The primes are some of the worst offenders, eg the transition from 647 (prime) to 648 (3×3×3×3×2×2×2), but as we approach infinity, the visualizations increasingly appear circular, and it's the least-primey (?) that break from the trend.

eg 854-856, & 857 (prime) are all virtually or perfectly circular. Or maybe I'm observing not mathematical but neuro-visual principles.