n!的双计素数对

yangchuanju · 发表于 2023-3-13 15:59

n!的双计素数对
n n! 哈李双哥单哥A062311 哈李/2/单哥
1 1 0 1 0 ——
2 2 5.49481411 2 0 ——
3 6 2.466980774 3 1 1.2335
4 24 6.273251085 4 3 1.0455
5 120 18.42925731 5 12 0.7679
6 720 58.54936936 6 39 0.7506
7 5040 292.9201381 7 184 0.7960
8 40320 1514.452344 8 951 0.7962
9 362880 9352.829167 9 5531 0.8455
10 3628800 67186.07384 10 38713 0.8677
11 39916800 611570.4339 11 346207 0.8832
12 479001600 5627478.155 12 3130812 0.8987
13 6227020800 62686473.8 13 34444964 0.9100
14 87178291200 703363570.2 14 382437428 0.9196
15 1307674368000 8601691238 15 4637235145 0.9275

随着n值的连续增大，哈李素数对计算值与真实值之比逐渐趋近于1。

yangchuanju · 发表于 2023-3-13 16:01

n!的双计素数对
n n! 1.32*n!/LN(n!)^2*波波动系数
1 1 —— 1.0000
2 2 5.49481411 1.0000
3 6 2.466980774 1.0000
4 24 6.273251085 2.0000
5 120 18.42925731 2.6667
6 720 58.54936936 2.6667
7 5040 292.9201381 3.2000
8 40320 1514.452344 3.2000
9 362880 9352.829167 3.2000
10 3628800 67186.07384 3.2000
11 39916800 611570.4339 3.5556
12 479001600 5627478.155 3.5556
13 6227020800 62686473.8 3.8788
14 87178291200 703363570.2 3.8788
15 1307674368000 8601691238 3.8788
16 2.09228E+13 1.1387E+11 3.8788
17 3.55687E+14 1.7304E+12 4.1374
18 6.40237E+15 2.63965E+13 4.1374
19 1.21645E+17 4.54518E+14 4.3807
20 2.4329E+18 7.84938E+15 4.3807
21 5.10909E+19 1.43461E+17 4.3807
22 1.124E+21 2.76644E+18 4.3807
23 2.5852E+22 5.88042E+19 4.5894
24 6.20448E+23 1.25231E+21 4.5894
25 1.55112E+25 2.79294E+22 4.5894
26 4.03291E+26 6.50978E+23 4.5894
27 1.08889E+28 1.58276E+25 4.5894
28 3.04888E+29 4.00736E+26 4.5894
29 8.84176E+30 1.09396E+28 4.7593
30 2.65253E+32 2.98968E+29 4.7593
31 8.22284E+33 8.76293E+30 4.9234
32 2.63131E+35 2.57088E+32 4.9234
33 8.68332E+36 7.80072E+33 4.9234
34 2.95233E+38 2.44528E+35 4.9234
35 1.03331E+40 7.91071E+36 4.9234
36 3.71993E+41 2.63861E+38 4.9234
37 1.37638E+43 9.32499E+39 5.0641
38 5.23023E+44 3.29755E+41 5.0641
39 2.03979E+46 1.19919E+43 5.0641
40 8.15915E+47 4.48135E+44 5.0641
41 3.34525E+49 1.76373E+46 5.1940
42 1.40501E+51 6.94493E+47 5.1940
43 6.04153E+52 2.87274E+49 5.3206
44 2.65827E+54 1.18882E+51 5.3206
45 1.19622E+56 5.03891E+52 5.3206
46 5.50262E+57 2.18632E+54 5.3206
47 2.58623E+59 9.92115E+55 5.4389
48 1.24139E+61 4.50366E+57 5.4389
49 6.08282E+62 2.08957E+59 5.4389
50 3.04141E+64 9.90457E+60 5.4389
51 1.55112E+66 4.79407E+62 5.4389
52 8.06582E+67 2.36852E+64 5.4389
53 4.27488E+69 1.21732E+66 5.5455
54 2.30844E+71 6.25826E+67 5.5455
55 1.26964E+73 3.28011E+69 5.5455
56 7.10999E+74 1.75206E+71 5.5455
57 4.05269E+76 9.53419E+72 5.5455
58 2.35056E+78 5.28378E+74 5.5455
59 1.38683E+80 3.03348E+76 5.6428
60 8.32099E+81 1.74193E+78 5.6428
61 5.0758E+83 1.03499E+80 5.7385
62 3.147E+85 6.15068E+81 5.7385
63 1.98261E+87 3.71684E+83 5.7385
64 1.26887E+89 2.28332E+85 5.7385
65 8.24765E+90 1.42556E+87 5.7385
66 5.44345E+92 9.04308E+88 5.7385
67 3.64711E+94 5.91677E+90 5.8267
68 2.48004E+96 3.87188E+92 5.8267
69 1.71122E+98 2.57252E+94 5.8267
70 1.1979E+100 1.73497E+96 5.8267
71 8.5048E+101 1.2047E+98 5.9112
72 6.1234E+103 8.3662E+99 5.9112
73 4.4701E+105 5.9768E+101 5.9944
74 3.3079E+107 4.2704E+103 5.9944
75 2.4809E+109 3.0939E+105 5.9944
76 1.8855E+111 2.2726E+107 5.9944
77 1.4518E+113 1.692E+109 5.9944
