10^1500以内的区间哥猜验证

cuikun-186 · 发表于 2022-8-15 15:06

根据r2(N^2)≥N
则有：
r2(10^1500)≥10^750

cuikun-186 · 发表于 2022-8-15 15:12

本帖最后由 cuikun-186 于 2022-8-17 15:40 编辑

哥猜数的下限值r2(N)≥[N/(lnN)^2]

则有：

r2(10^1500)≥[10^1500/(ln10^1500)^2≥10^1492

杨先生客气了，笔误难免。

关于“≥”有2种表示，第一种就是“>”,第二种就是“=”

当然，正如杨先生所言，这样更为明确些：

r2(10^1500)≥[10^1500/(ln10^1500)^2>10^1492

大傻8888888 · 发表于 2022-8-15 21:38

本帖最后由大傻8888888 于 2022-8-16 07:07 编辑

按照我的公式或者哈李公式10^1500的哥猜数的双计法个数如下：
r2(10^1500)～（4/3）×1.32032×[10^1500/(ln10^1500)^2]≈1.4757×10^1493
10^1500的哥猜数的单计法个数大约是7.3786×10^1492
时空伴随者的计算结果是否和上面的个数吻合？

cuikun-186 · 发表于 2022-8-16 08:13

本帖最后由 cuikun-186 于 2022-8-17 06:36 编辑

有人用：r2(N)～（4/3）×1.32032×[N/(lnN)^2]是错误的。

因为公式中的N≥6，根据公式的特点：可检性，稳定性来看：

r2(6)～（4/3）×1.32032×[6/(ln6)^2]=3（显然是错误的)

***
我特别强调公式在其定义域内无反例！

大傻8888888 · 发表于 2022-8-16 20:32

yangchuanju先生：
虽然10^1500还不是无穷大，但是已经可以算是离充分大比较接近的大数了，很有可能用10^1500得出的计算值与实际值之比接近1，如0.99或者0.999之类。只是怕时空伴随者先生也得不出10^1500的哥猜实际值的确切数据。同时经过用哈李公式计算10^1500的哥猜数，也可以看出哈李公式计算哥猜数的优越性。
另外有人r2(10^1500)≥[10^1500/(ln10^1500)^2>10^14992（显然是错误的，因为10^14992明显大于10^1500)

yangchuanju · 发表于 2022-8-17 06:22

本帖最后由 yangchuanju 于 2022-8-17 06:52 编辑

cuikun-186 发表于 2022-8-16 08:13
有人用：r2(N)～（4/3）×1.32032×[N/(lnN)^2]是错误的。

因为公式中的N≥6，根据公式的特点：可检性， ...

r2(N)～（4/3）×1.32032×[N/(lnN)^2]是错误的；
但r2(10^N)～（4/3）×1.32032×[10^N/(ln10^N)^2]是正确的；
因为r2(N)～∏(p-1)/(p-2)×1.32032×[N/(lnN)^2],
式中p为N平方根内的能够整除N的各个奇素数，
当N趋近于无穷大时，r2(N)/[∏(p-1)/(p-2)×1.32032×N/(lnN)^2]趋近于1。

yangchuanju · 发表于 2022-8-17 06:48

本帖最后由 yangchuanju 于 2022-8-17 06:49 编辑

A065577
10^n哥猜数偶数双计哥猜数 4/3*1.32032*N/(lnN)^2 4/3*.../双哥
1 2 10 3 3.32 1.1068
2 6 100 12 8.30 0.6917
3 28 1000 56 36.89 0.6588
4 127 10000 254 207.52 0.8170
5 810 100000 1620 1328.15 0.8198
6 5402 1000000 10804 9223.28 0.8537
7 38807 10000000 77614 67762.85 0.8731
8 291400 100000000 582800 518809.34 0.8902
9 2274205 1000000000 4548410 4099234.25 0.9012
10 18200488 10000000000 36400976 33203797.44 0.9122
11 149091160 1E+11 298182320 274411549.13 0.9203
12 1243722370 1E+12 2487444740 2305819267.00 0.9270
13 10533150855 1E+13 21066301710 19647217422.96 0.9326
14 90350630388 1E+14 180701260776 169407129820.45 0.9375
15 783538341852 1E+15 1567076683704 1475724330880.34 0.9417
【附注】10^15的哥猜数为愚公688先生计算值。

yangchuanju · 发表于 2022-8-17 08:05

更大的10的整幂次偶数的哈李对数式计算值（的对数）：
偶数的指数 4/3*1.32032*N/(lnN)^2的对数
15 12.16900524
150 145.1690052
1500 1493.169005
15000 14991.16901
150000 149989.169
1500000 1499987.169
15000000 14999985.17
150000000 149999983.17
1500000000 1499999981.17
15000000000 14999999979.17
150000000000 149999999977.17
1500000000000 1499999999975.17
15000000000000 14999999999973.17
150000000000000 149999999999971.17

