大偶数N的3个连乘积

yangchuanju · 发表于 2026-9-25 05:19

大偶数N的3个连乘积
（公式1）素数连乘积=∏(p-2)/p，式中p取尽N平方根内所有奇素数；
（公式2）奇合数连乘积=N/p*∏c/(c-2)≈√N*∏c/(c-2)，式中c取尽√N内最大奇素数前的奇合数，p是√N内最大奇素数；
（公式3）合数连乘积=N/p/(p-1)*∏d/(d-2)≈∏d/(d-2)，式中d取尽√N内最大奇素数前的所有合数，p是√N内最大奇素数。

（公式4）奇合数连乘积亦可用N/c*∏c/(c-2)表示，这里的c取尽√N内所有奇合数，N/c中的c是√N内最大奇合数；
（公式5）合数连乘积亦可用N/c/(c-1)*∏d/(d-2)表示，式中d取尽√N内所有合数，c是√N内最大奇合数。
（公式4和5的计算值与上面公式2和3的计算值会有稍微差别。）

对于10^17-10^308先按“C*N/ln(N)^2*波因”计算出哈李对数式哥猜数近似值，
再乘以1.260947作为连乘积哥猜数的近似值，
再乘以4、除以幂数、除以波因反算出各个幂数的素数连乘积，
再向下按小偶数的有关公式计算素数连乘积倒数、奇合数连乘积和合数连乘积近似值。

yangchuanju · 发表于 2026-9-25 05:22

由连乘积哥猜数约等于哈李对数计算式哥猜数的1.260947倍，估算10^17--10^308次方的连乘积（10^1--10^16连乘积是实际值）——
连乘积哥数=偶数/4*连乘积*波因
连乘积=连乘积哥数*4/偶数/波因

n 10^n 根内最大素数素数连乘积连乘积倒数奇合数连乘积合数连乘积 OEIS哥猜数
1 10 3 0.33333333 3.00 1.00 1.00 1 2
2 100 7 0.14285714 7.00 1.00 3.00 2 6
3 1000 31 0.06209152 16.11 1.92 28.87 3 28
4 10000 97 0.03829704 26.11 3.71 178.31 4 127
5 100000 313 0.02461160 40.63 7.70 1201.74 5 810
6 1000000 997 0.01731263 57.76 17.26 8595.83 6 5402
7 10000000 3137 0.01279268 78.17 40.13 62924.86 7 38807
8 100000000 9973 0.00978883 102.16 97.62 486753.39 8 291400
9 1000000000 31607 0.00774780 129.07 244.88 3869912.48 9 2274205
10 10000000000 99991 0.00627642 159.33 627.59 31376135.48 10 18200488
11 1E+11 316223 0.00518937 192.70 1641.00 259460084.46 11 149091160
12 1E+12 999983 0.00436093 229.31 4360.86 2180390944.49 12 1243722370
13 1E+13 3162277 0.00371592 269.11 11750.78 18579600553.32 13 10533150855
14 1E+14 9999991 0.00320414 312.10 32041.37 160206689684.95 14 90350630388
15 1E+15 31622743 0.00279115 358.27 88263.97 1395574399718.04 15 783538341852
16 1E+16 99999989 0.00245320 407.63 245319.65 12265981035910.60 16 6852674128787奚

