in both of these instances, a section is included in the main page that discusses a few of these special instances. ... I would imagine that each of these "named" cases will have its own page someday, and so perhaps it would be more appropriate to have most of this information in the "Related Pages" subpage
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I understand that if the pages on Mersenne Primes, Egyptian Fractions, etc. have not yet been written ... So I propose that leaving sections on special cases in the main page for now ... Later, when those pages are created, we could remove the section on special cases from the main page.
This seems like a good strategy to me.
On the other hand, are some special cases so important that they must be discussed in detail on the main page?
I think we should leave it up to the judgement of the article writers and editors. Some things may have types which are so important we want to cover them (briefly) in the main article on that thing. Others may not. I'm not sure a hard-and-fast rule makes sense.
I worry that casual readers will not find the "Related Pages" subpage.
This is something that there are occasional discussions about - whether stuff belongs on the main page, or on a subsidiary. One recent thread (too tired/low-energy to find it) discussed whether footnotes should be on a separate subpage (some people didn't like tha idea).
I personally am not so big on having links to related topics on a separate subpage, for precisely the reason you suggest. One possibility (one we tried out for the footnotes, but nobody seemed very interested) is to have them on the main page, but normally hidden, with a button to expand them. If people like this, it would be trivial to clone the template that was created to do this for footnotes.
Noel