I used to belong to the long primary crew, but once I started experimenting for myself I quickly learned that longer primaries didn't gain me anything for 95% of the beers I brew.
And I think it's a vocal minority who do advocate a super long primary. The people I talk with the most about brewing normally do something similar to what I do. And if they happen to leave the beer in primary for 3-4 weeks, it's usually not on purpose, just that life gets in the way sometimes. (I'm looking at you, lschiavo!
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I think anytime someone says to "leave your beer for XXXX days" or any other brewing absolute that it should be considered something that works for them and perhaps something to consider.
There are few absolutes in brewing. There are a few, like sanitizing, yeast health, temperature control, etc, that are always important. But even then, how you get there is up to differences in technique.
Even with water chemistry, my "imaginary" friend Mabrungard likes higher sulfate beers than I do. Neither one of us is wrong, as people like what they like. It's just another tool to use to get the results you want.
As far as fermentation, there are a few things touched on in here that are always true. The first is that a properly made beer (proper amount of yeast pitched at the proper temperature and kept at the proper temperature) will have a period of active fermentation that will drop off. After that, for about 24 hours or so, the yeast will keep working. That is when they go back, still scouring for digestible sugars and such, and digest other non-preferential foods. They then will even digest some of their own waste products. That's part of the "clean up" phase of fermentation. After that, the beer will start to clear.
That is why most experienced brewers will tell you to wait until the beer is done, and then wait 3 more days at least before transferring. That allows that process to finish, and does produce a better quality beer. If you go more than 3 days longer, that's fine. And some people do just that, and routinely go a month longer. Some people don't.
Try it for yourself, and see which flavors you prefer. That's the best way to determine the value of our advice!