'ey, I think a problem that might just be AGI complete or very nearly
such is figuring out exactly how stupid a dumbfuck Fermat was.
Having a day to waste, I dug into it a little bit.
A fermat number is like (in binary)
1[an ungodly number of 0's]1
I'm pretty sure that F5 and up are all composite (so is everyone else).
Apparently there's a proof that each fermat number has a factor k2^(n+2)
+ 1.
K may be even or odd (sometimes confused with a grater value of n), but
there must be an odd number of odd k.
Due to the nature of the numbers involved, this problem should only be
approached using binary numbers.
The problem here is nailing down the nature of K. The underlying issue
is that we don't really understand very much about how multiplication
actually works and we are forced to use brute force methods. For this
problem that's utterly intractable.
I multiplied F5 out by hand, which isn't too hard because it involves
adding three rows of the same number (in binary). Basically what the
number has to do is make sure that everything carries evenly such that
no 1-bits are left in the middle of the number. You can think of one
factor as a self-interlocking jigsaw puzzle piece and the other as the
instructions for assembling the puzzle.
The AGI task is to deduce enough of the design rules such that it can be
solved in short order, hopefully in polynomial time.
--
To anyone it may concern, I just retired a CISCO RV220W router from my
network because it was crashing constantly and returned a much older
Netgear WGR614 V7 to service. I feel obliged to expend effort to
bad-mouth the RV220W and its brand at this point.
Powers are not rights.
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AGI
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