yangchuanju · 发表于 2026-9-25 05:24

n 10^n 根内最大素数素数连乘积连乘积倒数奇合数连乘积合数连乘积
17 1E+17 316227731 0.00217309 460.17 687191.7813 1.08655E+14
18 1E+18 999999937 0.00193834 515.90 1938343.803 9.69172E+14
19 1E+19 3162277633 0.00173968 574.82 5501341.969 8.69839E+15
20 1E+20 9999999967 0.00157006 636.92 15700585.74 7.85029E+16
21 1E+21 31622776589 0.00142409 702.20 45033661.39 7.12045E+17
22 1E+22 99999999977 0.00129757 770.67 129756907.3 6.48785E+18
23 1E+23 3.162278E+11 0.00118719 842.33 3.754224E+08 5.935949E+19
24 1E+24 1.000000E+12 0.00109032 917.16 1.090318E+09 5.451592E+20
25 1E+25 3.162278E+12 0.00100484 995.19 3.177575E+09 5.024187E+21
26 1E+26 1.000000E+13 0.00092903 1076.39 9.290287E+09 4.645144E+22
27 1E+27 3.162278E+13 0.00086149 1160.78 2.724259E+10 4.307431E+23
28 1E+28 1.000000E+14 0.00080105 1248.36 8.010503E+10 4.005251E+24
29 1E+29 3.162278E+14 0.00074676 1339.12 2.361456E+11 3.733790E+25
30 1E+30 1.000000E+15 0.00069780 1433.07 6.978038E+11 3.489019E+26
31 1E+31 3.162278E+15 0.00065351 1530.20 2.066581E+12 3.267552E+27
32 1E+32 1.000000E+16 0.00061330 1630.51 6.133041E+12 3.066521E+28
33 1E+33 3.162278E+16 0.00057670 1734.01 1.823677E+13 2.883487E+29
34 1E+34 1.000000E+17 0.00054327 1840.70 5.432729E+13 2.716364E+30
35 1E+35 3.162278E+17 0.00051267 1950.56 1.621212E+14 2.563361E+31
36 1E+36 1.000000E+18 0.00048459 2063.62 4.845860E+14 2.422930E+32
37 1E+37 3.162278E+18 0.00045875 2179.85 1.450683E+15 2.293731E+33
38 1E+38 1.000000E+19 0.00043492 2299.28 4.349193E+15 2.174596E+34
39 1E+39 3.162278E+19 0.00041290 2421.88 1.305710E+16 2.064508E+35
40 1E+40 1.000000E+20 0.00039251 2547.68 3.925146E+16 1.962573E+36
41 1E+41 3.162278E+20 0.00037360 2676.65 1.181430E+17 1.868005E+37
42 1E+42 1.000000E+21 0.00035602 2808.81 3.560224E+17 1.780112E+38
43 1E+43 3.162278E+21 0.00033966 2944.16 1.074086E+18 1.698279E+39
44 1E+44 1.000000E+22 0.00032439 3082.69 3.243923E+18 1.621961E+40
45 1E+45 3.162278E+22 0.00031014 3224.40 9.807331E+18 1.550675E+41
46 1E+46 1.000000E+23 0.00029680 3369.30 2.967975E+19 1.483987E+42
47 1E+47 3.162278E+23 0.00028430 3517.38 8.990423E+19 1.421511E+43
48 1E+48 1.000000E+24 0.00027258 3668.65 2.725796E+20 1.362898E+44
49 1E+49 3.162278E+24 0.00026157 3823.11 8.271489E+20 1.307837E+45
50 1E+50 1.000000E+25 0.00025121 3980.74 2.512094E+21 1.256047E+46
51 1E+51 3.162278E+25 0.00024145 4141.57 7.635465E+21 1.207273E+47
52 1E+52 1.000000E+26 0.00023226 4305.57 2.322572E+22 1.161286E+48
53 1E+53 3.162278E+26 0.00022358 4472.76 7.070076E+22 1.117877E+49
54 1E+54 1.000000E+27 0.00021537 4643.14 2.153715E+23 1.076858E+50
55 1E+55 3.162278E+27 0.00020761 4816.70 6.565238E+23 1.038055E+51
56 1E+56 1.000000E+28 0.00020026 4993.44 2.002626E+24 1.001313E+52
57 1E+57 3.162278E+28 0.00019330 5173.37 6.112602E+24 9.664873E+52
58 1E+58 1.000000E+29 0.00018669 5356.49 1.866895E+25 9.334474E+53
59 1E+59 3.162278E+29 0.00018041 5542.79 5.705212E+25 9.020733E+54
60 1E+60 1.000000E+30 0.00017445 5732.27 1.744510E+26 8.722548E+55
61 1E+61 3.162278E+30 0.00016878 5924.94 5.337233E+26 8.438907E+56
62 1E+62 1.000000E+31 0.00016338 6120.79 1.633776E+27 8.168879E+57
63 1E+63 3.162278E+31 0.00015823 6319.83 5.003740E+27 7.911608E+58
64 1E+64 1.000000E+32 0.00015333 6522.05 1.533260E+28 7.666302E+59
65 1E+65 3.162278E+32 0.00014864 6727.46 4.700555E+28 7.432230E+60
66 1E+66 1.000000E+33 0.00014417 6936.05 1.441743E+29 7.208717E+61
67 1E+67 3.162278E+33 0.00013990 7147.82 4.424113E+29 6.995137E+62
68 1E+68 1.000000E+34 0.00013582 7362.78 1.358182E+30 6.790911E+63
69 1E+69 3.162278E+34 0.00013191 7580.93 4.171360E+30 6.595499E+64
70 1E+70 1.000000E+35 0.00012817 7802.26 1.281680E+31 6.408402E+65
71 1E+71 3.162278E+35 0.00012458 8026.77 3.939664E+31 6.229155E+66
72 1E+72 1.000000E+36 0.00012115 8254.47 1.211465E+32 6.057325E+67
73 1E+73 3.162278E+36 0.00011785 8485.35 3.726749E+32 5.892507E+68
74 1E+74 1.000000E+37 0.00011469 8719.42 1.146865E+33 5.734326E+69
75 1E+75 3.162278E+37 0.00011165 8956.67 3.530639E+33 5.582431E+70
76 1E+76 1.000000E+38 0.00010873 9197.11 1.087298E+34 5.436491E+71
77 1E+77 3.162278E+38 0.00010592 9440.73 3.349611E+34 5.296200E+72
78 1E+78 1.000000E+39 0.00010323 9687.54 1.032254E+35 5.161271E+73
79 1E+79 3.162278E+39 0.00010063 9937.53 3.182157E+35 5.031433E+74
