We synthesised observations of total particle number (CN) concentration from 36 sites around the world. We found that annual mean CN concentrations are typically 300-2000 cm(-3) in the marine boundary layer and free troposphere (FT) and 1000-10 000 cm(-3) in the continental boundary layer (BL). Many sites exhibit pronounced seasonality with summer time concentrations a factor of 2-10 greater than wintertime concentrations. We used these CN observations to evaluate primary and secondary sources of particle number in a global aerosol microphysics model. We found that emissions of primary particles can reasonably reproduce the spatial pattern of observed CN concentration (R-2=0.46) but fail to explain the observed seasonal cycle (R-2=0.1). The modeled CN concentration in the FT was biased low (normalised mean bias, NMB=-88%) unless a secondary source of particles was included, for example from binary homogeneous nucleation of sulfuric acid and water (NMB=-25%). Simulated CN concentrations in the continental BL were also biased low (NMB=-74%) unless the number emission of anthropogenic primary particles was increased or a mechanism that results in particle formation in the BL was included. We ran a number of simulations where we included an empirical BL nucleation mechanism either using the activation-type mechanism (nucleation rate, J, proportional to gas-phase sulfuric acid concentration to the power one) or kinetic-type mechanism (J proportional to sulfuric acid to the power two) with a range of nucleation coefficients. We found that the seasonal CN cycle observed at continental BL sites was better simulated by BL particle formation (R-2=0.3) than by increasing the number emission from primary anthropogenic sources (R-2=0.18). The nucleation constants that resulted in best overall match between model and observed CN concentrations were consistent with values derived in previous studies from detailed case studies at individual sites. In our model, kinetic and activation-type nucleation parameterizations gave similar agreement with observed monthly mean CN concentrations.