有用的素数个数表

cuikun-186 · 发表于 2022-10-20 16:41

杨老师的工作非常有实际意义！！！

yangchuanju · 发表于 2022-10-20 16:41

10^n/log(10^n)、10^n/[log(10^n)-1.08366]、10^n/[log(10^n)-1]、Li(10^n)与π(10^n)相当偏差表：
n       10^n/log(10^n)-π(10^n)：π(10^n)       减1.08-π(10^n)：π(10^n)       减1-π(10^n)：π(10^n)       Li-π(10^n)：π(10^n)
1       0.000000       1.000000       0.750000       0.500000
2       -0.120000       0.120000       0.080000       0.200000
3       -0.136905       0.023810       0.005952       0.059524
4       -0.116355       0.001627       -0.009764       0.013832
5       -0.094454       -0.000417       -0.008340       0.003962
6       -0.077913       0.000573       -0.005962       0.001656
7       -0.066445       0.000844       -0.004696       0.000510
8       -0.057759       0.001137       -0.003671       0.000131
9       -0.050988       0.001376       -0.002871       0.000033
10       -0.045617       0.001517       -0.002287       0.000007
11       -0.041263       0.001589       -0.001855       0.000003
12       -0.037670       0.001612       -0.001535       0.000001
13       -0.034655       0.001605       -0.001291       0.000000
14       -0.032087       0.001582       -0.001101       0.000000
15       -0.029875       0.001549       -0.000949       0.000000
16       -0.027948       0.001510       -0.000828       0.000000
17       -0.026256       0.001469       -0.000728       0.000000
18       -0.024757       0.001426       -0.000645       0.000000
19       -0.023420       0.001384       -0.000576       0.000000
20       -0.022220       0.001343       -0.000517       0.000000
21       -0.021138       0.001302       -0.000467       0.000000
22       -0.020156       0.001264       -0.000423       0.000000
23       -0.019261       0.001226       -0.000386       0.000000
24       -0.018442       0.001190       -0.000353       0.000000
25       -0.017691       0.001156       -0.000324       0.000000
26       -0.016998       0.001124       -0.000299       0.000000
27       -0.016357       0.001093       -0.000277       0.000000
28       -0.015763       0.001063       -0.000257       0.000000
29       -0.015211       0.001035       -0.000239       0.000000

当n值较大时，4类计算值的相当偏差都逐渐减小，其中积分式Li(10^n)值偏差最小几乎是0，其次是10^n/[log(10^n)-1.08366]的偏差都从正方向趋近于0；再次是10^n/[log(10^n)-1]的偏差都从负方向趋近于0；负偏差最大的是素数定理式10^n/log(10^n)，负偏差虽逐渐减小，但进度慢得多。

