TITLE: Classes of Numbers that are easy to factorize using Classical Computers?
QUESTION [5 upvotes]: The Carmichael Numbers can be factorized in polynomial time.
Are weak fermat pseudoprimes (w.r.t. a given base) easy to factorize as well? 
What are some large/broad classes of numbers that are easy to factorize (i.e. in polynomial time). This part is pretty broad, so i would be thankful if someone can provide some examples of these classes and more importantly a few good up-to date sources, that studies/lists the classes of numbers and their factorization difficulty ?

REPLY [3 votes]: Here is a large class of numbers that can be factored in polynomial time: products of a smooth number and large prime. More precisely, a number less than $x$ whose second largest prime factor is less than $\exp(O((\log \log x)^2/\log \log \log x))$ can be factored in polynomial time. There are about $$x(\log\log x)^2/(\log x \log\log\log x)$$ such numbers, so this is quite a large class. You can read more in Granville's survey Smooth numbers: computational number theory and beyond.