The bit string representation actually isn't that bad for modulo computations: 2^n mod 3 is just 1 + (n % 2), and 2^n mod 5 is just {1,2,4,3}[n % 4]. Perfectly

The bit string representation actually isn't that bad for modulo computations: 2^n mod 3 is just 1 + (n % 2), and 2^n mod 5 is just {1,2,4,3}[n % 4]. Perfectly learnable to add them all up with the right weights? Given we're doing mod N, negative weights fit in naturally. So, pretty good seems plausible.