We report on a computational study of the statics and dynamics of long flexible linear polymers that spontaneously knot and unknot. Specifically, the equilibrium self-entanglement properties, such as the knotting probability, knot length and position, are investigated with extensive Monte Carlo sampling of chains of up to 15 000 beads. Tens of such equilibrated chains of up to similar to 4000 beads are next used as starting points for Langevin dynamics simulations. The complex interplay of chain dynamics and self knotting is addressed by monitoring the time evolution of various metric and entanglement properties. In particular, the extensive duration of the simulations allows for observing the spontaneous formation and disappearance of prime and composite physical knots in linear chains. Notably, a sizable fraction of self-knotting and unknotting events is found to involve regions that are far away from the chain termini. To the best of our knowledge, this represents the first instance where spontaneous changes in knotting for linear homopolymers are systematically characterized using unbiased dynamics simulations.