An unsolved problem in the viscoelastic properties of entangled linear polymers is the viscosity molecular weight relationship. Experiments indicate a power law, eta(0) proportional to M-a, with a = 3.5 +/- 0.2, whereas the theoretical prediction for "pure reptation" is an exponent equal to 3.0. This discrepancy is ascribed to dynamic modes that compete with reptation so that a cubic dependence on M is observed only at sufficiently high molecular weights. That is, almost all existing experimental data are for polymers with too few entanglements to exhibit eta(0) proportional to M-a. To address this issue, we carried out experiments on polyisobutylene having as many as 430 entanglements per chain. Because reentanglement of polymer melts prepared from solution takes extraordinarily long times (another unsolved problem in rheology), annealing was carried out for 5 years prior to the viscosity measurements. We determined that at all temperatures, eta(0) was less than the extrapolation assuming the M-3.5 dependence of lower molecular weight polyisobutylene. This result is consistent with the idea that only at sufficiently high degrees of entanglement is pure reptation the operative mechanism, whereby linear flexible-chain polymers exhibit the predicted behavior. Our work is in good agreement with an earlier study on polybutadiene [Colby, R. H.; Fetters, L. J.; Graessley, W. W. Melt viscosity-molecular weight relationship for linear polymers. Macromolecules 1987, 20, 2226-2237.].