78 1.1324E+115 1.2767E+111 5.9944
79 8.9462E+116 9.8883E+112 6.0723
80 7.1569E+118 7.6593E+114 6.0723
81 5.7971E+120 6.0095E+116 6.0723
82 4.7536E+122 4.7752E+118 6.0723
83 3.9455E+124 3.8897E+120 6.1473
84 3.3142E+126 3.1687E+122 6.1473
85 2.8171E+128 2.6131E+124 6.1473
86 2.4227E+130 2.1811E+126 6.1473
87 2.1078E+132 1.8423E+128 6.1473
88 1.8548E+134 1.5746E+130 6.1473
89 1.6508E+136 1.3773E+132 6.2179
90 1.4857E+138 1.2047E+134 6.2179
91 1.352E+140 1.0659E+136 6.2179
92 1.2438E+142 9.5367E+137 6.2179
93 1.1568E+144 8.6284E+139 6.2179
94 1.0874E+146 7.893E+141 6.2179
95 1.033E+148 7.2993E+143 6.2179
96 9.9168E+149 6.8233E+145 6.2179
97 9.6193E+151 6.5146E+147 6.2834
98 9.4269E+153 6.2202E+149 6.2834
99 9.3326E+155 6.0015E+151 6.2834
100 9.3326E+157 5.8505E+153 6.2834
101 9.4259E+159 5.82E+155 6.3468
102 9.6145E+161 5.7901E+157 6.3468
103 9.9029E+163 5.8759E+159 6.4097
104 1.0299E+166 5.9634E+161 6.4097
105 1.0814E+168 6.1118E+163 6.4097
106 1.1463E+170 6.3251E+165 6.4097
107 1.2265E+172 6.6721E+167 6.4707
108 1.3246E+174 7.0386E+169 6.4707
109 1.4439E+176 7.5657E+171 6.5312
110 1.5882E+178 8.1327E+173 6.5312
111 1.763E+180 8.8236E+175 6.5312
112 1.9745E+182 9.6615E+177 6.5312
113 2.2312E+184 1.0772E+180 6.5900
114 2.5436E+186 1.201E+182 6.5900
115 2.9251E+188 1.3512E+184 6.5900
116 3.3931E+190 1.5336E+186 6.5900
117 3.9699E+192 1.7559E+188 6.5900
118 4.6845E+194 2.0281E+190 6.5900
119 5.5746E+196 2.3628E+192 6.5900
120 6.6895E+198 2.7764E+194 6.5900
121 8.0943E+200 3.2901E+196 6.5900
122 9.875E+202 3.9319E+198 6.5900
123 1.2146E+205 4.7382E+200 6.5900
124 1.5061E+207 5.7572E+202 6.5900
125 1.8827E+209 7.053E+204 6.5900
126 2.3722E+211 8.711E+206 6.5900
127 3.0127E+213 1.0933E+209 6.6428
128 3.8562E+215 1.3722E+211 6.6428
129 4.9745E+217 1.7359E+213 6.6428
130 6.4669E+219 2.2135E+215 6.6428
131 8.4716E+221 2.8667E+217 6.6943
132 1.1182E+224 3.7128E+219 6.6943
133 1.4873E+226 4.8457E+221 6.6943
134 1.9929E+228 6.3728E+223 6.6943
135 2.6905E+230 8.4449E+225 6.6943
136 3.659E+232 1.1275E+228 6.6943
137 5.0129E+234 1.528E+230 6.7438
138 6.9178E+236 2.0707E+232 6.7438
139 9.6157E+238 2.8475E+234 6.7931
140 1.3462E+241 3.9158E+236 6.7931
141 1.8981E+243 5.4241E+238 6.7931
142 2.6954E+245 7.5678E+240 6.7931
143 3.8544E+247 1.0634E+243 6.7931
144 5.5503E+249 1.505E+245 6.7931
145 8.0479E+251 2.1449E+247 6.7931
146 1.175E+254 3.0785E+249 6.7931
147 1.7272E+256 4.4492E+251 6.7931
148 2.5563E+258 6.4746E+253 6.7931
149 3.8089E+260 9.5515E+255 6.8393
150 5.7134E+262 1.4091E+258 6.8393
151 8.6272E+264 2.1069E+260 6.8852
152 1.3113E+267 3.1504E+262 6.8852
153 2.0063E+269 4.7422E+264 6.8852
154 3.0898E+271 7.1858E+266 6.8852
155 4.7891E+273 1.096E+269 6.8852
156 7.4711E+275 1.6828E+271 6.8852
157 1.173E+278 2.6171E+273 6.9296
158 1.8533E+280 4.0705E+275 6.9296
159 2.9467E+282 6.3715E+277 6.9296
160 4.7147E+284 1.0037E+280 6.9296
161 7.5907E+286 1.5912E+282 6.9296
162 1.2297E+289 2.5385E+284 6.9296
163 2.0044E+291 4.1005E+286 6.9726
164 3.2872E+293 6.6237E+288 6.9726
165 5.4239E+295 1.0766E+291 6.9726
166 9.0037E+297 1.7606E+293 6.9726
167 1.5036E+300 2.9144E+295 7.0149
168 2.5261E+302 4.8244E+297 7.0149
169 4.2691E+304 8.0343E+299 7.0149
170 7.2574E+306 1.3461E+302 7.0149

