探索高精度计算素数对个数的弥合计算公式

vfbpgyfk · 发表于 2023-3-14 11:55

14位的十位等于1，个数大于等于0的5个连续偶数计算数度对照表：

愚工688 · 发表于 2023-3-14 14:53

愚工688 发表于 2023-3-14 02:44
这是因为相对误差修正系数取自的区域与计算的连续偶数区域重合，故计算精度高。下面我在计算1200000000 ...

实际计算精度如下：

G(12000000000000)= 24963244283；
Sp( 12000000000000 *)≈  24967794114.5 , Δ≈ 0.00018 , k(m)= 2.66667
G(12000000000002)= 11238627904；
Sp( 12000000000002 *)≈  11240581228 , Δ≈ 0.00017, k(m)= 1.20054
G(12000000000004)= 9505240144；
Sp( 12000000000004 *)≈  9506967759 , Δ≈ 0.00018, k(m)= 1.01538
G(12000000000006)= 19187133668；
Sp( 12000000000006 *)≈  19190753728.9 , Δ≈ 0.00019, k(m)= 2.04965
start time :10:36:32, end time:12:31:37use time :

重生888@ · 发表于 2023-3-14 17:28

（1） 24750923231
（2） 11137915453
（3） 9424389998
（4） 19015953211
（5） 9281596211

vfbpgyfk · 发表于 2023-3-14 17:48

本帖最后由 vfbpgyfk 于 2023-3-15 15:02 编辑

愚工辛苦苦啦！
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回复愚工688：
只要愿意接收并给发表的，基本费用在每个字一元左右。
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在国家开始重视科学发展力度条件下，真正的科学争呜天地总是要被打开的，过去那种人治现象，对科学发展只能起到阻碍作用。不过，现在是否真正地放开，还没有达到那么明朗化程度。

重生888@ · 发表于 2023-3-14 18:34

愚工是辛苦！谁的公式在变？

yangchuanju · 发表于 2023-3-14 19:58

本帖最后由 yangchuanju 于 2023-3-14 20:38 编辑

yangchuanju 发表于 2023-3-14 07:09
为验证重生系数是否适用于无穷大，下面先引用几组哥猜数据表：
网页A065577给出10的1-14次方的无序哥猜数 ...

