A direct numerical simulation at resolution 2403 is usedto obtain a statistically stationary three-dimensional homogeneousand isotropic turbulent field at a Reynolds number around 1000(Rλ ≈ 150). The energy spectrumdisplays an inertial subrange. The velocity derivative distribution,known to be strongly non-Gaussian, is found to be close to, but not,exponential. The nth-order moments of thisdistribution, as well as the velocity structure functions, do notscale with n as predicted by intermittency models.Visualization of the flow confirms the previous finding that thestrongest vorticity is organized in very elongated thin tubes. Thewidth of these tubes is of the order of a few dissipation scales,while their length can reach the integral scale of the flow.