yangchuanju · 发表于 2023-3-13 16:03

本帖最后由 yangchuanju 于 2023-3-13 16:08 编辑

n!的双计素数对
第4列数字为双计素数对的常用对数值，已考虑了波动系数的影响，采用哈李对数计算式，当n相当大时，计算值应该接近于真实值。

n lg(n!) ln(n!) lg(1.32)+lgN-2*lg(lnN)+lg波 R2(n!)/R2((n-1)!) 波动系数
1 0 0 —— —— 1.0000
2 0.301029996 0.693147181 0.739953005 —— 1.0000
3 0.77815125 1.791759469 0.392165765 0.448965283 1.0000
4 1.380211242 3.17805383 0.496462675 1.271443043 2.0000
5 2.079181246 4.787491743 0.839539101 2.203314166 2.6667
6 2.857332496 6.579251212 1.341553489 3.176979321 2.6667
7 3.702430536 8.525161361 1.961599252 4.169133122 3.2000
8 4.605520523 10.6046029 2.675105633 5.170188549 3.2000
9 5.559763033 12.80182748 3.465793024 6.175717055 3.2000
10 6.559763033 15.10441257 4.322129285 7.183502728 3.2000
11 7.601155718 17.50230785 5.235539013 8.192373197 3.5556
12 8.680336964 19.9872145 6.199406349 9.201684455 3.5556
13 9.794280316 22.55216385 7.208477811 10.21107491 3.8788
14 10.94040835 25.19122118 8.258483841 11.22034033 3.8788
15 12.11649961 27.89927138 9.34588782 12.22936701 3.8788
16 13.32061959 30.67186011 10.4677133 13.23809447 3.8788
17 14.55106852 33.50507345 11.6214213 14.24649409 4.1374
18 15.80634102 36.39544521 12.80482088 15.25455634 4.1374
19 17.08509462 39.33988419 14.0160024 16.26228318 4.3807
20 18.38612462 42.33561646 15.25328677 17.26968332 4.3807
21 19.70834391 45.3801389 16.5151862 18.27676927 4.3807
22 21.05076659 48.47118135 17.80037331 19.28355555 4.3807
23 22.41249443 51.60667557 19.10765659 20.29005754 4.5894
24 23.79270567 54.7847294 20.43596056 21.29629071 4.5894
25 25.19064568 58.00360522 21.78430963 22.30227026 4.5894
26 26.60561903 61.26170176 23.15181484 23.3080108 4.5894
27 28.03698279 64.55753863 24.53766279 24.31352624 4.5894
28 29.48414082 67.88974314 25.94110642 25.31882971 4.5894
29 30.94653882 71.25703897 27.36145721 26.32393354 4.7593
30 32.42366007 74.65823635 28.79807855 27.32884926 4.7593
31 33.91502177 78.09222355 30.25038012 28.33358763 4.9234
32 35.42017175 81.55795946 31.71781298 29.33815868 4.9234
33 36.93868569 85.05446702 33.19986536 30.34257176 4.9234
34 38.4701646 88.58082754 34.69605907 31.34683555 4.9234
35 40.01423265 92.1361756 36.20594622 32.35095814 4.9234
36 41.57053515 95.71969454 37.72910647 33.35494707 4.9234
37 43.13873687 99.33061245 39.26514458 34.35880935 5.0641
38 44.71852047 102.9681986 40.81368817 35.36255151 5.0641
39 46.30958508 106.6317603 42.37438585 36.36617966 5.0641
40 47.91164507 110.3206397 43.94690546 37.36969948 5.0641
41 49.52442892 114.0342118 45.53093253 38.37311628 5.1940
42 51.14767822 117.7718814 47.12616892 39.37643504 5.1940
43 52.78114667 121.5330815 48.73233158 40.37966039 5.3206
44 54.42459935 125.3172711 50.34915142 41.38279669 5.3206
45 56.07781186 129.1239336 51.9763723 42.38584801 5.3206
46 57.74056969 132.952575 53.61375012 43.3888182 5.3206