lg(ln(10^N)^2)=2*lg(ln(10^n))=2*lg(N*(ln(10))=2*lg(N)+2*lg(ln(10))

yangchuanju · 发表于 2022-8-17 11:23

本帖最后由 yangchuanju 于 2022-8-17 11:27 编辑

10的1-313次偶数的哈李对数式计算值及对数：
偶数的指数 4/3*1.32032*N/(lnN)^2的对数 4/3*1.32032*N/(lnN)^2 双哥数 4/3*.../双哥
1 0.521187756 3.320379744 3 1.1068
2 0.919127765 8.300949361 12 0.6917
3 1.566945246 36.89310827 56 0.6588
4 2.317067773 207.523734 254 0.8170
5 3.123247747 1328.151898 1620 0.8198
6 3.964885255 9223.277068 10804 0.8537
7 4.830991676 67762.85193 77614 0.8731
8 5.715007782 518809.3351 582800 0.8902
9 6.612702737 4099234.252 4548410 0.9012
10 7.521187756 33203797.44 36400976 0.9122
11 8.438402386 274411549.1 298182320 0.9203
12 9.362825264 2305819267 2487444740 0.9270
13 10.29330105 19647217423 21066301710 0.9326
14 11.22893168 1.69407E+11 180701260776 0.9375
15 12.16900524 1.47572E+12 1567076683704 0.9417

