My conjecture is that the loops (especially the loops outside the main clump at the center) might correspond to newly-introduced prime factors.
As a new batch of integers is introduced in going from frame N to frame N+1, the prime numbers within that batch would become new points in the 2d projection, because they have not been seen before.
Then, as you go from frame N+1 to frame N+2, etc., the new prime factors from frame N start to re-occur in those successive frames, and new points are added to the loop.
As a new batch of integers is introduced in going from frame N to frame N+1, the prime numbers within that batch would become new points in the 2d projection, because they have not been seen before.
Then, as you go from frame N+1 to frame N+2, etc., the new prime factors from frame N start to re-occur in those successive frames, and new points are added to the loop.