80 1E+80 1.000000E+40 0.00009813 10190.70 9.812866E+35 4.906433E+75
81 1E+81 3.162278E+40 0.00009572 10447.06 3.026954E+36 4.786034E+76
82 1E+82 1.000000E+41 0.00009340 10706.61 9.340027E+36 4.670014E+77
83 1E+83 3.162278E+41 0.00009116 10969.34 2.882834E+37 4.558161E+78
84 1E+84 1.000000E+42 0.00008901 11235.25 8.900559E+37 4.450279E+79
85 1E+85 3.162278E+42 0.00008692 11504.35 2.748767E+38 4.346183E+80
86 1E+86 1.000000E+43 0.00008491 11776.63 8.491393E+38 4.245697E+81
87 1E+87 3.162278E+43 0.00008297 12052.10 2.623840E+39 4.148655E+82
88 1E+88 1.000000E+44 0.00008110 12330.75 8.109807E+39 4.054903E+83
89 1E+89 3.162278E+44 0.00007929 12612.59 2.507240E+40 3.964294E+84
90 1E+90 1.000000E+45 0.00007753 12897.61 7.753376E+40 3.876688E+85
91 1E+91 3.162278E+45 0.00007584 13185.81 2.398242E+41 3.791954E+86
92 1E+92 1.000000E+46 0.00007420 13477.20 7.419937E+41 3.709968E+87
93 1E+93 3.162278E+46 0.00007261 13771.78 2.296201E+42 3.630613E+88
94 1E+94 1.000000E+47 0.00007108 14069.54 7.107554E+42 3.553777E+89
95 1E+95 3.162278E+47 0.00006959 14370.48 2.200537E+43 3.479354E+90
96 1E+96 1.000000E+48 0.00006814 14674.61 6.814490E+43 3.407245E+91
97 1E+97 3.162278E+48 0.00006675 14981.93 2.110729E+44 3.337355E+92
98 1E+98 1.000000E+49 0.00006539 15292.42 6.539186E+44 3.269593E+93
99 1E+99 3.162278E+49 0.00006408 15606.11 2.026308E+45 3.203874E+94
100 1E+100 1.000000E+50 0.00006280 15922.97 6.280234E+45 3.140117E+95
101 1E+101 3.162278E+50 0.00006156 16243.02 1.946853E+46 3.078244E+96
102 1E+102 1.000000E+51 0.00006036 16566.26 6.036365E+46 3.018183E+97
103 1E+103 3.162278E+51 0.00005920 16892.68 1.871981E+47 2.959862E+98
104 1E+104 1.000000E+52 0.00005806 17222.29 5.806430E+47 2.903215E+99
105 1E+105 3.162278E+52 0.00005696 17555.08 1.801346E+48 2.848179E+100
106 1E+106 1.000000E+53 0.00005589 17891.05 5.589386E+48 2.794693E+101
107 1E+107 3.162278E+53 0.00005485 18230.21 1.734636E+49 2.742700E+102
108 1E+108 1.000000E+54 0.00005384 18572.56 5.384289E+49 2.692144E+103
109 1E+109 3.162278E+54 0.00005286 18918.08 1.671563E+50 2.642974E+104
110 1E+110 1.000000E+55 0.00005190 19266.80 5.190276E+50 2.595138E+105
111 1E+111 3.162278E+55 0.00005097 19618.69 1.611870E+51 2.548590E+106
112 1E+112 1.000000E+56 0.00005007 19973.78 5.006564E+51 2.503282E+107
113 1E+113 3.162278E+56 0.00004918 20332.04 1.555317E+52 2.459172E+108
114 1E+114 1.000000E+57 0.00004832 20693.50 4.832436E+52 2.416218E+109
115 1E+115 3.162278E+57 0.00004749 21058.13 1.501690E+53 2.374380E+110
116 1E+116 1.000000E+58 0.00004667 21425.95 4.667237E+53 2.333619E+111
117 1E+117 3.162278E+58 0.00004588 21796.96 1.450789E+54 2.293898E+112
118 1E+118 1.000000E+59 0.00004510 22171.15 4.510367E+54 2.255183E+113
119 1E+119 3.162278E+59 0.00004435 22548.52 1.402432E+55 2.217440E+114
120 1E+120 1.000000E+60 0.00004361 22929.08 4.361274E+55 2.180637E+115
121 1E+121 3.162278E+60 0.00004289 23312.82 1.356454E+56 2.144742E+116
122 1E+122 1.000000E+61 0.00004219 23699.75 4.219453E+56 2.109727E+117
123 1E+123 3.162278E+61 0.00004151 24089.87 1.312700E+57 2.075562E+118
124 1E+124 1.000000E+62 0.00004084 24483.16 4.084440E+57 2.042220E+119
125 1E+125 3.162278E+62 0.00004019 24879.64 1.271030E+58 2.009675E+120
126 1E+126 1.000000E+63 0.00003956 25279.31 3.955804E+58 1.977902E+121
127 1E+127 3.162278E+63 0.00003894 25682.16 1.231313E+59 1.946877E+122
128 1E+128 1.000000E+64 0.00003833 26088.20 3.833151E+59 1.916575E+123
129 1E+129 3.162278E+64 0.00003774 26497.42 1.193429E+60 1.886976E+124
130 1E+130 1.000000E+65 0.00003716 26909.82 3.716115E+60 1.858057E+125
131 1E+131 3.162278E+65 0.00003660 27325.41 1.157266E+61 1.829798E+126
132 1E+132 1.000000E+66 0.00003604 27744.19 3.604359E+61 1.802179E+127
133 1E+133 3.162278E+66 0.00003550 28166.15 1.122723E+62 1.775181E+128
134 1E+134 1.000000E+67 0.00003498 28591.29 3.497569E+62 1.748784E+129
135 1E+135 3.162278E+67 0.00003446 29019.62 1.089703E+63 1.722972E+130
136 1E+136 1.000000E+68 0.00003395 29451.13 3.395455E+63 1.697728E+131
137 1E+137 3.162278E+68 0.00003346 29885.83 1.058119E+64 1.673034E+132
138 1E+138 1.000000E+69 0.00003298 30323.71 3.297750E+64 1.648875E+133
139 1E+139 3.162278E+69 0.00003250 30764.78 1.027889E+65 1.625235E+134
140 1E+140 1.000000E+70 0.00003204 31209.03 3.204201E+65 1.602101E+135