47 59.41266755 136.8027226 55.261052 44.39171083 5.4389
48 61.09390879 140.6739236 56.91805552 45.39452929 5.4389
49 62.78410487 144.5657439 58.58454801 46.39727676 5.4389
50 64.48307487 148.477767 60.26032595 47.39995623 5.4389
51 66.19064505 152.4095926 61.94519438 48.40257052 5.4389
52 67.90664839 156.3608363 63.63896635 49.4051223 5.4389
53 69.63092426 160.3311282 65.3414625 50.40761407 5.5455
54 71.36331802 164.3201123 67.05251051 51.41004821 5.5455
55 73.10368071 168.3274454 68.77194478 52.41242697 5.5455
56 74.85186874 172.3527971 70.499606 53.41475246 5.5455
57 76.60774359 176.3958484 72.23534081 54.41702671 5.5455
58 78.37117159 180.4562914 73.97900146 55.41925163 5.5455
59 80.1420236 184.5338289 75.73044554 56.42142901 5.6428
60 81.92017485 188.6281734 77.48953566 57.42356058 5.6428
61 83.70550468 192.7390473 79.2561392 58.42564798 5.7385
62 85.49789637 196.8661817 81.03012807 59.42769276 5.7385
63 87.29723692 201.0093164 82.81137848 60.42969638 5.7385
64 89.1034169 205.1681995 84.59977073 61.43166027 5.7385
65 90.91633025 209.3425868 86.39518901 62.43358575 5.7385
66 92.73587419 213.5322415 88.1975212 63.43547411 5.7385
67 94.56194899 217.7369341 90.00665872 64.43732657 5.8267
68 96.3944579 221.9564418 91.82249633 65.43914427 5.8267
69 98.233307 226.1905483 93.64493202 66.44092835 5.8267
70 100.078405 230.4390436 95.47386684 67.44267985 5.8267
71 101.9296634 234.7017234 97.30920476 68.44439979 5.9112
72 103.7869959 238.9783896 99.15085255 69.44608915 5.9112
73 105.6503187 243.268849 100.9987197 70.44774884 5.9944
74 107.5195505 247.5729141 102.8527181 71.44937977 5.9944
75 109.3946117 251.8904022 104.7127624 72.45098277 5.9944
76 111.2754253 256.2211356 106.5787693 73.45255868 5.9944
77 113.161916 260.564941 108.450658 74.45410827 5.9944
78 115.0540106 264.9216498 110.3283497 75.45563229 5.9944
79 116.9516377 269.2910977 112.2117677 76.45713148 6.0723
80 118.8547277 273.6731243 114.1008374 77.45860651 6.0723
81 120.7632127 278.0675734 115.995486 78.46005806 6.0723
82 122.6770266 282.4742927 117.8956427 79.46148678 6.0723
83 124.5961047 286.8931333 119.8012383 80.46289326 6.1473
84 126.520384 291.3239501 121.7122055 81.46427812 6.1473
85 128.4498029 295.7666014 123.6284786 82.46564191 6.1473
86 130.3843013 300.2209486 125.5499933 83.4669852 6.1473
87 132.3238206 304.6868568 127.4766871 84.4683085 6.1473
88 134.2683033 309.1641936 129.4084988 85.46961233 6.1473
89 136.2176933 313.6528299 131.3453688 86.47089719 6.2179
90 138.1719358 318.1526396 133.2872387 87.47216354 6.2179
91 140.1309772 322.6634991 135.2340514 88.47341185 6.2179
92 142.094765 327.1852877 137.1857514 89.47464255 6.2179
93 144.063248 331.7178872 139.1422841 90.47585608 6.2179
94 146.0363758 336.261182 141.1035963 91.47705285 6.2179
95 148.0140994 340.8150589 143.0696358 92.47823325 6.2179