重生、愚公、那宝吉计算式对比（10的n次幂）
对于10的n次幂的单计素数对，当采用哈李计算式时为0.660161816*N/ln(N)^2*4/3，在偶数为有限时，计算值小于真实值；
对于10的n次幂，重生、愚公、那宝吉三人所用波动系数一样都是4/3=1.3333，与哈李计算式中的波动系数相同，不再单独成列；
重生在N/ln(N)^2*4/3前要乘以（1+F/ln(N)），再乘以0.625，
愚公在N/ln(N)^2*4/3前要乘以t2=1.358-ln(N)^(0.5)*.05484，再乘以0.660161816，
那宝吉在N/ln(N)^2*4/3前要乘以DT=(1/ln(WS+1)^(1/2.7289))*(1-ln(N)^2/(N*FL))；
下面分别计算如下：
指数 N/ln(N)^2 重生F （1+F/ln(N)）重生计算值
1 1.88611697 1.000000 1.434294 2.254372635
2 4.715292425 2.000000 1.434294 5.635931588
3 20.95685522 2.500000 1.361912 23.78449503
4 117.8823106 2.833333 1.307625 128.4549057
5 754.446788 3.033333 1.263472 794.3519845
6 5239.213806 3.158333 1.228608 5364.115745
7 38492.18306 3.235256 1.200722 38515.34256
8 294705.7766 3.282875 1.178217 289356.0899
9 2328539.469 3.312287 1.159834 2250599.817
10 18861169.7 3.330469 1.144640 17991047.87
11 155877435.5 3.341705 1.131935 147035926.2
12 1309803451 3.348649 1.121192 1223783927
13 11160455444 3.352941 1.112013 10342139300
14 96230457659 3.355594 1.104094 88539558373
15 8.38274E+11 3.357233 1.097202 7.66463E+11
16 7.36764E+12 3.358246 1.091154 6.69936E+12
17 6.52636E+13 3.358872 1.085808 5.90531E+13
18 5.82135E+14 3.359259 1.081050 5.24431E+14
19 5.2247E+15 3.359499 1.076790 4.68825E+15
20 4.71529E+16 3.359646 1.072954 4.21608E+16
21 4.27691E+17 3.359738 1.069482 3.81173E+17
22 3.89694E+18 3.359794 1.066325 3.46283E+18
23 3.56544E+19 3.359829 1.063442 3.1597E+19
24 3.27451E+20 3.359851 1.060799 2.89466E+20
25 3.01779E+21 3.359864 1.058367 2.6616E+21
26 2.79011E+22 3.359872 1.056122 2.45558E+22
27 2.58727E+23 3.359877 1.054044 2.27258E+23
28 2.40576E+24 3.359881 1.052113 2.10928E+24
29 2.24271E+25 3.359883 1.050316 1.96296E+25
30 2.09569E+26 3.359884 1.048639 1.83135E+26
31 1.96266E+27 3.359884 1.047070 1.71254E+27
32 1.84191E+28 3.359885 1.045599 1.60492E+28
33 1.73197E+29 3.359885 1.044218 1.50713E+29
34 1.63159E+30 3.359885 1.042917 1.41801E+30
35 1.53969E+31 3.359885 1.041691 1.33657E+31
36 1.45534E+32 3.359886 1.040533 1.26194E+32
37 1.37773E+33 3.359886 1.039437 1.19339E+33
38 1.30618E+34 3.359886 1.038399 1.13028E+34
39 1.24005E+35 3.359886 1.037415 1.07204E+35
40 1.17882E+36 3.359886 1.036479 1.01819E+36
41 1.12202E+37 3.359886 1.035590 9.68294E+36
42 1.06923E+38 3.359886 1.034742 9.21979E+37
43 1.02007E+39 3.359886 1.033934 8.78908E+38
44 9.74234E+39 3.359886 1.033163 8.38786E+39
45 9.31416E+40 3.359886 1.032426 8.01348E+40
46 8.9136E+41 3.359886 1.031721 7.66362E+41
47 8.53833E+42 3.359886 1.031046 7.33618E+42
48 8.18627E+43 3.359886 1.030400 7.02928E+43
49 7.85555E+44 3.359886 1.029779 6.74123E+44
50 7.54447E+45 3.359886 1.029184 6.47054E+45
51 7.25151E+46 3.359886 1.028611 6.21582E+46
52 6.97528E+47 3.359886 1.028061 5.97585E+47
53 6.71455E+48 3.359886 1.027532 5.74951E+48
54 6.46817E+49 3.359886 1.027022 5.53579E+49
55 6.2351E+50 3.359886 1.026531 5.33376E+50
56 6.0144E+51 3.359886 1.026057 5.1426E+51
57 5.80522E+52 3.359886 1.025600 4.96153E+52
58 5.60677E+53 3.359886 1.025158 4.78985E+53
59 5.41832E+54 3.359886 1.024732 4.62694E+54
60 5.23921E+55 3.359886 1.024320 4.47219E+55
61 5.06884E+56 3.359886 1.023921 4.32508E+56
62 4.90665E+57 3.359886 1.023535 4.18511E+57
63 4.75212E+58 3.359886 1.023162 4.05182E+58
64 4.60478E+59 3.359886 1.022800 3.9248E+59
65 4.46418E+60 3.359886 1.022449 3.80367E+60
66 4.32993E+61 3.359886 1.022109 3.68805E+61
67 4.20164E+62 3.359886 1.021779 3.57762E+62
68 4.07897E+63 3.359886 1.021459 3.47208E+63
