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(abridged for arXiv) We make use of the Planck all-sky survey to derivenumber counts and spectral indices of extragalactic sources -- infrared andradio sources -- from the Planck Early Catalogue (ERCSC) at 100 to 857GHz. Oursample contains, after the 80% completeness cut, between 122 and 452 andsources, with flux densities above 0.3 and 1.9Jy at 100 and 857GHz, over about31 to 40% of the sky. Using Planck HFI, all the sources have been classified aseither dust-dominated or synchrotron-dominated on the basis of their spectralenergy distributions (SED). Our sample is thus complete, flux-limited andcolor-selected to differentiate between the two populations. We find anapproximately equal number of synchrotron and dusty sources between 217 and353GHz; at 353GHz or higher (or 217GHz and lower) frequencies, the number isdominated by dusty (synchrotron) sources, as expected. For most of the sources,the spectral indices are also derived. We provide for the first time counts ofbright sources from 353 to 857GHz and the contributions from dusty andsynchrotron sources at all HFI frequencies in the key spectral range wherethese spectra are crossing. The observed counts are in the Euclidean regime.The number counts are compared to previously published data (earlier Planck,Herschel, BLAST, SCUBA, LABOCA, SPT, and ACT) and models taking into accountboth radio or infrared galaxies. We derive the multi-frequency Euclidean leveland compare it to WMAP, Spitzer and IRAS results. The submillimetre numbercounts are not well reproduced by current evolution models of dusty galaxies,whereas the millimetre part appears reasonably well fitted by the most recentmodel for synchrotron-dominated sources. Finally we provide estimates of thelocal luminosity density of dusty galaxies, providing the first suchmeasurements at 545 and 857GHz.

astronomy and astrophysics

Planck intermediate results. VII. Statistical properties of infrared and  radio extragalactic sources from the Planck Early Release Compact Source  Catalogue at frequencies between 100 and 857 GHz