141 1E+141 3.162278E+70 0.00003159 31656.46 9.989359E+65 1.579456E+136
142 1E+142 1.000000E+71 0.00003115 32107.08 3.114578E+66 1.557289E+137
143 1E+143 3.162278E+71 0.00003071 32560.89 9.711890E+66 1.535585E+138
144 1E+144 1.000000E+72 0.00003029 33017.88 3.028662E+67 1.514331E+139
145 1E+145 3.162278E+72 0.00002987 33478.05 9.445824E+67 1.493516E+140
146 1E+146 1.000000E+73 0.00002946 33941.41 2.946254E+68 1.473127E+141
147 1E+147 3.162278E+73 0.00002906 34407.95 9.190543E+68 1.453152E+142
148 1E+148 1.000000E+74 0.00002867 34877.68 2.867163E+69 1.433582E+143
149 1E+149 3.162278E+74 0.00002829 35350.59 8.945473E+69 1.414403E+144
150 1E+150 1.000000E+75 0.00002791 35826.69 2.791215E+70 1.395608E+145
151 1E+151 3.162278E+75 0.00002754 36305.97 8.710076E+70 1.377184E+146
152 1E+152 1.000000E+76 0.00002718 36788.44 2.718245E+71 1.359123E+147
153 1E+153 3.162278E+76 0.00002683 37274.09 8.483850E+71 1.341414E+148
154 1E+154 1.000000E+77 0.00002648 37762.92 2.648100E+72 1.324050E+149
155 1E+155 3.162278E+77 0.00002614 38254.94 8.266325E+72 1.307021E+150
156 1E+156 1.000000E+78 0.00002581 38750.15 2.580635E+73 1.290318E+151
157 1E+157 3.162278E+78 0.00002548 39248.54 8.057059E+73 1.273933E+152
158 1E+158 1.000000E+79 0.00002516 39750.11 2.515716E+74 1.257858E+153
159 1E+159 3.162278E+79 0.00002484 40254.87 7.855640E+74 1.242086E+154
160 1E+160 1.000000E+80 0.00002453 40762.81 2.453217E+75 1.226608E+155
161 1E+161 3.162278E+80 0.00002423 41273.94 7.661682E+75 1.211418E+156
162 1E+162 1.000000E+81 0.00002393 41788.25 2.393017E+76 1.196509E+157
163 1E+163 3.162278E+81 0.00002364 42305.75 7.474818E+76 1.181873E+158
164 1E+164 1.000000E+82 0.00002335 42826.43 2.335007E+77 1.167503E+159
165 1E+165 3.162278E+82 0.00002307 43350.29 7.294709E+77 1.153395E+160
166 1E+166 1.000000E+83 0.00002279 43877.34 2.279081E+78 1.139540E+161
167 1E+167 3.162278E+83 0.00002252 44407.58 7.121031E+78 1.125934E+162
168 1E+168 1.000000E+84 0.00002225 44941.00 2.225140E+79 1.112570E+163
169 1E+169 3.162278E+84 0.00002199 45477.60 6.953484E+79 1.099442E+164
170 1E+170 1.000000E+85 0.00002173 46017.39 2.173091E+80 1.086546E+165
171 1E+171 3.162278E+85 0.00002148 46560.36 6.791780E+80 1.073875E+166
172 1E+172 1.000000E+86 0.00002123 47106.52 2.122848E+81 1.061424E+167
173 1E+173 3.162278E+86 0.00002098 47655.87 6.635653E+81 1.049189E+168
174 1E+174 1.000000E+87 0.00002074 48208.39 2.074328E+82 1.037164E+169
175 1E+175 3.162278E+87 0.00002051 48764.10 6.484847E+82 1.025344E+170
176 1E+176 1.000000E+88 0.00002027 49323.00 2.027452E+83 1.013726E+171
177 1E+177 3.162278E+88 0.00002005 49885.08 6.339125E+83 1.002304E+172
178 1E+178 1.000000E+89 0.00001982 50450.35 1.982147E+84 9.910735E+172
179 1E+179 3.162278E+89 0.00001960 51018.80 6.198260E+84 9.800309E+173
180 1E+180 1.000000E+90 0.00001938 51590.43 1.938344E+85 9.691720E+174
181 1E+181 3.162278E+90 0.00001917 52165.25 6.062039E+85 9.584925E+175
182 1E+182 1.000000E+91 0.00001896 52743.25 1.895977E+86 9.479885E+176
183 1E+183 3.162278E+91 0.00001875 53324.44 5.930259E+86 9.376563E+177
184 1E+184 1.000000E+92 0.00001855 53908.82 1.854984E+87 9.274921E+178
185 1E+185 3.162278E+92 0.00001835 54496.37 5.802730E+87 9.174922E+179
186 1E+186 1.000000E+93 0.00001815 55087.12 1.815306E+88 9.076532E+180
187 1E+187 3.162278E+93 0.00001796 55681.04 5.679272E+88 8.979717E+181
188 1E+188 1.000000E+94 0.00001777 56278.15 1.776888E+89 8.884442E+182
189 1E+189 3.162278E+94 0.00001758 56878.45 5.559711E+89 8.790675E+183
190 1E+190 1.000000E+95 0.00001740 57481.93 1.739677E+90 8.698385E+184
191 1E+191 3.162278E+95 0.00001722 58088.60 5.443887E+90 8.607541E+185
192 1E+192 1.000000E+96 0.00001704 58698.45 1.703623E+91 8.518113E+186
193 1E+193 3.162278E+96 0.00001686 59311.48 5.331645E+91 8.430071E+187
194 1E+194 1.000000E+97 0.00001669 59927.70 1.668677E+92 8.343387E+188
195 1E+195 3.162278E+97 0.00001652 60547.10 5.222839E+92 8.258033E+189
196 1E+196 1.000000E+98 0.00001635 61169.69 1.634797E+93 8.173983E+190
197 1E+197 3.162278E+98 0.00001618 61795.47 5.117330E+93 8.091209E+191
198 1E+198 1.000000E+99 0.00001602 62424.42 1.601937E+94 8.009686E+192
199 1E+199 3.162278E+99 0.00001586 63056.56 5.014986E+94 7.929389E+193
200 1E+200 1.000000E+100 0.00001570 63691.89 1.570059E+95 7.850293E+194