cuikun-186 · 发表于 2022-10-20 16:44

杨老师的工作极大地推进了哥猜的研究，这是划时代的工程！

cuikun-186 · 发表于 2022-10-20 16:56

本帖最后由 cuikun-186 于 2022-10-20 16:57 编辑

回想1984年春天，我用省下的生活费钱，去供销社商店买来一个计算器，自己自认为可以计算一些数值。

现在看来，当时是多么的幼稚，但正是那时的“种子”支持着我，不断地跟着老师们学习，

在这个科学研究的进程中，今天得到了杨老师无私的帮助，实在是我崔坤今生的福气啊！！！

让我由衷地向杨老师道一声：老师您辛苦了！

yangchuanju · 发表于 2022-10-20 22:27

A003617-1000
n位最小素数
1 2
2 11
3 101
4 1009
5 10007
6 100003
7 1000003
8 10000019
9 100000007
10 1000000007
11 10000000019
12 100000000003
13 1000000000039
14 10000000000037
15 100000000000031
16 1000000000000037
17 10000000000000061
18 100000000000000003
19 1000000000000000003
20 10000000000000000051
21 100000000000000000039
22 1000000000000000000117
23 10000000000000000000009
24 100000000000000000000117
25 1000000000000000000000007
26 10000000000000000000000013
27 100000000000000000000000067
28 1000000000000000000000000103
29 10000000000000000000000000331
30 100000000000000000000000000319
31 1000000000000000000000000000057
32 10000000000000000000000000000033
33 100000000000000000000000000000049
34 1000000000000000000000000000000061
35 10000000000000000000000000000000193
36 100000000000000000000000000000000069
37 1000000000000000000000000000000000067
38 10000000000000000000000000000000000043
39 100000000000000000000000000000000000133
40 1000000000000000000000000000000000000003
41 10000000000000000000000000000000000000121
42 100000000000000000000000000000000000000109
43 1000000000000000000000000000000000000000063
44 10000000000000000000000000000000000000000057
45 100000000000000000000000000000000000000000031
46 1000000000000000000000000000000000000000000009
47 10000000000000000000000000000000000000000000121
48 100000000000000000000000000000000000000000000033
49 1000000000000000000000000000000000000000000000193
50 10000000000000000000000000000000000000000000000009
…………
51-1000略

yangchuanju · 发表于 2022-10-20 22:28

A003618-1000
n位最大素数
1 7
2 97
3 997
4 9973
5 99991
6 999983
7 9999991
8 99999989
9 999999937
10 9999999967
11 99999999977
12 999999999989
13 9999999999971
14 99999999999973
15 999999999999989
16 9999999999999937
17 99999999999999997
18 999999999999999989
19 9999999999999999961
20 99999999999999999989
21 999999999999999999899
22 9999999999999999999973
23 99999999999999999999977
24 999999999999999999999743
25 9999999999999999999999877
26 99999999999999999999999859
27 999999999999999999999999901
28 9999999999999999999999999791
29 99999999999999999999999999973
30 999999999999999999999999999989
31 9999999999999999999999999999973
32 99999999999999999999999999999979
33 999999999999999999999999999999991
34 9999999999999999999999999999999589
35 99999999999999999999999999999999977
36 999999999999999999999999999999999841
37 9999999999999999999999999999999999919
38 99999999999999999999999999999999999941
39 999999999999999999999999999999999999943
40 9999999999999999999999999999999999999983
41 99999999999999999999999999999999999999881
42 999999999999999999999999999999999999999917
43 9999999999999999999999999999999999999999919
44 99999999999999999999999999999999999999999947
45 999999999999999999999999999999999999999999991
46 9999999999999999999999999999999999999999999967
47 99999999999999999999999999999999999999999999959
48 999999999999999999999999999999999999999999999967
49 9999999999999999999999999999999999999999999999943
50 99999999999999999999999999999999999999999999999943
…………
51-1000略