96 149.9963707 345.3794071 145.0403517 93.47939768 6.2179
97 151.9831424 349.954118 147.0156941 94.4805465 6.2834
98 153.9743685 354.5390855 148.9956142 95.48168007 6.2834
99 155.9700037 359.1342054 150.980064 96.48279875 6.2834
100 157.9700037 363.7393756 152.968997 97.48390286 6.2834
101 159.974325 368.3544961 154.962367 98.48499275 6.3468
102 161.9829252 372.9794689 156.9601293 99.48606872 6.3468
103 163.9957624 377.6141979 158.9622397 100.4871311 6.4097
104 166.0127958 382.2585888 160.9686552 101.4881801 6.4097
105 168.0339851 386.9125491 162.9793334 102.4892162 6.4097
106 170.0592909 391.5759882 164.9942328 103.4902394 6.4097
107 172.0886747 396.2488171 167.0133127 104.4912502 6.4707
108 174.1220985 400.9309483 169.0365332 105.4922488 6.4707
109 176.159525 405.6222962 171.0638553 106.4932355 6.5312
110 178.2009176 410.3227765 173.0952403 107.4942104 6.5312
111 180.2462406 415.0323067 175.1306507 108.4951739 6.5312
112 182.2954586 419.7508056 177.1700495 109.4961261 6.5312
113 184.3485371 424.4781934 179.2134003 110.4970673 6.5900
114 186.4054419 429.2143919 181.2606673 111.4979977 6.5900
115 188.4661398 433.959324 183.3118157 112.4989176 6.5900
116 190.5305978 438.7129142 185.3668109 113.4998271 6.5900
117 192.5987836 443.4750881 187.4256191 114.5007264 6.5900
118 194.6706656 448.2457727 189.4882072 115.5016157 6.5900
119 196.7462126 453.0248962 191.5545424 116.5024953 6.5900
120 198.8253938 457.812388 193.6245927 117.5033653 6.5900
121 200.9081792 462.6081785 195.6983265 118.5042259 6.5900
122 202.994539 467.4121996 197.7757129 119.5050772 6.5900
123 205.0844442 472.2243839 199.8567213 120.5059195 6.5900
124 207.1778658 477.0446655 201.9413217 121.5067529 6.5900
125 209.2747759 481.8729792 204.0294846 122.5075775 6.5900
126 211.3751464 486.7092611 206.1211811 123.5083936 6.5900
127 213.4789501 491.5534482 208.2163826 124.5092013 6.6428
128 215.5861601 496.4054785 210.3150609 125.5100007 6.6428
129 217.6967498 501.2652909 212.4171885 126.510792 6.6428
130 219.8106932 506.1328253 214.5227381 127.5115753 6.6428
131 221.9279645 511.0080227 216.6316829 128.5123507 6.6943
132 224.0485384 515.8908246 218.7439967 129.5131185 6.6943
133 226.17239 520.7811737 220.8596534 130.5138787 6.6943
134 228.2994948 525.6790135 222.9786275 131.5146314 6.6943
135 230.4298286 530.5842883 225.1008938 132.5153768 6.6943
136 232.5633675 535.4969432 227.2264274 133.5161151 6.6943
137 234.7000881 540.4169241 229.3552041 134.5168463 6.7438
138 236.8399672 545.3441778 231.4871997 135.5175705 6.7438
139 238.982982 550.2786517 233.6223906 136.5182879 6.7931
140 241.12911 555.2202941 235.7607533 137.5189985 6.7931
141 243.2783291 560.169054 237.9022648 138.5197026 6.7931
142 245.4306174 565.1248811 240.0469025 139.5204001 6.7931
143 247.5859535 570.0877257 242.194644 140.5210912 6.7931
