11 has a certain mystery to it, as do all smallish primes -- perhaps not to the degree that 23 does, but that's mostly because Robert Anton Wilson never really grabbed hold of it.
And 4 is full of curiosities: the self-sum, -multiple and -power of 2, the only number with such a characteristic. It has plenty of elemental mystery, cropping up everywhere ritual can be found.
So overall, not bad -- for a number that isn't a multiple of hands, it does reasonably well, and should serve for a year. Certainly, it should be a great improvement over the terribly bland 43...