"How do chain molecules spontaneously entangle from completely disentangled polymer melt?" remains the most interesting unsolved problem. In order to solve this problem, we used the concept that the melt of "nascent" polymer crystallized during polymerization just after melting does not include any entanglements. We succeeded in detecting the increase of entanglement density v(e) with the increase of annealing time At above the equilibrium melting temperature before isothermal crystallization. The increase of v(e) was detected by observing the decrease of nucleation rate I from the melt of nascent polymer with different Delta ts. I is a very sensitive detector of entanglements because the nucleation is a rearrangement process of chains to the crystalline lattice through the disentanglement. Therefore, I is significantly suppressed with the increase of v(e). We found a two-step decrease of I with an increase of Delta t for the first time. This should correspond to a two-step increase of v(e) with an increase of Delta t. This indicates that simple entanglements such as twist or knot with lower order (one time knot) were formed within short time and then the complicated ones such as knot with higher order (two or three times knots) or loops (entanglements by loop conformation) were formed. (c) 2006 Elsevier Ltd. All rights reserved.