144 249.744316 575.057539 244.3454673 141.5217761 6.7931
145 251.905684 580.0342728 246.4993506 142.5224547 6.7931
146 254.0700368 585.0178794 248.6562725 143.5231272 6.7931
147 256.2373542 590.008312 250.8162118 144.5237938 6.7931
148 258.4076159 595.0055242 252.9791478 145.5244544 6.7931
149 260.5808022 600.0094706 255.1450599 146.5251091 6.8393
150 262.7568934 605.0201058 257.3139277 147.5257582 6.8393
151 264.9358704 610.0373857 259.4857314 148.5264016 6.8852
152 267.1177139 615.0612662 261.6604511 149.5270394 6.8852
153 269.3024054 620.0917041 263.8380675 150.5276718 6.8852
154 271.4899261 625.1286567 266.0185612 151.5282987 6.8852
155 273.6802578 630.1720818 268.2019134 152.5289204 6.8852
156 275.8733824 635.2219379 270.3881053 153.5295368 6.8852
157 278.069282 640.2781837 272.5771186 154.530148 6.9296
158 280.2679391 645.3407787 274.7689348 155.5307542 6.9296
159 282.4693363 650.4096829 276.9635362 156.5313553 6.9296
160 284.6734562 655.4848567 279.1609048 157.5319515 6.9296
161 286.8802821 660.5662611 281.3610233 158.5325429 6.9296
162 289.0897971 665.6538574 283.5638742 159.5331294 6.9296
163 291.3019847 670.7476076 285.7694404 160.5337112 6.9726
164 293.5168286 675.847474 287.9777051 161.5342884 6.9726
165 295.7343125 680.9534195 290.1886516 162.5348609 6.9726
166 297.9544206 686.0654073 292.4022635 163.5354289 6.9726
167 300.1771371 691.1834011 294.6185244 164.5359925 7.0149
168 302.4024464 696.3073651 296.8374183 165.5365516 7.0149
169 304.6303331 701.4372638 299.0589293 166.5371063 7.0149
170 306.860782 706.5730622 301.2830418 167.5376568 7.0149
171 309.0937781 711.7147258 303.5097401 168.5382031 7.0149
200 374.8968886 863.2319872 369.1452075 197.5524274 7.2845
300 614.485803 1414.90585 608.3049219 297.5861493 7.7676
400 868.8064142 2000.500698 862.3247107 397.607602 8.1342
500 1134.086409 2611.330458 1127.373259 497.6229691 8.4498
600 1408.102287 3242.275335 1401.201161 597.634765 8.6672
700 1689.384181 3889.950832 1682.324867 697.6442403 8.8859
800 1976.887084 4551.950731 1969.691263 797.6520999 9.0544
900 2269.829476 5226.475515 2262.513632 897.6587774 9.2165
1000 2567.604644 5912.128178 2560.18173 997.6645568 9.3533
2000 5735.520651 13206.52435 5727.399647 1997.698497 10.2800
3000 9130.617981 21024.02485 9122.093123 2997.715516 10.8248
4000 12673.26217 29181.26454 12664.45253 3997.726522 11.2053
5000 16325.62619 37591.14351 16316.5966 4997.734512 11.5075
6000 20065.42878 46202.3572 20056.22003 5997.740714 11.7494
7000 23877.94655 54981.00378 23868.5867 6997.745743 11.9632
8000 27752.71468 63902.98711 27743.22421 7997.749948 12.1352
9000 31681.90846 72950.29014 31672.30298 8997.753547 12.2935
10000 35659.45427 82108.92784 35649.74607 9997.756682 12.4396
20000 77337.25988 178075.6217 77326.87925 19997.7755 13.3667
30000 121287.4408 279274.6532 121276.6693 29997.78524 13.9119

