Just looking at this (first time I've really looked at this ridiculous feat >_>), I think maybe a way to make this a bit easier, especially for the higher numbers, is breaking down all the prime numbers by subtracting 1 and then going into prime factorization. So say for 9th level adjustment, a target of 101, it breaks down pretty easily to (2x2x5x5)+1 .

Now some of the other ones will be a little more complicated, say 107 -> (2x53)+1 . So you'd have to do that step a few more times -> 2x([2x2x13]+1)+1 -> 2x([2x2x([2x2x3]+1)+1])+1.

Once you have the base factors down, I think the plugging in of numbers may be a little easier to manipulate as needed with a varied set of numbers. Granted, you could probably leave in 4s and 6s when you do the factorization, since those are possible values of the dice rolls. But either way, keeping those sets of prime factors on hand might make the math on it a bit easier, giving a bunch of smaller, easier targets to hit rather than one large daunting one to manipulate. Or at the very least gives a secondary way to calculate it, since there are many different ways to approach the math.

[[Addendum: After doing the below for the minimum dice requirement, this factorization process doesn't net you a "lowest number of minimal dice req. to meet it" scenario, as the above example would require 16 dice written in that fashion, whereas below it can be done with 14. Just was a thought I figured I'd bring up before someone else pointed it out.]]

RE: the 12 dice minimum, I can't figure out a way to make twelve 1s(statistically improbable put still possible) equal 101, 103, or 107 -- going something like (1+1+1)x(1+1+1)x(1+1+1)x(1+1+1), 81 is the highest number I can produce. I could do it with fourteen 1s -> (1+1+1+1)x(1+1+1)x(1+1+1)x(1+1+1)-1 -> 4x3x3x3-1 -> 108-1 = 107 , so maybe 14 was the benchmark number? Whether it's 100% successful at that point or not, I don't know, but that's at least the minimum # of dice I could see being required to get 100%. Maybe I'm missing something in the math that makes 12 dice possible? Dunno...too much math for the holidays already haha.

About the use for this feat...in a RL scenario, it's a nightmare: takes *WAAAAY* too long to confidently come up with a success/failure decision in a way that doesn't completely shatter immersion and game flow. In PBP, however...I could see it as being possible, as long as the GM is on top of the player using the feat to ensure everything is being handled correctly (Player makes post stating its use and how, and rolls dice, no edits allowed to that post kinda thing). Would I ever allow it personally? Gods, no; I'd send their butts back to the 3.5 Munch-kiddy table for even thinking about bringing this nonsense to the table.