The 177-digit number we factored was the last composite factor, the
other known factors all being primes; so now this last piece has been
reduced to primes, and we're done with this number. The one we're
going on to is the next one on the "Status of Numbers" list, ordered by
completion date, 2,853+.

Hope this clarifies matters. -bdodson