yangchuanju · 发表于 2026-9-25 05:25

n 10^n 根内最大素数素数连乘积连乘积倒数奇合数连乘积合数连乘积
201 1E+201 3.162278E+100 0.00001554 64330.40 4.915681E+95 7.772375E+195
202 1E+202 1.000000E+101 0.00001539 64972.10 1.539122E+96 7.695611E+196
203 1E+203 3.162278E+101 0.00001524 65616.98 4.819298E+96 7.619979E+197
204 1E+204 1.000000E+102 0.00001509 66265.04 1.509091E+97 7.545456E+198
205 1E+205 3.162278E+102 0.00001494 66916.29 4.725722E+97 7.472022E+199
206 1E+206 1.000000E+103 0.00001480 67570.73 1.479931E+98 7.399654E+200
207 1E+207 3.162278E+103 0.00001466 68228.35 4.634844E+98 7.328332E+201
208 1E+208 1.000000E+104 0.00001452 68889.15 1.451607E+99 7.258037E+202
209 1E+209 3.162278E+104 0.00001438 69553.14 4.546564E+99 7.188748E+203
210 1E+210 1.000000E+105 0.00001424 70220.31 1.424089E+100 7.120447E+204
211 1E+211 3.162278E+105 0.00001411 70890.67 4.460781E+100 7.053115E+205
212 1E+212 1.000000E+106 0.00001397 71564.21 1.397347E+101 6.986733E+206
213 1E+213 3.162278E+106 0.00001384 72240.94 4.377404E+101 6.921284E+207
214 1E+214 1.000000E+107 0.00001371 72920.85 1.371350E+102 6.856750E+208
215 1E+215 3.162278E+107 0.00001359 73603.94 4.296343E+102 6.793114E+209
216 1E+216 1.000000E+108 0.00001346 74290.22 1.346072E+103 6.730361E+210
217 1E+217 3.162278E+108 0.00001334 74979.69 4.217513E+103 6.668473E+211
218 1E+218 1.000000E+109 0.00001321 75672.34 1.321487E+104 6.607434E+212
219 1E+219 3.162278E+109 0.00001309 76368.17 4.140832E+104 6.547230E+213
220 1E+220 1.000000E+110 0.00001298 77067.19 1.297569E+105 6.487845E+214
221 1E+221 3.162278E+110 0.00001286 77769.39 4.066224E+105 6.429265E+215
222 1E+222 1.000000E+111 0.00001274 78474.78 1.274295E+106 6.371474E+216
223 1E+223 3.162278E+111 0.00001263 79183.35 3.993614E+106 6.314459E+217
224 1E+224 1.000000E+112 0.00001252 79895.11 1.251641E+107 6.258205E+218
225 1E+225 3.162278E+112 0.00001241 80610.05 3.922932E+107 6.202701E+219
226 1E+226 1.000000E+113 0.00001230 81328.18 1.229586E+108 6.147931E+220
227 1E+227 3.162278E+113 0.00001219 82049.49 3.854110E+108 6.093883E+221
228 1E+228 1.000000E+114 0.00001208 82773.98 1.208109E+109 6.040545E+222
229 1E+229 3.162278E+114 0.00001198 83501.66 3.787084E+109 5.987905E+223
230 1E+230 1.000000E+115 0.00001187 84232.53 1.187190E+110 5.935949E+224
231 1E+231 3.162278E+115 0.00001177 84966.57 3.721790E+110 5.884667E+225
232 1E+232 1.000000E+116 0.00001167 85703.81 1.166809E+111 5.834046E+226
233 1E+233 3.162278E+116 0.00001157 86444.23 3.658171E+111 5.784076E+227
234 1E+234 1.000000E+117 0.00001147 87187.83 1.146949E+112 5.734745E+228
235 1E+235 3.162278E+117 0.00001137 87934.62 3.596169E+112 5.686043E+229
236 1E+236 1.000000E+118 0.00001128 88684.59 1.127592E+113 5.637958E+230
237 1E+237 3.162278E+118 0.00001118 89437.75 3.535731E+113 5.590481E+231
238 1E+238 1.000000E+119 0.00001109 90194.09 1.108720E+114 5.543601E+232
239 1E+239 3.162278E+119 0.00001099 90953.61 3.476803E+114 5.497308E+233
240 1E+240 1.000000E+120 0.00001090 91716.32 1.090318E+115 5.451592E+234
241 1E+241 3.162278E+120 0.00001081 92482.22 3.419336E+115 5.406445E+235
242 1E+242 1.000000E+121 0.00001072 93251.30 1.072371E+116 5.361856E+236
243 1E+243 3.162278E+121 0.00001064 94023.56 3.363282E+116 5.317816E+237
244 1E+244 1.000000E+122 0.00001055 94799.01 1.054863E+117 5.274317E+238
245 1E+245 3.162278E+122 0.00001046 95577.64 3.308596E+117 5.231349E+239
246 1E+246 1.000000E+123 0.00001038 96359.46 1.037781E+118 5.188904E+240
247 1E+247 3.162278E+123 0.00001029 97144.46 3.255232E+118 5.146974E+241
248 1E+248 1.000000E+124 0.00001021 97932.65 1.021110E+119 5.105549E+242
249 1E+249 3.162278E+124 0.00001013 98724.02 3.203149E+119 5.064623E+243
250 1E+250 1.000000E+125 0.00001005 99518.58 1.004837E+120 5.024187E+244
251 1E+251 3.162278E+125 0.00000997 100316.32 3.152306E+120 4.984234E+245
252 1E+252 1.000000E+126 0.00000989 101117.25 9.889510E+120 4.944755E+246
253 1E+253 3.162278E+126 0.00000981 101921.36 3.102664E+121 4.905743E+247
254 1E+254 1.000000E+127 0.00000973 102728.65 9.734383E+121 4.867191E+248
255 1E+255 3.162278E+127 0.00000966 103539.13 3.054186E+122 4.829092E+249
256 1E+256 1.000000E+128 0.00000958 104352.79 9.582877E+122 4.791439E+250
257 1E+257 3.162278E+128 0.00000951 105169.64 3.006835E+123 4.754224E+251
258 1E+258 1.000000E+129 0.00000943 105989.68 9.434881E+123 4.717441E+252
259 1E+259 3.162278E+129 0.00000936 106812.89 2.960577E+124 4.681083E+253
260 1E+260 1.000000E+130 0.00000929 107639.30 9.290287E+124 4.645144E+254
261 1E+261 3.162278E+130 0.00000922 108468.88 2.915378E+125 4.609617E+255
262 1E+262 1.000000E+131 0.00000915 109301.65 9.148992E+125 4.574496E+256
263 1E+263 3.162278E+131 0.00000908 110137.61 2.871206E+126 4.539775E+257
264 1E+264 1.000000E+132 0.00000901 110976.75 9.010896E+126 4.505448E+258
265 1E+265 3.162278E+132 0.00000894 111819.08 2.828031E+127 4.471509E+259
266 1E+266 1.000000E+133 0.00000888 112664.59 8.875904E+127 4.437952E+260
267 1E+267 3.162278E+133 0.00000881 113513.28 2.785822E+128 4.404771E+261
268 1E+268 1.000000E+134 0.00000874 114365.16 8.743922E+128 4.371961E+262
269 1E+269 3.162278E+134 0.00000868 115220.22 2.744551E+129 4.339516E+263
270 1E+270 1.000000E+135 0.00000861 116078.47 8.614862E+129 4.307431E+264
271 1E+271 3.162278E+135 0.00000855 116939.90 2.704190E+130 4.275700E+265
272 1E+272 1.000000E+136 0.00000849 117804.52 8.488639E+130 4.244319E+266
273 1E+273 3.162278E+136 0.00000843 118672.32 2.664714E+131 4.213282E+267
274 1E+274 1.000000E+137 0.00000837 119543.31 8.365169E+131 4.182585E+268
275 1E+275 3.162278E+137 0.00000830 120417.48 2.626095E+132 4.152221E+269
276 1E+276 1.000000E+138 0.00000824 121294.84 8.244374E+132 4.122187E+270
277 1E+277 3.162278E+138 0.00000818 122175.38 2.588310E+133 4.092478E+271
278 1E+278 1.000000E+139 0.00000813 123059.10 8.126177E+133 4.063088E+272
279 1E+279 3.162278E+139 0.00000807 123946.01 2.551335E+134 4.034014E+273
280 1E+280 1.000000E+140 0.00000801 124836.11 8.010503E+134 4.005251E+274
281 1E+281 3.162278E+140 0.00000795 125729.39 2.515146E+135 3.976795E+275
282 1E+282 1.000000E+141 0.00000790 126625.85 7.897282E+135 3.948641E+276
283 1E+283 3.162278E+141 0.00000784 127525.50 2.479722E+136 3.920785E+277
284 1E+284 1.000000E+142 0.00000779 128428.33 7.786444E+136 3.893222E+278
285 1E+285 3.162278E+142 0.00000773 129334.35 2.445041E+137 3.865949E+279
286 1E+286 1.000000E+143 0.00000768 130243.55 7.677924E+137 3.838962E+280
287 1E+287 3.162278E+143 0.00000762 131155.93 2.411082E+138 3.812256E+281
288 1E+288 1.000000E+144 0.00000757 132071.51 7.571656E+138 3.785828E+282
289 1E+289 3.162278E+144 0.00000752 132990.26 2.377826E+139 3.759674E+283
290 1E+290 1.000000E+145 0.00000747 133912.20 7.467579E+139 3.733790E+284
291 1E+291 3.162278E+145 0.00000742 134837.33 2.345254E+140 3.708172E+285
292 1E+292 1.000000E+146 0.00000737 135765.64 7.365634E+140 3.682817E+286
293 1E+293 3.162278E+146 0.00000732 136697.13 2.313346E+141 3.657721E+287
294 1E+294 1.000000E+147 0.00000727 137631.81 7.265762E+141 3.632881E+288
295 1E+295 3.162278E+147 0.00000722 138569.67 2.282085E+142 3.608293E+289
296 1E+296 1.000000E+148 0.00000717 139510.72 7.167908E+142 3.583954E+290
297 1E+297 3.162278E+148 0.00000712 140454.95 2.251453E+143 3.559860E+291
298 1E+298 1.000000E+149 0.00000707 141402.37 7.072017E+143 3.536009E+292
299 1E+299 3.162278E+149 0.00000702 142352.97 2.221434E+144 3.512396E+293
300 1E+300 1.000000E+150 0.00000698 143306.75 6.978038E+144 3.489019E+294
301 1E+301 3.162278E+150 0.00000693 144263.73 2.192012E+145 3.465875E+295
302 1E+302 1.000000E+151 0.00000689 145223.88 6.885920E+145 3.442960E+296
303 1E+303 3.162278E+151 0.00000684 146187.22 2.163170E+146 3.420272E+297
304 1E+304 1.000000E+152 0.00000680 147153.75 6.795614E+146 3.397807E+298
305 1E+305 3.162278E+152 0.00000675 148123.45 2.134893E+147 3.375563E+299
306 1E+306 1.000000E+153 0.00000671 149096.35 6.707072E+147 3.353536E+300
307 1E+307 3.162278E+153 0.00000666 150072.43 2.107168E+148 3.331725E+301
308 1E+308 1.000000E+154 0.00000662 151051.69 6.620250E+148 3.310125E+302