16 13.11294779 1.29702E+13
17 14.06028991 1.14892E+14
18 15.01064275 1.02481E+15
19 15.96368055 9.19773E+15
20 16.91912776 8.30095E+16
21 17.87674917 7.52921E+17
22 18.83634239 6.86029E+18
23 19.79773208 6.27671E+19
24 20.76076527 5.76455E+20
25 21.72530774 5.31261E+21
26 22.69124106 4.9118E+22
27 23.65846023 4.5547E+23
28 24.62687169 4.23518E+24
29 25.59639176 3.94813E+25
30 26.56694525 3.68931E+26
31 27.53846437 3.45513E+27
32 28.5108878 3.24256E+28
33 29.48415988 3.04902E+29
34 30.45822992 2.8723E+30
35 31.43305167 2.71051E+31
36 32.40858275 2.56202E+32
37 33.38478431 2.42541E+33
38 34.36162056 2.29943E+34
39 35.33905854 2.18302E+35
40 36.31706777 2.07524E+36
41 37.29562004 1.97524E+37
42 38.27468918 1.8823E+38
43 39.25425084 1.79577E+39
44 40.2342824 1.71507E+40
45 41.21476273 1.63969E+41
46 42.19567209 1.56918E+42
47 43.17699204 1.50311E+43
48 44.15870528 1.44114E+44
49 45.1407956 1.38292E+45
50 46.12324775 1.32815E+46
51 47.1060474 1.27658E+47
52 48.08918107 1.22795E+48
53 49.07263602 1.18205E+49
54 50.05640024 1.13868E+50
55 51.04046238 1.09765E+51
56 52.0248117 1.05879E+52
57 53.00943804 1.02197E+53
58 53.99433177 9.87033E+53
59 54.97948373 9.53858E+54
60 55.96488526 9.22328E+55
61 56.95052809 8.92335E+56
62 57.93640438 8.63782E+57
63 58.92250666 8.36578E+58
64 59.90882781 8.1064E+59
65 60.89536104 7.85889E+60
66 61.88209988 7.62254E+61
67 62.86903815 7.3967E+62
68 63.85616993 7.18075E+63
69 64.84348957 6.97412E+64
70 65.83099168 6.77629E+65
71 66.81867106 6.58675E+66
72 67.80652276 6.40505E+67
73 68.79454204 6.23077E+68
74 69.78272432 6.06351E+69
75 70.77106523 5.9029E+70
76 71.75956057 5.74858E+71
77 72.74820631 5.60024E+72
78 73.73699855 5.45756E+73
79 74.72593357 5.32027E+74
80 75.71500778 5.18809E+75
81 76.70421772 5.06078E+76
82 77.69356005 4.9381E+77
83 78.68303157 4.81983E+78
84 79.67262918 4.70575E+79
85 80.6623499 4.59568E+80
86 81.65219085 4.48943E+81
87 82.64214925 4.38681E+82
88 83.63222241 4.28768E+83
89 84.62240774 4.19187E+84
90 85.61270274 4.09923E+85
91 86.60310497 4.00964E+86
92 87.5936121 3.92294E+87
93 88.58422186 3.83903E+88
94 89.57493205 3.75779E+89
95 90.56574055 3.67909E+90
96 91.55664529 3.60284E+91
97 92.54764429 3.52894E+92
98 93.5387356 3.45729E+93
99 94.52991737 3.3878E+94
100 95.52118776 3.32038E+95
101 96.51254501 3.25496E+96
102 97.50398741 3.19145E+97
103 98.49551331 3.12978E+98
104 99.48712108 3.0699E+99
105 100.4788092 3.0117E+100
106 101.470576 2.9551E+101
107 102.4624202 2.9001E+102
108 103.4543402 2.8467E+103
109 104.4463348 2.7947E+104
110 105.4384024 2.7441E+105
111 106.4305418 2.6949E+106
112 107.4227517 2.647E+107
113 108.4150309 2.6003E+108
114 109.4073781 2.5549E+109
115 110.3997921 2.5107E+110
116 111.3922718 2.4676E+111
117 112.384816 2.4256E+112
118 113.3774237 2.3846E+113
119 114.3700938 2.3447E+114
120 115.3628253 2.3058E+115
121 116.355617 2.2679E+116
122 117.3484681 2.2308E+117
123 118.3413775 2.1947E+118
124 119.3343444 2.1595E+119
125 120.3273677 2.125E+120
126 121.3204467 2.0914E+121
127 122.3135803 2.0586E+122
128 123.3067678 2.0266E+123
129 124.3000083 1.9953E+124
130 125.2933011 1.9647E+125
131 126.2866452 1.9348E+126
132 127.2800399 1.9056E+127
133 128.2734845 1.8771E+128
134 129.2669782 1.8492E+129
135 130.2605202 1.8219E+130
136 131.2541099 1.7952E+131
137 132.2477466 1.7691E+132
138 133.2414296 1.7435E+133
139 134.2351582 1.7185E+134
140 135.2289317 1.6941E+135
141 136.2227495 1.6701E+136
142 137.2166111 1.6467E+137
143 138.2105157 1.6237E+138
144 139.2044628 1.6013E+139
145 140.1984518 1.5793E+140
146 141.192482 1.5577E+141
147 142.1865531 1.5366E+142
148 143.1806643 1.5159E+143
149 144.1748152 1.4956E+144
150 145.1690052 1.4757E+145
151 146.1632339 1.4562E+146
152 147.1575006 1.4371E+147
153 148.1518049 1.4184E+148
154 149.1461463 1.4001E+149
155 150.1405244 1.3821E+150
156 151.1349386 1.3644E+151
157 152.1293885 1.3471E+152
158 153.1238736 1.3301E+153
159 154.1183935 1.3134E+154
160 155.1129478 1.297E+155
161 156.107536 1.281E+156
162 157.1021577 1.2652E+157
163 158.0968125 1.2497E+158
164 159.0915001 1.2345E+159
165 160.0862199 1.2196E+160
166 161.0809716 1.205E+161
167 162.0757548 1.1906E+162
168 163.0705692 1.1764E+163
169 164.0654143 1.1626E+164
170 165.0602899 1.1489E+165
171 166.0551955 1.1355E+166
172 167.0501309 1.1224E+167
173 168.0450955 1.1094E+168
