People need to experiment with cure times. I'll say generally CP is 4 weeks but I've discovered some of my soap (depending on the ingredients) have actually improved after 6 weeks or even longer. Let's not even discuss castile.
As for the cure times for CPOP and HP, I also cure those at least 3-4 weeks to ensure water has evaporated and the soap is milder. However, I'm fussy about quality and I like to make sure my soap has reached the optimal stage before giving it out. One of the things soapmaking has taught me is patience. I know positively all of my HP batches aren't cured after only a week. They dissolve quickly at only a week ('cuz I test new recipes); although, I
suppose it's possible for some people's HP to be ready after only a week depending on their recipes. However, I sure would be unhappy if I bought soap which dissolved quickly.
@ lenarenee -
There is more than just water evaporation happening over several weeks. There have been informative discussions about cure and the changes which occur during it. You might find these topics helpful but there are a lot more than just these threads.
http://www.soapmakingforum.com/showthread.php?t=35831
http://www.soapmakingforum.com/f11/curing-process-32821/
http://www.soapmakingforum.com/showthread.php?t=32870
http://www.soapmakingforum.com/showthread.php?t=7913
I also agree with My Mountain Soaps about fragrances changing over time. I've noticed morphing and fading during curing. It can be frustrating to find out a scent you just love morphs in a few weeks or fades in a month or two. I'm currently in this situation right now with a HP batch I made 2 weeks ago. The scent has altered so much that I keep wavering between 'like', 'don't like', 'like again', 'I can't believe it changed again', 'for crying out loud...is this scent ever going to stop changing?"
It's certainly been an interesting couple of weeks and I guess this is what I get for blending FOs to create a new scent.