yangchuanju · 发表于 2022-10-20 22:34

A033874-8000 A033873-14000
n位最大素数与10^n的差 n位最小素数与10^n的差
—————— 0 1——2-1=1
1 3——10-7=3 1 1——11-10=1
2 3——100-97=3 2 1——101-100=1
3 3 3 9
4 27 4 7
5 9 5 3
6 17 6 3
7 9 7 19
8 11 8 7
9 63 9 7
10 33 10 19
11 23 11 3
12 11 12 39
13 29 13 37
14 27 14 31
15 11 15 37
16 63 16 61
17 3 17 3
18 11 18 3
19 39 19 51
20 11 20 39
21 101 21 117
22 27 22 9
23 23 23 117
24 257 24 7
25 123 25 13
26 141 26 67
27 99 27 103
28 209 28 331
29 27 29 319
30 11 30 57
31 27 31 33
32 21 32 49
33 9 33 61
34 411 34 193
35 23 35 69
36 159 36 67
37 81 37 43
38 59 38 133
39 57 39 3
40 17 40 121
41 119 41 109
42 83 42 63
43 81 43 57
44 53 44 31
45 9 45 9
46 33 46 121
47 41 47 33
48 33 48 193
49 57 49 9
50 57 50 151
51 323 51 121
52 231 52 327
53 177 53 171
54 291 54 31
55 111 55 21
56 593 56 3
57 93 57 279
58 149 58 159
59 141 59 19
60 161 60 7
61 39 61 93
62 83 62 447
63 123 63 121
64 51 64 57
65 269 65 49
66 621 66 49
67 111 67 49
68 393 68 99
69 189 69 9
70 93 70 33
71 53 71 273
72 117 72 39
73 149 73 79
74 47 74 207
75 191 75 129
76 363 76 133
77 543 77 21
78 63 78 93
79 251 79 49
80 11 80 129
81 173 81 13
82 363 82 391
83 53 83 27
84 399 84 261
85 27 85 103
86 17 86 151
87 273 87 373
88 41 88 181
89 221 89 31
90 143 90 289
91 81 91 79
92 783 92 399
93 173 93 153
94 567 94 97
95 53 95 151
96 269 96 127
97 159 97 469
98 71 98 49
99 621 99 289
100 797 100 267
101 203 101 3
102 39 102 117
103 77 103 129
104 449 104 267
105 9 105 3
106 57 106 79
107 267 107 3
108 21 108 19
109 83 109 457
110 69 110 7
111 299 111 139
112 807 112 207
113 317 113 99
114 153 114 271
115 603 115 79
116 209 116 93
117 1031 117 279
118 143 118 709
119 513 119 69
120 173 120 79
121 33 121 87
122 299 122 1119
123 773 123 3
124 63 124 753
125 177 125 237
126 513 126 679
127 71 127 283
128 17 128 387
129 267 129 459
130 41 130 1113
131 113 131 63
132 483 132 169
133 207 133 21
134 117 134 7
135 1463 135 1143
136 387 136 91
137 269 137 283
138 69 138 273
139 429 139 513
140 3 140 13
141 299 141 129
142 519 142 13
143 11 143 81
144 569 144 91
145 69 145 73
146 339 146 9
147 123 147 987
148 281 148 247
149 357 149 183
150 273 150 67
151 71 151 901
152 11 152 13
153 453 153 87
154 33 154 453
155 471 155 189
156 899 156 451
157 821 157 583
158 33 158 151
159 53 159 187
160 257 160 303
161 23 161 403
162 279 162 133
163 209 163 217
164 11 164 1527
165 339 165 559
166 401 166 267
167 423 167 27
168 699 168 1323
169 903 169 37
170 33 170 63
171 171 171 193
172 281 172 441
173 339 173 337
174 137 174 691
175 299 175 339
176 11 176 151
177 119 177 723
178 239 178 261
179 221 179 979
180 2183 180 313
181 551 181 217
182 207 182 231
183 443 183 999
184 273 184 37
185 1211 185 927
186 479 186 721
187 57 187 163
188 179 188 183
189 537 189 181
190 1449 190 253
191 83 191 57
192 1173 192 1153
193 177 193 357
194 207 194 951
195 39 195 21
196 33 196 39
197 9 197 1107
198 1571 198 553
199 9 199 153
200 189 200 357
…………
201-800/1400略

