  We present the results of a 2-10 keV BeppoSAX survey based on 140 high
galactic latitude MECS fields, 12 of which are deep exposures of ``blank''
parts of the sky. The limiting sensitivity is 5 10^-14 erg cm^-2 s^-1 where
about 25% of the Cosmic X-ray Background (CXB) is resolved into discrete
sources. The logN-logS function, built with a statistically complete sample of
177 sources, is steep and in good agreement with the counts derived from ASCA
surveys. A CXB fluctuation analysis allowed us to probe the logN-logS down to
about 1.5 10^-14 erg cm^-2 s^-1 where the contribution of discrete sources to
the CXB grows to 40-50%. A hardness ratio analysis reveals the presence of a
wide range of spectral shapes and that a fairly large fraction of sources
appear to be heavily absorbed, some of which showing soft components. A
comparison of the flux distribution of different subsamples confirms the
existence of a spectral hardening with decreasing flux. This effect is probably
due to an increasing percentage of absorbed sources at faint fluxes, rather
than to a gradual flattening of the spectral slope. Nearly all the sources for
which adequate ROSAT exposures exist, have been detected in the soft X-rays.
This confirms that soft spectral components are present even in strongly
absorbed objects, and that a large population of sources undetectable below a
few keV does not exist. A Ve/Va test provides evidence for the presence of
cosmological evolution of a magnitude similar to that found in soft X-ray
extragalactic sources. Evolution is present both in normal and absorbed
sources, with the latter population possibly evolving faster,although this
effect could also be the result of complex selection effects.
