There is renewed focus on the thermoelectric properties of Bi-Sb. Reduced dimensionality samples of these alloys, such as nanowires, may exhibit exotic behavior that relate to the properties of the surfaces of topological insulators. It has been predicted that surface states of topological insulators have large thermopower and also ultrahigh mobilities. The authors report results of magneto-thermoelectric investigation of single crystal Bi _1-xSb_x nanowires in a glass cover with diameters ranging from 90 nm to 5 μm. The wide-ranging antimony concentration (0.01 < x < 0.2) enabled us to study the effect of nanowire dimensionality the (bulk) semimetal (x <0.05), semi-conductor 0.08 <x <0.2) and gapless (x=0.04-0.06) regimes. Bi-2at%Sn nanowires are particularly interesting. Quantum size effect, shown in temperature dependences of resistance R (T) and thermopower α(T) at the diameters significantly higher than the critical diameter for pure Bi-wires, are observed. The thermopower is very large; in weak magnetic fields (to 1 T), reaches values as high as + 400 μV/K at T= 20-40 K. We will show that this effect in not related to phonon drag effect but, rather, is associated with the large hole band partial thermopower. Power factor α²σ depending on diameter of wires, structure, temperature and a magnetic field is calculated. In connection with topological insulators, we will discuss the effect of the surface in the thermoelectric properties that we observe.