cuikun-186 · 发表于 2023-3-13 16:21

本帖最后由 cuikun-186 于 2023-3-13 17:46 编辑

不一定，因为余项问题肯定不会接近于真实值。

没有理论证明哈李公式r2(N)=主项（1+a)中的余项a≠-1

yangchuanju · 发表于 2023-3-13 19:16

本帖最后由 yangchuanju 于 2023-3-14 06:14 编辑

网页 Goldbach conjecture verification
网址 https://sweet.ua.pt/tos/goldbach.html
推荐的偶数n的哥德巴赫分区（素数对）计算式是：
N2(n)=2c*n/[ln(n)*ln(n-2)]*∏(p-1)/(p-2)，p为能够整除偶数n的奇素因子，没有表明是全部素因子还是根内素因子；
与通常所说的哈李计算式相比，分母的自然对数号中的一个偶数n减了一个2，小了一点点，当n很大时，减2不会对总计算值有很大影响。
式中c——孪生素数常数，等于0.66016181584686957392…
通常计算式不减2，仅取偶数n的平方根内的奇素因子；分母减2，分数值大了一点点；波动系数取偶数n的全部奇素因子，又大了一点点；
两个大了一点点，能不能弥补通常的计算式小于偶数素数对的问题？

网页推荐的另一计算式是积分式：
N2(n)=2c*∫1/[ln(x)*ln(x-2)]*dx*∏(p-1)/(p-2)，积分区间为2至n-2，
网页没有给出积分式，这个对数积分很难计算。

yangchuanju · 发表于 2023-3-13 20:20

本帖最后由 yangchuanju 于 2023-3-13 20:23 编辑

算一算减2和整除奇素因子的影响
偶数n 平方根波动系数1 波动系数2 分解式
50000000000 223606.80 1.333333 1.333333 50000000000=2^10*5^11
50000000002 223606.80 1.000057 1.000058 50000000002=2*17573*1422637
50000000004 223606.80 2.000000 2.000000 50000000004=2^2*3^3*462962963
50000000006 223606.80 1.149425 1.149425 50000000006=2*11*31*73313783
50000000008 223606.80 1.200000 1.200000 50000000008=2^3*7*892857143
500000000000 707106.78 1.333333 1.333333 500000000000=2^11*5^12
500000000002 707106.78 1.079430 1.079432 500000000002=2*17*149*197*501001
500000000004 707106.78 2.001201 2.001201 500000000004=2^2*3^2*1667*8331667
500000000006 707106.78 1.155080 1.155080 500000000006=2*13*19*1012145749
500000000008 707106.78 1.000076 1.000076 500000000008=2^3*13177*4743113

yangchuanju · 发表于 2023-3-13 20:24

本帖最后由 yangchuanju 于 2023-3-14 06:31 编辑

算一算减2和整除奇素因子的影响
偶数n 单计素数对波动系数1 0.66*波1*n/ln(n)^2 比值1
50000000000 79004202 1.333333 72517667.1 0.917896
50000000002 59262284 1.000057 54391345.7 0.917807
50000000004 118490110 2.000000 108776500.7 0.918022
50000000006 68100948 1.149425 62515230.3 0.917979
50000000008 71099519 1.200000 65265900.4 0.917951
500000000000 655630055 1.333333 606502380.2 0.925068
500000000002 530781937 1.079430 491007738.9 0.925065
500000000004 984045373 2.001201 910299968.9 0.925059
500000000006 567966779 1.155080 525419174.3 0.925088
500000000008 491750094 1.000076 454911310.9 0.925086