174 169.0400893 1.0967E+169
175 170.0351117 1.0842E+170
176 171.0301624 1.0719E+171
177 172.0252412 1.0598E+172
178 173.0203478 1.048E+173
179 174.0154817 1.0363E+174
180 175.0106427 1.0248E+175
181 176.0058306 1.0135E+176
182 177.001045 1.0024E+177
183 177.9962856 9.9148E+177
184 178.9915521 9.8074E+178
185 179.9868443 9.7016E+179
186 180.9821619 9.5976E+180
187 181.9775045 9.4952E+181
188 182.9728721 9.3945E+182
189 183.9682641 9.2953E+183
190 184.9636806 9.1977E+184
191 185.959121 9.1017E+185
192 186.9545853 9.0071E+186
193 187.9500731 8.914E+187
194 188.9455843 8.8224E+188
195 189.9411185 8.7321E+189
196 190.9366756 8.6432E+190
197 191.9322553 8.5557E+191
198 192.9278574 8.4695E+192
199 193.9234816 8.3846E+193
200 194.9191278 8.3009E+194
201 195.9147956 8.2186E+195
202 196.910485 8.1374E+196
203 197.9061957 8.0574E+197
204 198.9019274 7.9786E+198
205 199.89768 7.901E+199
206 200.8934533 7.8244E+200
207 201.8892471 7.749E+201
208 202.8850611 7.6747E+202
209 203.8808952 7.6014E+203
210 204.8767492 7.5292E+204
211 205.8726228 7.458E+205
212 206.868516 7.3878E+206
213 207.8644285 7.3186E+207
214 208.8603602 7.2504E+208
215 209.8563108 7.1831E+209
216 210.8522803 7.1167E+210
217 211.8482683 7.0513E+211
218 212.8442748 6.9867E+212
219 213.8402995 6.9231E+213
220 214.8363424 6.8603E+214
221 215.8324032 6.7983E+215
222 216.8284818 6.7372E+216
223 217.824578 6.6769E+217
224 218.8206917 6.6175E+218
225 219.8168227 6.5588E+219
226 220.8129709 6.5009E+220
227 221.809136 6.4437E+221
228 222.8053181 6.3873E+222
229 223.8015168 6.3316E+223
230 224.7977321 6.2767E+224
231 225.7939638 6.2225E+225
232 226.7902118 6.169E+226
233 227.7864759 6.1161E+227
234 228.782756 6.064E+228
235 229.779052 6.0125E+229
236 230.7753637 5.9616E+230
237 231.7716911 5.9114E+231
238 232.7680338 5.8618E+232
239 233.764392 5.8129E+233
240 234.7607653 5.7645E+234
241 235.7571537 5.7168E+235
242 236.753557 5.6697E+236
243 237.7499752 5.6231E+237
244 238.7464081 5.5771E+238
245 239.7428556 5.5317E+239
246 240.7393175 5.4868E+240
247 241.7357938 5.4424E+241
248 242.7322844 5.3986E+242
249 243.7287891 5.3554E+243
250 244.7253077 5.3126E+244
251 245.7218403 5.2704E+245
252 246.7183867 5.2286E+246
253 247.7149467 5.1874E+247
254 248.7115203 5.1466E+248
255 249.7081074 5.1063E+249
256 250.7047078 5.0665E+250
257 251.7013215 5.0271E+251
258 252.6979483 4.9883E+252
259 253.6945882 4.9498E+253
260 254.6912411 4.9118E+254
261 255.6879067 4.8742E+255
262 256.6845852 4.8371E+256
263 257.6812763 4.8004E+257
264 258.6779799 4.7641E+258
265 259.674696 4.7282E+259
266 260.6714245 4.6927E+260
267 261.6681652 4.6576E+261
268 262.6649182 4.6229E+262
269 263.6616832 4.5886E+263
270 264.6584602 4.5547E+264
271 265.6552492 4.5212E+265
272 266.6520499 4.488E+266
273 267.6488625 4.4552E+267
274 268.6456866 4.4227E+268
275 269.6425224 4.3906E+269
276 270.6393696 4.3588E+270
277 271.6362282 4.3274E+271
278 272.6330982 4.2963E+272
279 273.6299793 4.2656E+273
280 274.6268717 4.2352E+274
281 275.6237751 4.2051E+275
282 276.6206895 4.1753E+276
283 277.6176149 4.1459E+277
284 278.6145511 4.1167E+278
285 279.611498 4.0879E+279
286 280.6084557 4.0593E+280
287 281.605424 4.0311E+281
288 282.6024028 4.0032E+282
289 283.5993921 3.9755E+283
290 284.5963918 3.9481E+284
291 285.5934018 3.921E+285
292 286.5904221 3.8942E+286
293 287.5874525 3.8677E+287
294 288.5844931 3.8414E+288
295 289.5815437 3.8154E+289
296 290.5786043 3.7897E+290
297 291.5756749 3.7642E+291
298 292.5727552 3.739E+292
299 293.5698454 3.714E+293
300 294.5669452 3.6893E+294
301 295.5640548 3.6648E+295
302 296.5611739 3.6406E+296
303 297.5583025 3.6166E+297
304 298.5554406 3.5929E+298
305 299.5525881 3.5693E+299
306 300.5497449 3.5461E+300
307 301.546911 3.523E+301
308 302.5440863 3.5001E+302
309 303.5412708 3.4775E+303
310 304.5384644 3.4551E+304
311 305.535667 3.4329E+305
312 306.5328786 3.411E+306
313 307.5300991 3.3892E+307

yangchuanju · 发表于 2022-8-17 11:41

本帖最后由 yangchuanju 于 2022-8-17 11:43 编辑

大傻8888888 发表于 2022-8-16 20:32
yangchuanju先生：
虽然10^1500还不是无穷大，但是已经可以算是离充分大比较接近的大数了，很有可能用10^1 ...

10^1500的双计哥猜数约等于10^1493.169005，肯定大于10^750喽！
10^1500/ln(10^1500)^2约等于10^1492.923386，10^1500的双计哥猜数也是大于10^1500/ln(10^1500)^2的呀！

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10^1500以内的区间哥猜验证

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