1.one question about the LFSR

1.In the LFSR, does the chosen prime field GF(2^31-1) has other good properties than GF(2^n) for certain n's except high linear complexity ?
2.The ZUC algorithm is more complicated than SNOW in form, does it has any practical efficiency?

I think mod 2^n-1 is easy to compute. We need only add the length n periods of the number.