偶数单计素数对波动系数2 0.66*波2*n/[ln(n)*ln(n-2)] 比值2 比2/比1
50000000000 79004202 1.333333 72517667.1 0.917896 1
50000000002 59262284 1.000058 54391383.9 0.917808 1.000000703
50000000004 118490110 2.000000 108776501.0 0.918022 1.000000002
50000000006 68100948 1.149425 62515231.2 0.917979 1.000000014
50000000008 71099519 1.200000 65265900.5 0.917951 1.000000001
500000000000 655630055 1.333333 606502380.2 0.925068 1
500000000002 530781937 1.079432 491008719.0 0.925067 1.000001996
500000000004 984045373 2.001201 910300078.1 0.925059 1.00000012
500000000006 567966779 1.155080 525419174.8 0.925088 1.000000001
500000000008 491750094 1.000076 454911406.8 0.925087 1.000000211
虽然比值2比比值1大一些，但增大极为有限；比值2仍然只有0.92左右。

大傻8888888 · 发表于 2023-3-13 21:25

本帖最后由大傻8888888 于 2023-3-14 20:10 编辑

yangchuanju 发表于 2023-3-13 19:16
网页 Goldbach conjecture verification
网址 https://sweet.ua.pt/tos/goldbach.html
推荐的偶数n的哥德 ...

偶数n的哥德巴赫分区（素数对）计算式是：
N2(n)=2c∏(p-1)/(p-2)*n/[ln(n)*ln(n-2)]中的ln(n-2)改为ln(n)基本上不影响计算结果。
所以偶数n的哥德巴赫分区（素数对）计算式是：
N2(n)=2c∏(p-1)/(p-2)*n/[ln(n)*ln(n)]，p为能够整除根号n的奇素因子，因为在实际中大于根号n的奇素因子不会增加素数对的个数，同时大于根号n的奇素因子最多只有一个即使算上也增加不了多少。所以由此可见由ln(n-2)改为ln(n)，并取偶数n以内的奇素因子不能弥补通常的计算式小于偶数素数对的问题。
同时计算式N2(n)=2c∏(p-1)/(p-2)*n/[ln(n)*ln(n)]
和我的公式r(n)～∏[(p-1)/(p-2)](n/2)∏(1-2/p)[1/2e^(-γ)]^2]等价
我们从实际上知道∏[(p-1)/(p-2)](n/2)∏(1-2/p)计算偶数里的素数对在数值比较小时精确度比较高，随着数值加大计算偶数里的素数对比实际值也在增加，根据我的公式计算偶数里的素数对比实际值最大不会超过[2e^(-γ)]^2=1.2609......倍，由此可见由ln(n-2)改为ln(n)，并取偶数n以内的奇素因子并不能弥补通常的计算式小于偶数素数对的问题。

cuikun-186 · 发表于 2023-3-13 22:03

大傻8888888 发表于 2023-3-13 21:25
偶数n的哥德巴赫分区（素数对）计算式是：
N2(n)=2c∏(p-1)/(p-2)*n/[ln(n)*ln(n-2)]中的ln(n-2)改为ln( ...

把天都吹黑了！！！

yangchuanju · 发表于 2023-3-14 12:15

cuikun-186 发表于 2023-3-13 16:21
不一定，因为余项问题肯定不会接近于真实值。

没有理论证明哈李公式r2(N)=主项（1+a)中的余项a≠-1

杨计算ln(10000!)等于82108.92784，崔计算ln(10000!)等于82109;
杨计算ln(30000!)等于279274.6532，崔计算ln(30000!)等于279274.3429;
计算误差所致，没有争论必要。

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