A large database from direct numerical simulations of isotropic turbulence, including recent simulations for box sizes up to 40963 and the TaylorReynolds number
R1000, is used to investigate the bottleneck effect in the three-dimensional energy spectrum and second-order structure functions, and to determine the Kolmogorov constant, CK. The difficulties in estimating CKat any finite Reynolds number, introduced by intermittency and the bottleneck, are assessed. The data conclusively show that the bottleneck effect decreases with the Reynolds number. On this basis, an alternative to the usual procedure for determining CKis suggested; this proposal does not depend on the particular choices of fitting ranges or power-law behaviour in the inertial range. Within the resolution of the numerical data, CKthus determined is a Reynolds-number-independent constant of 1.58 in the three-dimensional spectrum. A simple model including non-local transfer is proposed to reproduce the observed scaling features of the bottleneck.