  Using SDSS Data Release 6, we construct two independent samples of candidate
stellar wide binaries selected as i) pairs of unresolved sources with angular
separation in the range 3'' - 16'', ii) common proper motion pairs with 5'' -
30'' angular separation, and make them publicly available. These samples are
dominated by disk stars, and we use them to constrain the shape of the
main-sequence photometric parallax relation M_r(r-i) and to study the
properties of wide binary systems. We estimate M_r(r-i) by searching for a
relation that minimizes the difference between distance moduli of primary and
secondary components of wide binary candidates. We model M_r(r-i) by a fourth
degree polynomial and determine the coefficients using Markov Chain Monte Carlo
fitting, independently for each sample. Aided by the derived photometric
parallax relation, we construct a series of high-quality catalogs of candidate
main-sequence binary stars. Using these catalogs, we study the distribution of
semi-major axes of wide binaries, a, in the 2,000 < a < 47,000 AU range. We
find the observations to be well described by the Opik distribution, f(a)~1/a,
for a<a_{break}, where a_{break} increases roughly linearly with the height Z
above the Galactic plane (a_{break}~12,300 Z[kpc]^0.7 AU). The number of wide
binary systems with 100 AU < a < a_{break}, as a fraction of the total number
of stars, decreases from 0.9% at Z=0.5 kpc to 0.5% at Z=3 kpc. The probability
for a star to be in a wide binary system is independent of its color. Given
this color, the companions of red components seem to be drawn randomly from the
stellar luminosity function, while blue components have a larger blue-to-red
companion ratio than expected from luminosity function.