yangchuanju · 发表于 2026-9-25 05:31

大幂数的哥猜数增比
n 10^n 哈李哥数增比
17 1E+17 5.7446E+13 8.858131
18 1E+18 5.12404E+14 8.919753
19 1E+19 4.59886E+15 8.975069
20 1E+20 4.15047E+16 9.025000
21 1E+21 3.7646E+17 9.070295
22 1E+22 3.43014E+18 9.111570
23 1E+23 3.13836E+19 9.149338
24 1E+24 2.88227E+20 9.184028
25 1E+25 2.6563E+21 9.216000
26 1E+26 2.4559E+22 9.245562
27 1E+27 2.27735E+23 9.272977
28 1E+28 2.11759E+24 9.298469
29 1E+29 1.97407E+25 9.322235
30 1E+30 1.84466E+26 9.344444
31 1E+31 1.72756E+27 9.365245
32 1E+32 1.62128E+28 9.384766
33 1E+33 1.52451E+29 9.403122
34 1E+34 1.43615E+30 9.420415
35 1E+35 1.35526E+31 9.436735
36 1E+36 1.28101E+32 9.452160
37 1E+37 1.2127E+33 9.466764
38 1E+38 1.14972E+34 9.480609
39 1E+39 1.09151E+35 9.493754
40 1E+40 1.03762E+36 9.506250
41 1E+41 9.8762E+36 9.518144
42 1E+42 9.41151E+37 9.529478
43 1E+43 8.97885E+38 9.540292
44 1E+44 8.57536E+39 9.550620
45 1E+45 8.19847E+40 9.560494
46 1E+46 7.84589E+41 9.569943
47 1E+47 7.51557E+42 9.578995
48 1E+48 7.20569E+43 9.587674
49 1E+49 6.91458E+44 9.596002
50 1E+50 6.64076E+45 9.604000
51 1E+51 6.38289E+46 9.611688
52 1E+52 6.13976E+47 9.619083
53 1E+53 5.91025E+48 9.626201
54 1E+54 5.69338E+49 9.633059
55 1E+55 5.48823E+50 9.639669
56 1E+56 5.29397E+51 9.646046
57 1E+57 5.10985E+52 9.652201
58 1E+58 4.93517E+53 9.658145
59 1E+59 4.76929E+54 9.663890
60 1E+60 4.61164E+55 9.669444
61 1E+61 4.46168E+56 9.674819
62 1E+62 4.31891E+57 9.680021
63 1E+63 4.18289E+58 9.685059
64 1E+64 4.0532E+59 9.689941
65 1E+65 3.92944E+60 9.694675
66 1E+66 3.81127E+61 9.699265
67 1E+67 3.69835E+62 9.703720
68 1E+68 3.59038E+63 9.708045
69 1E+69 3.48706E+64 9.712245
70 1E+70 3.38814E+65 9.716327
71 1E+71 3.29337E+66 9.720294
72 1E+72 3.20253E+67 9.724151
73 1E+73 3.11539E+68 9.727904
74 1E+74 3.03176E+69 9.731556
75 1E+75 2.95145E+70 9.735111
76 1E+76 2.87429E+71 9.738573
77 1E+77 2.80012E+72 9.741946
78 1E+78 2.72878E+73 9.745233
79 1E+79 2.66013E+74 9.748438
80 1E+80 2.59405E+75 9.751563
81 1E+81 2.53039E+76 9.754611
82 1E+82 2.46905E+77 9.757585
83 1E+83 2.40991E+78 9.760488
84 1E+84 2.35288E+79 9.763322
85 1E+85 2.29784E+80 9.766090
86 1E+86 2.24471E+81 9.768794
87 1E+87 2.19341E+82 9.771436
88 1E+88 2.14384E+83 9.774019
89 1E+89 2.09593E+84 9.776543
90 1E+90 2.04962E+85 9.779012
91 1E+91 2.00482E+86 9.781427
92 1E+92 1.96147E+87 9.783790
93 1E+93 1.91952E+88 9.786102
94 1E+94 1.87889E+89 9.788366
95 1E+95 1.83955E+90 9.790582
96 1E+96 1.80142E+91 9.792752
97 1E+97 1.76447E+92 9.794877
98 1E+98 1.72864E+93 9.796960
99 1E+99 1.6939E+94 9.799000
100 1E+100 1.66019E+95 9.801000
101 1E+101 1.62748E+96 9.802960
102 1E+102 1.59572E+97 9.804883
103 1E+103 1.56489E+98 9.806768
104 1E+104 1.5349E+99 9.808617
105 1E+105 1.5058E+100 9.810431
106 1E+106 1.4776E+101 9.812211
107 1E+107 1.4501E+102 9.813958
108 1E+108 1.4233E+103 9.815672
109 1E+109 1.3973E+104 9.817355
110 1E+110 1.3721E+105 9.819008
111 1E+111 1.3474E+106 9.820631
112 1E+112 1.3235E+107 9.822226
113 1E+113 1.3002E+108 9.823792
114 1E+114 1.2775E+109 9.825331
115 1E+115 1.2553E+110 9.826843
116 1E+116 1.2338E+111 9.828329
117 1E+117 1.2128E+112 9.829790
118 1E+118 1.1923E+113 9.831227
119 1E+119 1.1724E+114 9.832639
120 1E+120 1.1529E+115 9.834028
121 1E+121 1.1339E+116 9.835394
122 1E+122 1.1154E+117 9.836737
123 1E+123 1.0974E+118 9.838059
124 1E+124 1.0797E+119 9.839360
125 1E+125 1.0625E+120 9.840640
126 1E+126 1.0457E+121 9.841900
127 1E+127 1.0293E+122 9.843140
128 1E+128 1.0133E+123 9.844360
129 1E+129 9.9765E+123 9.845562
130 1E+130 9.8236E+124 9.846746
131 1E+131 9.6742E+125 9.847911
132 1E+132 9.5282E+126 9.849059
133 1E+133 9.3854E+127 9.850189
134 1E+134 9.2459E+128 9.851303
135 1E+135 9.1094E+129 9.852401
136 1E+136 8.9759E+130 9.853482
137 1E+137 8.8454E+131 9.854547
138 1E+138 8.7177E+132 9.855598
139 1E+139 8.5927E+133 9.856633
140 1E+140 8.4704E+134 9.857653
141 1E+141 8.3506E+135 9.858659
142 1E+142 8.2334E+136 9.859651
143 1E+143 8.1187E+137 9.860629
144 1E+144 8.0063E+138 9.861593
145 1E+145 7.8963E+139 9.862545
146 1E+146 7.7885E+140 9.863483
147 1E+147 7.6829E+141 9.864408
148 1E+148 7.5794E+142 9.865321
149 1E+149 7.478E+143 9.866222
150 1E+150 7.3786E+144 9.867111
151 1E+151 7.2812E+145 9.867988
152 1E+152 7.1857E+146 9.868854
153 1E+153 7.0921E+147 9.869708
154 1E+154 7.0003E+148 9.870552
155 1E+155 6.9103E+149 9.871384
156 1E+156 6.822E+150 9.872206
157 1E+157 6.7353E+151 9.873017
158 1E+158 6.6503E+152 9.873818
159 1E+159 6.5669E+153 9.874609
160 1E+160 6.4851E+154 9.875391
161 1E+161 6.4048E+155 9.876162
162 1E+162 6.326E+156 9.876924
163 1E+163 6.2486E+157 9.877677
164 1E+164 6.1726E+158 9.878421
