Using the photometric redshifts of galaxies from the Sloan Digital Sky Survey III (SDSS-III), we identify 132,684 clusters in the redshift range of 0.05<z<0.8. Monte Carlo simulations show that the false detection rate is less than 6% for the whole sample. The completeness is more than 95% for clusters with a mass of M_{200}>1.0*10^{14} M_{odot} in the redshift range of 0.05<z<0.42, while clusters of z>0.42 are less complete and have a biased smaller richness than the real one due to incompleteness of member galaxies. We compare our sample with other cluster samples, and find that more than 90% of previously known rich clusters of 0.05<z<0.42 are matched with clusters in our sample. Richer clusters tend to have more luminous brightest cluster galaxies (BCGs). Correlating with X-ray and the Planck data, we show that the cluster richness is closely related to the X-ray luminosity, temperature and Sunyaev-Zeldovich measurements. Comparison of the BCGs with the SDSS luminous red galaxy (LRG) sample shows that 25% of LRGs are BCGs of our clusters and 36% of LRGs are cluster member galaxies. In our cluster sample, 63% of BCGs of r_{petro}<19.5 satisfy the SDSS LRG selection criteria.
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