[Cressi]

66 is a sphenic number, a triangular number, a hexagonal number, and a semi-meandric number. Being a multiple of a perfect number, 66 is itself a semiperfect number.
Since it is possible to find sequences of 66 consecutive integers such that each inner member shares a factor with either the first or the last member, 66 is an Erdős–Woods number.

Indeed, my dear fellow human being.

67 is impossible to factorize, as it is a Pillai prime (18! + 1), as well as a Heegner number.