165 1E+165 6.098E+159 9.879155
166 1E+166 6.0248E+160 9.879881
167 1E+167 5.9528E+161 9.880598
168 1E+168 5.8822E+162 9.881307
169 1E+169 5.8128E+163 9.882007
170 1E+170 5.7446E+164 9.882699
171 1E+171 5.6776E+165 9.883383
172 1E+172 5.6118E+166 9.884059
173 1E+173 5.5471E+167 9.884727
174 1E+174 5.4835E+168 9.885388
175 1E+175 5.421E+169 9.886041
176 1E+176 5.3596E+170 9.886686
177 1E+177 5.2992E+171 9.887325
178 1E+178 5.2398E+172 9.887956
179 1E+179 5.1815E+173 9.888580
180 1E+180 5.124E+174 9.889198
181 1E+181 5.0676E+175 9.889808
182 1E+182 5.012E+176 9.890412
183 1E+183 4.9574E+177 9.891009
184 1E+184 4.9037E+178 9.891600
185 1E+185 4.8508E+179 9.892184
186 1E+186 4.7988E+180 9.892762
187 1E+187 4.7476E+181 9.893334
188 1E+188 4.6972E+182 9.893900
189 1E+189 4.6477E+183 9.894460
190 1E+190 4.5989E+184 9.895014
191 1E+191 4.5508E+185 9.895562
192 1E+192 4.5036E+186 9.896105
193 1E+193 4.457E+187 9.896642
194 1E+194 4.4112E+188 9.897173
195 1E+195 4.366E+189 9.897699
196 1E+196 4.3216E+190 9.898219
197 1E+197 4.2778E+191 9.898735
198 1E+198 4.2347E+192 9.899245
199 1E+199 4.1923E+193 9.899750
200 1E+200 4.1505E+194 9.900250
201 1E+201 4.1093E+195 9.900745
202 1E+202 4.0687E+196 9.901235
203 1E+203 4.0287E+197 9.901720
204 1E+204 3.9893E+198 9.902201
205 1E+205 3.9505E+199 9.902677
206 1E+206 3.9122E+200 9.903148
207 1E+207 3.8745E+201 9.903615
208 1E+208 3.8373E+202 9.904077
209 1E+209 3.8007E+203 9.904535
210 1E+210 3.7646E+204 9.904989
211 1E+211 3.729E+205 9.905438
212 1E+212 3.6939E+206 9.905883
213 1E+213 3.6593E+207 9.906324
214 1E+214 3.6252E+208 9.906760
215 1E+215 3.5915E+209 9.907193
216 1E+216 3.5584E+210 9.907622
217 1E+217 3.5256E+211 9.908046
218 1E+218 3.4934E+212 9.908467
219 1E+219 3.4615E+213 9.908884
220 1E+220 3.4301E+214 9.909298
221 1E+221 3.3992E+215 9.909707
222 1E+222 3.3686E+216 9.910113
223 1E+223 3.3385E+217 9.910515
224 1E+224 3.3087E+218 9.910914
225 1E+225 3.2794E+219 9.911309
226 1E+226 3.2504E+220 9.911700
227 1E+227 3.2219E+221 9.912088
228 1E+228 3.1937E+222 9.912473
229 1E+229 3.1658E+223 9.912854
230 1E+230 3.1384E+224 9.913233
231 1E+231 3.1112E+225 9.913607
232 1E+232 3.0845E+226 9.913979
233 1E+233 3.0581E+227 9.914347
234 1E+234 3.032E+228 9.914713
235 1E+235 3.0062E+229 9.915075
236 1E+236 2.9808E+230 9.915434
237 1E+237 2.9557E+231 9.915790
238 1E+238 2.9309E+232 9.916143
239 1E+239 2.9064E+233 9.916493
240 1E+240 2.8823E+234 9.916840
241 1E+241 2.8584E+235 9.917185
242 1E+242 2.8348E+236 9.917526
243 1E+243 2.8115E+237 9.917865
244 1E+244 2.7885E+238 9.918201
245 1E+245 2.7658E+239 9.918534
246 1E+246 2.7434E+240 9.918864
247 1E+247 2.7212E+241 9.919192
248 1E+248 2.6993E+242 9.919517
249 1E+249 2.6777E+243 9.919840
250 1E+250 2.6563E+244 9.920160
251 1E+251 2.6352E+245 9.920477
252 1E+252 2.6143E+246 9.920792
253 1E+253 2.5937E+247 9.921105
254 1E+254 2.5733E+248 9.921415
255 1E+255 2.5532E+249 9.921722
256 1E+256 2.5332E+250 9.922028
257 1E+257 2.5136E+251 9.922330
258 1E+258 2.4941E+252 9.922631
259 1E+259 2.4749E+253 9.922929
260 1E+260 2.4559E+254 9.923225
261 1E+261 2.4371E+255 9.923518
262 1E+262 2.4186E+256 9.923810
263 1E+263 2.4002E+257 9.924099
264 1E+264 2.382E+258 9.924386
265 1E+265 2.3641E+259 9.924671
266 1E+266 2.3464E+260 9.924953
267 1E+267 2.3288E+261 9.925234
268 1E+268 2.3115E+262 9.925512
269 1E+269 2.2943E+263 9.925789
270 1E+270 2.2774E+264 9.926063
271 1E+271 2.2606E+265 9.926335
272 1E+272 2.244E+266 9.926606
273 1E+273 2.2276E+267 9.926874
274 1E+274 2.2113E+268 9.927140
275 1E+275 2.1953E+269 9.927405
276 1E+276 2.1794E+270 9.927668
277 1E+277 2.1637E+271 9.927928
278 1E+278 2.1482E+272 9.928187
279 1E+279 2.1328E+273 9.928444
280 1E+280 2.1176E+274 9.928699
281 1E+281 2.1025E+275 9.928952
282 1E+282 2.0877E+276 9.929204
283 1E+283 2.0729E+277 9.929453
284 1E+284 2.0584E+278 9.929701
285 1E+285 2.0439E+279 9.929948
286 1E+286 2.0297E+280 9.930192
287 1E+287 2.0156E+281 9.930435
288 1E+288 2.0016E+282 9.930676
289 1E+289 1.9878E+283 9.930916
290 1E+290 1.9741E+284 9.931153
291 1E+291 1.9605E+285 9.931390
292 1E+292 1.9471E+286 9.931624
293 1E+293 1.9338E+287 9.931857
294 1E+294 1.9207E+288 9.932088
295 1E+295 1.9077E+289 9.932318
296 1E+296 1.8948E+290 9.932547
297 1E+297 1.8821E+291 9.932773
298 1E+298 1.8695E+292 9.932999
299 1E+299 1.857E+293 9.933222
300 1E+300 1.8447E+294 9.933444
301 1E+301 1.8324E+295 9.933665
302 1E+302 1.8203E+296 9.933884
303 1E+303 1.8083E+297 9.934102
304 1E+304 1.7964E+298 9.934319
305 1E+305 1.7847E+299 9.934534
306 1E+306 1.773E+300 9.934747
307 1E+307 1.7615E+301 9.934960
308 1E+308 1.7501E+302 9.935170

