Primordial or big bang nucleosynthesis (BBN) is one of the three historical strong evidences for the big bang model. The recent results by the Planck satellite mission have slightly changed the estimate of the baryonic density compared to the previous WMAP analysis. This article updates the BBN predictions for the light elements using the cosmological parameters determined by Planck, as well as an improvement of the nuclear network and new spectroscopic observations. There is a slight lowering of the primordial Li/H abundance, however, this lithium value still remains typically 3 times larger than its observed spectroscopic abundance in halo stars of the Galaxy. According to the importance of this lithium problem, we trace the small changes in its BBN calculated abundance following updates of the baryonic density, neutron lifetime and networks. In addition, for the first time, we provide confidence limits for the production of 6Li, 9Be, 11B and CNO, resulting from our extensive Monte Carlo calculation with our extended network. A specific focus is cast on CNO primordial production. Considering uncertainties on the nuclear rates around the CNO formation, we obtain CNO/H approx (5-30) x 10^{-15}. We further improve this estimate by analyzing correlations between yields and reaction rates and identified new influential reaction rates. These uncertain rates, if simultaneously varied could lead to a significant increase of CNO production: CNO/H sim 10^{-13}. This result is important for the study of population III star formation during the dark ages.
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