I have been pondering about certain conjectures and theorems viewed as either low vs high dimensions, or smaller vs larger primes, or anything of the sort "low vs high order". Let me mention a couple of such mathematical phenomena that might be more familiar.
Poincaré's conjecture (now a theorem) in dimension $3$ persisted much longer than in higher dimensions.
Hoping that these citations shed light, I like to ask:
QUESTION. Do you know of conjectures (problems) which manifested to be either notoriously harder or unsolved for "lower dimensions/orders/primes" compared to their "higher dimensional/order/prime" cousins?