yangchuanju · 发表于 2022-10-20 22:40

本帖最后由 yangchuanju 于 2022-10-20 22:50 编辑

A114429-100
n位最大孪生素数之大素
1 7
2 73
3 883
4 9931
5 99991
6 999961
7 9999973
8 99999589
9 999999193
10 9999999703
11 99999999763
12 999999999961
13 9999999998491
14 99999999999973
15 999999999997969
16 9999999999999643
17 99999999999998809
18 999999999999998929
19 9999999999999998503
20 99999999999999997741
21 999999999999999994999
22 9999999999999999997573
23 99999999999999999998209
24 999999999999999999995671
25 9999999999999999999999169
26 99999999999999999999994123
27 999999999999999999999999643
28 9999999999999999999999999223
29 99999999999999999999999997189
30 999999999999999999999999998941
31 9999999999999999999999999997903
32 99999999999999999999999999998191
33 999999999999999999999999999996721
34 9999999999999999999999999999994801
35 99999999999999999999999999999999469
36 999999999999999999999999999999994519
37 9999999999999999999999999999999998323
38 99999999999999999999999999999999998581
39 999999999999999999999999999999999973201
40 9999999999999999999999999999999999987913
41 99999999999999999999999999999999999997159
42 999999999999999999999999999999999999972229
43 9999999999999999999999999999999999999990361
44 99999999999999999999999999999999999999989161
45 999999999999999999999999999999999999999995239
46 9999999999999999999999999999999999999999997873
47 99999999999999999999999999999999999999999998983
48 999999999999999999999999999999999999999999979471
49 9999999999999999999999999999999999999999999991483
50 99999999999999999999999999999999999999999999985663
51 999999999999999999999999999999999999999999999994243
52 9999999999999999999999999999999999999999999999975613
53 99999999999999999999999999999999999999999999999949813
54 999999999999999999999999999999999999999999999999988699
55 9999999999999999999999999999999999999999999999999994981
56 99999999999999999999999999999999999999999999999999985219
57 999999999999999999999999999999999999999999999999999984919
58 9999999999999999999999999999999999999999999999999999994933
59 99999999999999999999999999999999999999999999999999999978709
60 999999999999999999999999999999999999999999999999999999992911
61 9999999999999999999999999999999999999999999999999999999997321
62 99999999999999999999999999999999999999999999999999999999941383
63 999999999999999999999999999999999999999999999999999999999999349
64 9999999999999999999999999999999999999999999999999999999999993331
65 99999999999999999999999999999999999999999999999999999999999995191
66 999999999999999999999999999999999999999999999999999999999999993361
67 9999999999999999999999999999999999999999999999999999999999999999421
68 99999999999999999999999999999999999999999999999999999999999999992953
69 999999999999999999999999999999999999999999999999999999999999999974359
70 9999999999999999999999999999999999999999999999999999999999999999942223
71 99999999999999999999999999999999999999999999999999999999999999999985609
72 999999999999999999999999999999999999999999999999999999999999999999997459
73 9999999999999999999999999999999999999999999999999999999999999999999970843
74 99999999999999999999999999999999999999999999999999999999999999999999991093
75 999999999999999999999999999999999999999999999999999999999999999999999981343
76 9999999999999999999999999999999999999999999999999999999999999999999999978973
77 99999999999999999999999999999999999999999999999999999999999999999999999994729
78 999999999999999999999999999999999999999999999999999999999999999999999999978751
79 9999999999999999999999999999999999999999999999999999999999999999999999999985399
80 99999999999999999999999999999999999999999999999999999999999999999999999999993319
…………
81-100略

