I think that number (100) is a bit too low. There are students, graduates, post-grad fellows, and otherwise thousands of people living and breathing number theory. Sure, they might not directly stare at a blackboard with The Problem of Factoring staring back at them, but they are very much doing that indirectly.
Just like the AKS primality testing algorithm depends on clever number theory, any progress, any new trick would be very likely reported, and we'd see it in charts like these:
I think the core point of the OP you are missing is that he doesn't consider people indirectly, tangentially working on related things as doing "serious" work on factoring.
I tend to agree. Look at Fermat's last theorem: it went over a century as one of mathematics hardest unsolved problems, and in reality all it took was one guy dedicating a couple of months of exclusive work to it. Factoring (and discrete log?) is probably similar.
I work in this field as a non-academically-trained cryptographer. Cryptographers prefer to assume their assumed-hard functions are in fact hard and move on. Especially those that have academic training--they supposedly know better than to waste their time on such a hard problem.. but by induction that means approximately nobody is really looking at it.
> it went over a century as one of mathematics hardest unsolved problems, and in reality all it took was one guy dedicating a couple of months of exclusive work to it.
Six years, not a couple of months.
There were plenty of people who tackled this problem and who failed to make any headway. {Edit: I phrased this last sentence really clumsily, sorry.}
Also Andrew Wiles' six years of focused worked fundamentally depended on very deep work that Ken Ribet had just completed, which in turn relied on decades of highly nontrivial work by Mazur, Katz, and others on modular curves and modular forms, which made surprising connections with other areas of mathematics. Finally, Wiles' first announced proof of FLT was wrong, and Richard Taylor collaborated with him to find a correct and quite different proof. (Disclaimer: I published a book on modular forms, and cowrote papers with some of the people mentioned above.)
> There were plenty of people who tackled this problem and who failed to make any headway.
There was also plenty of meaningful progress throughout the 20th century at least, showing that the FLT was implied by other statements which would be easier to prove. Wiles's work was a follow-on to this progress; it's quite misleading to say that it "took" a single guy working over six years to prove FLT.
By his own report, it was a few months of tackling the problem from various angles until he found the pathway that would eventually bear fruit, and formalizing that and fixing little problems along the way was what the next six years were spent on.
He was the lucky one. Many many mathematicians thought they saw a path. And spent years. And it did not lead anywhere/there in the end.
See also the many P = NP proof attempts. (Sure, most of them are complete crackpot garbage, but that doesn't mean serious attempts are not made, and probably more serious attempts are made that then go nowhere so the author doesn't disclose it.)
Just like the AKS primality testing algorithm depends on clever number theory, any progress, any new trick would be very likely reported, and we'd see it in charts like these:
https://aiimpacts.org/progress-in-general-purpose-factoring/