yangchuanju · 发表于 2026-9-25 05:42

本帖最后由 yangchuanju 于 2026-9-25 05:44 编辑

烦请鲁思顺老哥哥，在度假之余将3楼、4楼给出的10^17--10^308的合数连乘积近似数乘上你的加强系数，计算并发布你的定理17--定理308吧！

yangchuanju · 发表于 2026-9-25 05:52

A132153
Largest prime <= square root of 10^n.
10的1--2000次方平方根内的最大素数
（这里仅给出前100个素数）
1 3
2 7
3 31
4 97
5 313
6 997
7 3137
8 9973
9 31607
10 99991
11 316223
12 999983
13 3162277
14 9999991
15 31622743
16 99999989
17 316227731
18 999999937
19 3162277633
20 9999999967
21 31622776589
22 99999999977
23 316227766003
24 999999999989
25 3162277660153
26 9999999999971
27 31622776601657
28 99999999999973
29 316227766016779
30 999999999999989
31 3162277660168279
32 9999999999999937
33 31622776601683777
34 99999999999999997
35 316227766016837933
36 999999999999999989
37 3162277660168379281
38 9999999999999999961
39 31622776601683793293
40 99999999999999999989
41 316227766016837933179
42 999999999999999999899
43 3162277660168379331989
44 9999999999999999999973
45 31622776601683793319839
46 99999999999999999999977
47 316227766016837933199881
48 999999999999999999999743
49 3162277660168379331998873
50 9999999999999999999999877
51 31622776601683793319988927
52 99999999999999999999999859
53 316227766016837933199889291
54 999999999999999999999999901
55 3162277660168379331998893501
56 9999999999999999999999999791
57 31622776601683793319988935437
58 99999999999999999999999999973
59 316227766016837933199889354357
60 999999999999999999999999999989
61 3162277660168379331998893544423
62 9999999999999999999999999999973
63 31622776601683793319988935444299
64 99999999999999999999999999999979
65 316227766016837933199889354443271
66 999999999999999999999999999999991
67 3162277660168379331998893544432689
68 9999999999999999999999999999999589
69 31622776601683793319988935444327133
70 99999999999999999999999999999999977
71 316227766016837933199889354443271843
72 999999999999999999999999999999999841
73 3162277660168379331998893544432718523
74 9999999999999999999999999999999999919
75 31622776601683793319988935444327185329
76 99999999999999999999999999999999999941
77 316227766016837933199889354443271853287
78 999999999999999999999999999999999999943
79 3162277660168379331998893544432718533629
80 9999999999999999999999999999999999999983
81 31622776601683793319988935444327185337143
82 99999999999999999999999999999999999999881
83 316227766016837933199889354443271853371921
84 999999999999999999999999999999999999999917
85 3162277660168379331998893544432718533719547
86 9999999999999999999999999999999999999999919
87 31622776601683793319988935444327185337195547
88 99999999999999999999999999999999999999999947
89 316227766016837933199889354443271853371955491
90 999999999999999999999999999999999999999999991
91 3162277660168379331998893544432718533719554829
92 9999999999999999999999999999999999999999999967
93 31622776601683793319988935444327185337195551381
94 99999999999999999999999999999999999999999999959
95 316227766016837933199889354443271853371955513857
96 999999999999999999999999999999999999999999999967
97 3162277660168379331998893544432718533719555139317
98 9999999999999999999999999999999999999999999999943
99 31622776601683793319988935444327185337195551393147
100 99999999999999999999999999999999999999999999999943
……

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