yangchuanju · 发表于 2022-10-20 22:41

本帖最后由 yangchuanju 于 2022-10-20 22:49 编辑

A092245-101
n位最小孪生素数之小素
1 3
2 11
3 101
4 1019
5 10007
6 100151
7 1000037
8 10000139
9 100000037
10 1000000007
11 10000000277
12 100000000817
13 1000000000061
14 10000000001267
15 100000000000097
16 1000000000002371
17 10000000000001549
18 100000000000000019
19 1000000000000000619
20 10000000000000000097
21 100000000000000000391
22 1000000000000000000409
23 10000000000000000000649
24 100000000000000000005527
25 1000000000000000000002731
26 10000000000000000000000559
27 100000000000000000000000949
28 1000000000000000000000000427
29 10000000000000000000000000601
30 100000000000000000000000002797
31 1000000000000000000000000001681
32 10000000000000000000000000007189
33 100000000000000000000000000002449
34 1000000000000000000000000000006751
35 10000000000000000000000000000007597
36 100000000000000000000000000000008419
37 1000000000000000000000000000000016879
38 10000000000000000000000000000000000871
39 100000000000000000000000000000000005569
40 1000000000000000000000000000000000010327
41 10000000000000000000000000000000000016111
42 100000000000000000000000000000000000002131
43 1000000000000000000000000000000000000006121
44 10000000000000000000000000000000000000023329
45 100000000000000000000000000000000000000005179
46 1000000000000000000000000000000000000000004249
47 10000000000000000000000000000000000000000002641
48 100000000000000000000000000000000000000000002257
49 1000000000000000000000000000000000000000000003997
50 10000000000000000000000000000000000000000000008281
51 100000000000000000000000000000000000000000000018307
52 1000000000000000000000000000000000000000000000007537
53 10000000000000000000000000000000000000000000000041347
54 100000000000000000000000000000000000000000000000025831
55 1000000000000000000000000000000000000000000000000003397
56 10000000000000000000000000000000000000000000000000007687
57 100000000000000000000000000000000000000000000000000006637
58 1000000000000000000000000000000000000000000000000000007381
59 10000000000000000000000000000000000000000000000000000016597
60 100000000000000000000000000000000000000000000000000000009091
61 1000000000000000000000000000000000000000000000000000000023599
62 10000000000000000000000000000000000000000000000000000000027319
63 100000000000000000000000000000000000000000000000000000000004711
64 1000000000000000000000000000000000000000000000000000000000022249
65 10000000000000000000000000000000000000000000000000000000000006517
66 100000000000000000000000000000000000000000000000000000000000007579
67 1000000000000000000000000000000000000000000000000000000000000004051
68 10000000000000000000000000000000000000000000000000000000000000001777
69 100000000000000000000000000000000000000000000000000000000000000012949
70 1000000000000000000000000000000000000000000000000000000000000000038119
71 10000000000000000000000000000000000000000000000000000000000000000017887
72 100000000000000000000000000000000000000000000000000000000000000000003319
73 1000000000000000000000000000000000000000000000000000000000000000000038671
74 10000000000000000000000000000000000000000000000000000000000000000000000829
75 100000000000000000000000000000000000000000000000000000000000000000000019219
76 1000000000000000000000000000000000000000000000000000000000000000000000024721
77 10000000000000000000000000000000000000000000000000000000000000000000000004489
78 100000000000000000000000000000000000000000000000000000000000000000000000045469
79 1000000000000000000000000000000000000000000000000000000000000000000000000002581
80 10000000000000000000000000000000000000000000000000000000000000000000000000030511
…………
81-101略

