有用的素数个数表

yangchuanju · 发表于 2022-10-20 16:34

本帖最后由 yangchuanju 于 2022-10-20 16:43 编辑

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)绝对偏差表：
n 10^n/log(10^n)-π(10^n) 减1.08-π(10^n) 减1-π(10^n) Li(10^n)-π(10^n)
1 0 4 3 2
2 -3 3 2 5
3 -23 4 1 10
4 -143 2 -12 17
5 -906 -4 -80 38
6 -6116 45 -468 130
7 -44158 561 -3121 339
8 -332774 6549 -21152 754
9 -2592592 69985 -145992 1701
10 -20758029 690493 -1040540 3104
11 -169923159 6545056 -7638513 11588
12 -1416705193 60615397 -57718369 38263
13 -11992858452 555560046 -446676619 108971
14 -1.028383E+11 5070271362 -3527115022 314890
15 -8.916050E+11 46223804313 -28336573669 1052619
16 -7.804290E+12 4.216926E+11 -2.310828E+11 3214632
17 -6.888373E+13 3.853432E+12 -1.909191E+12 7956589
18 -6.124831E+14 3.528985E+13 -1.595550E+13 21949555
19 -5.481624E+15 3.239791E+14 -1.347057E+14 99877775
20 -4.934719E+16 2.981921E+15 -1.147629E+15 222744644
21 -4.465799E+17 2.751657E+16 -9.857223E+15 597394254
22 -4.060704E+18 2.545624E+17 -8.529084E+16 1932355208
23 -3.708351E+19 2.360830E+18 -7.429324E+17 7250186216
24 -3.399964E+20 2.194656E+19 -6.510871E+18 17146907278
25 -3.128517E+21 2.044826E+20 -5.737835E+19 55160980939
26 -2.888336E+22 1.909370E+21 -5.082529E+20 1.558917E+11
27 -2.674796E+23 1.786582E+22 -4.523362E+21 5.086667E+11
28 -2.484097E+24 1.674986E+23 -4.043323E+22 1.427746E+12
29 -2.313093E+25 1.573306E+24 -3.628895E+23 4.551194E+12

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

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