69 3.9616E+64 3.359886 1.021148 3.37115E+64
70 3.84922E+65 3.359886 1.020845 3.27455E+65
71 3.74155E+66 3.359886 1.020552 3.18204E+66
72 3.63834E+67 3.359886 1.020266 3.0934E+67
73 3.53935E+68 3.359886 1.019989 3.00841E+68
74 3.44433E+69 3.359886 1.019719 2.92688E+69
75 3.3531E+70 3.359886 1.019456 2.84861E+70
76 3.26544E+71 3.359886 1.019200 2.77344E+71
77 3.18117E+72 3.359886 1.018950 2.70121E+72
78 3.10013E+73 3.359886 1.018707 2.63177E+73
79 3.02214E+74 3.359886 1.018471 2.56497E+74
80 2.94706E+75 3.359886 1.018240 2.50068E+75
81 2.87474E+76 3.359886 1.018015 2.43877E+76
82 2.80505E+77 3.359886 1.017795 2.37914E+77
83 2.73787E+78 3.359886 1.017580 2.32167E+78
84 2.67307E+79 3.359886 1.017371 2.26625E+79
85 2.61054E+80 3.359886 1.017167 2.2128E+80
86 2.55019E+81 3.359886 1.016967 2.16121E+81
87 2.4919E+82 3.359886 1.016772 2.11141E+82
88 2.43558E+83 3.359886 1.016582 2.06331E+83
89 2.38116E+84 3.359886 1.016395 2.01683E+84
90 2.32854E+85 3.359886 1.016213 1.97191E+85
91 2.27764E+86 3.359886 1.016035 1.92847E+86
92 2.2284E+87 3.359886 1.015861 1.88645E+87
93 2.18073E+88 3.359886 1.015690 1.84579E+88
94 2.13458E+89 3.359886 1.015523 1.80643E+89
95 2.08988E+90 3.359886 1.015360 1.76832E+90
96 2.04657E+91 3.359886 1.015200 1.7314E+91
97 2.00459E+92 3.359886 1.015043 1.69562E+92
98 1.96389E+93 3.359886 1.014890 1.66094E+93
99 1.92441E+94 3.359886 1.014739 1.62731E+94
100 1.88612E+95 3.359886 1.014592 1.5947E+95
101 1.84895E+96 3.359886 1.014447 1.56305E+96
102 1.81288E+97 3.359886 1.014306 1.53234E+97
103 1.77785E+98 3.359886 1.014167 1.50253E+98
104 1.7438E+99 3.359886 1.014031 1.4736E+99
105 1.7108E+100 3.359886 1.013897 1.4454E+100
106 1.6786E+101 3.359886 1.013766 1.4181E+101
107 1.6474E+102 3.359886 1.013637 1.3916E+102
108 1.617E+103 3.359886 1.013511 1.3657E+103
109 1.5875E+104 3.359886 1.013387 1.3406E+104
110 1.5588E+105 3.359886 1.013265 1.3162E+105
111 1.5308E+106 3.359886 1.013146 1.2924E+106
112 1.5036E+107 3.359886 1.013028 1.2693E+107
113 1.4771E+108 3.359886 1.012913 1.2468E+108
114 1.4513E+109 3.359886 1.012800 1.2249E+109
115 1.4262E+110 3.359886 1.012689 1.2036E+110
116 1.4017E+111 3.359886 1.012579 1.1828E+111
117 1.3778E+112 3.359886 1.012472 1.1625E+112
118 1.3546E+113 3.359886 1.012366 1.1428E+113
119 1.3319E+114 3.359886 1.012262 1.1235E+114
120 1.3098E+115 3.359886 1.012160 1.1048E+115
121 1.2882E+116 3.359886 1.012059 1.0865E+116
122 1.2672E+117 3.359886 1.011960 1.0686E+117
123 1.2467E+118 3.359886 1.011863 1.0512E+118
124 1.2267E+119 3.359886 1.011768 1.0342E+119
125 1.2071E+120 3.359886 1.011673 1.0177E+120
126 1.188E+121 3.359886 1.011581 1.0015E+121
127 1.1694E+122 3.359886 1.011490 9.8569E+121
128 1.1512E+123 3.359886 1.011400 9.7026E+122
129 1.1334E+124 3.359886 1.011311 9.552E+123
130 1.116E+125 3.359886 1.011224 9.4048E+124
131 1.0991E+126 3.359886 1.011139 9.261E+125
132 1.0825E+127 3.359886 1.011054 9.1204E+126
133 1.0663E+128 3.359886 1.010971 8.983E+127
134 1.0504E+129 3.359886 1.010889 8.8487E+128
135 1.0349E+130 3.359886 1.010809 8.7174E+129
136 1.0197E+131 3.359886 1.010729 8.589E+130
137 1.0049E+132 3.359886 1.010651 8.4634E+131
138 9.904E+132 3.359886 1.010574 8.3406E+132
139 9.762E+133 3.359886 1.010498 8.2204E+133
140 9.623E+134 3.359886 1.010423 8.1028E+134
141 9.487E+135 3.359886 1.010349 7.9877E+135
142 9.3539E+136 3.359886 1.010276 7.875E+136
143 9.2235E+137 3.359886 1.010204 7.7647E+137