yangchuanju · 发表于 2022-10-20 22:46

A327133-1250 A124001-475
n位最大孪生素数之小素与10^n的差 n位最小孪生素数之小素与10^n的差
—————— 0  2——3-1=2
1 5——10-5=5 1  1——11-10=1
2 29——100-71=29 2  1——101-100=1
3 119 3  19
4 71 4  7
5 11 5  151
6 41 6  37
7 29 7  139
8 413 8  37
9 809 9  7
10 299 10  277
11 239 11  817
12 41 12  61
13 1511 13  1267
14 29 14  97
15 2033 15  2371
16 359 16  1549
17 1193 17  19
18 1073 18  619
19 1499 19  97
20 2261 20  391
21 5003 21  409
22 2429 22  649
23 1793 23  5527
24 4331 24  2731
25 833 25  559
26 5879 26  949
27 359 27  427
28 779 28  601
29 2813 29  2797
30 1061 30  1681
31 2099 31  7189
32 1811 32  2449
33 3281 33  6751
34 5201 34  7597
35 533 35  8419
36 5483 36  16879
37 1679 37  871
38 1421 38  5569
39 26801 39  10327
40 12089 40  16111
41 2843 41  2131
42 27773 42  6121
43 9641 43  23329
44 10841 44  5179
45 4763 45  4249
46 2129 46  2641
47 1019 47  2257
48 20531 48  3997
49 8519 49  8281
50 14339 50  18307
51 5759 51  7537
52 24389 52  41347
53 50189 53  25831
54 11303 54  3397
55 5021 55  7687
56 14783 56  6637
57 15083 57  7381
58 5069 58  16597
59 21293 59  9091
60 7091 60  23599
61 2681 61  27319
62 58619 62  4711
63 653 63  22249
64 6671 64  6517
65 4811 65  7579
66 6641 66  4051
67 581 67  1777
68 7049 68  12949
69 25643 69  38119
70 57779 70  17887
71 14393 71  3319
72 2543 72  38671
73 29159 73  829
74 8909 74  19219
75 18659 75  24721
76 21029 76  4489
77 5273 77  45469
78 21251 78  2581
79 14603 79  30511
80 6683 80  37759
81 8129 81  1867
82 33581 82  67549
83 13763 83  4849
84 29099 84  44317
85 4109 85  59587
86 25031 86  27379
87 4613 87  78757
88 23399 88  7177
89 4043 89  5407
90 43721 90  29101
91 22763 91  2677
92 96899 92  23899
93 39959 93  60811
94 133121 94  121
95 59 95  46897
96 6533 96  42007
97 2801 97  127939
98 24251 98  45487
99 7691 99  6001
100 35219 100  35737
101 38651 101  139201
102 160223 102  106759
103 2669 103  29659
104 15191 104  3457
105 83573 105  113617
106 12161 106  94789
107 5669 107  52819
108 67331 108  66517
109 26741 109  35371
110 120851 110  90577
111 32123 111  85417
112 48191 112  164191
113 6563 113  36769
114 32093 114  88237
115 28193 115  8107
116 10823 116  1831
117 165029 117  38119
118 27359 118  86989
119 83309 119  39199
120 14051 120  126997
121 38651 121  6697
122 13991 122  46201
123 10463 123  74011
124 19469 124  2149
125 78131 125  103429
126 18221 126  28471
127 71033 127  111889
128 138683 128  75901
129 893 129  73021
130 14933 130  46471
131 137003 131  29161
132 60911 132  99997
133 113969 133  11959
134 153089 134  142039
135 36923 135  76771
136 35873 136  52681
137 58943 137  16087
138 7889 138  15967
139 32741 139  184267
140 49973 140  92149
141 81491 141  84199
142 84491 142  6727
143 177113 143  227959
144 171371 144  198259
145 8723 145  52759
146 99473 146  88627
147 203231 147  10657
148 8291 148  140581
149 8039 149  181627
150 74921 150  87157
151 234329 151  23731
152 324773 152  35317
153 39893 153  431629
154 206519 154  30991
155 301811 155  155821
156 21923 156  10489
157 8693 157  62749
158 330203 158  361
159 66371 159  39637
160 56999 160  14179
161 38123 161  24277
162 46979 162  151537
163 144269 163  1819
164 22301 164  169429
165 15851 165  14317
166 17159 166  47581
167 118001 167  40207
168 48113 168  225151
169 89669 169  66907
170 228563 170  18151
171 29969 171  23359
172 3113 172  194887
173 5693 173  513631
174 75761 174  47899
175 79979 175  42559
176 86663 176  361711
177 40199 177  13297
178 28973 178  90577
179 11621 179  50947
180 50561 180  85477
181 269861 181  41929
182 6683 182  198841
183 205553 183  57781
184 182891 184  75871
185 6791 185  31267
186 242171 186  11581
187 544901 187  183109
188 293051 188  54151
189 219761 189  136561
190 17939 190  17899
191 476759 191  5107
192 122273 192  118681
193 244433 193  15727
194 171731 194  236887
195 23279 195  251881
196 204851 196  39559
197 832661 197  62497
198 15713 198  7729
199 63401 199  62209
200 17081 200  168961
…………
201-1250、201-475略

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