144 9.0959E+138 3.359886 1.010133 7.6567E+138
145 8.9708E+139 3.359886 1.010063 7.5509E+139
146 8.8484E+140 3.359886 1.009994 7.4473E+140
147 8.7284E+141 3.359886 1.009926 7.3459E+141
148 8.6108E+142 3.359886 1.009859 7.2464E+142
149 8.4956E+143 3.359886 1.009793 7.149E+143
150 8.3827E+144 3.359886 1.009728 7.0536E+144
151 8.2721E+145 3.359886 1.009663 6.96E+145
152 8.1636E+146 3.359886 1.009600 6.8683E+146
153 8.0572E+147 3.359886 1.009537 6.7784E+147
154 7.9529E+148 3.359886 1.009475 6.6902E+148
155 7.8506E+149 3.359886 1.009414 6.6038E+149
156 7.7503E+150 3.359886 1.009354 6.519E+150
157 7.6519E+151 3.359886 1.009294 6.4358E+151
158 7.5553E+152 3.359886 1.009235 6.3543E+152
159 7.4606E+153 3.359886 1.009177 6.2742E+153
160 7.3676E+154 3.359886 1.009120 6.1957E+154
161 7.2764E+155 3.359886 1.009063 6.1186E+155
162 7.1869E+156 3.359886 1.009007 6.043E+156
163 7.0989E+157 3.359886 1.008952 5.9687E+157
164 7.0126E+158 3.359886 1.008897 5.8959E+158
165 6.9279E+159 3.359886 1.008844 5.8243E+159
166 6.8447E+160 3.359886 1.008790 5.754E+160
167 6.7629E+161 3.359886 1.008738 5.685E+161
168 6.6827E+162 3.359886 1.008686 5.6173E+162
169 6.6038E+163 3.359886 1.008634 5.5507E+163
170 6.5264E+164 3.359886 1.008583 5.4853E+164
171 6.4502E+165 3.359886 1.008533 5.4211E+165
172 6.3755E+166 3.359886 1.008484 5.358E+166
173 6.302E+167 3.359886 1.008435 5.2959E+167
174 6.2297E+168 3.359886 1.008386 5.235E+168
175 6.1587E+169 3.359886 1.008338 5.1751E+169
176 6.089E+170 3.359886 1.008291 5.1162E+170
177 6.0204E+171 3.359886 1.008244 5.0583E+171
178 5.9529E+172 3.359886 1.008198 5.0014E+172
179 5.8866E+173 3.359886 1.008152 4.9455E+173
180 5.8213E+174 3.359886 1.008107 4.8904E+174
181 5.7572E+175 3.359886 1.008062 4.8363E+175
182 5.6941E+176 3.359886 1.008017 4.7831E+176
183 5.632E+177 3.359886 1.007974 4.7308E+177
184 5.571E+178 3.359886 1.007930 4.6793E+178
185 5.5109E+179 3.359886 1.007887 4.6287E+179
186 5.4518E+180 3.359886 1.007845 4.5788E+180
187 5.3937E+181 3.359886 1.007803 4.5298E+181
188 5.3365E+182 3.359886 1.007762 4.4816E+182
189 5.2801E+183 3.359886 1.007721 4.4341E+183
190 5.2247E+184 3.359886 1.007680 4.3874E+184
191 5.1701E+185 3.359886 1.007640 4.3414E+185
192 5.1164E+186 3.359886 1.007600 4.2961E+186
193 5.0635E+187 3.359886 1.007561 4.2515E+187
194 5.0115E+188 3.359886 1.007522 4.2076E+188
195 4.9602E+189 3.359886 1.007483 4.1644E+189
196 4.9097E+190 3.359886 1.007445 4.1219E+190
197 4.86E+191 3.359886 1.007407 4.08E+191
198 4.811E+192 3.359886 1.007370 4.0387E+192
199 4.7628E+193 3.359886 1.007333 3.9981E+193
200 4.7153E+194 3.359886 1.007296 3.9581E+194
201 4.6685E+195 3.359886 1.007260 3.9187E+195
202 4.6224E+196 3.359886 1.007224 3.8798E+196
203 4.577E+197 3.359886 1.007188 3.8415E+197
204 4.5322E+198 3.359886 1.007153 3.8038E+198
205 4.4881E+199 3.359886 1.007118 3.7667E+199
206 4.4446E+200 3.359886 1.007083 3.7301E+200
207 4.4018E+201 3.359886 1.007049 3.694E+201
208 4.3596E+202 3.359886 1.007015 3.6584E+202
209 4.3179E+203 3.359886 1.006982 3.6234E+203
210 4.2769E+204 3.359886 1.006948 3.5889E+204
211 4.2365E+205 3.359886 1.006916 3.5548E+205
212 4.1966E+206 3.359886 1.006883 3.5212E+206
213 4.1573E+207 3.359886 1.006851 3.4881E+207
214 4.1185E+208 3.359886 1.006819 3.4555E+208
215 4.0803E+209 3.359886 1.006787 3.4233E+209
216 4.0426E+210 3.359886 1.006755 3.3916E+210
217 4.0054E+211 3.359886 1.006724 3.3603E+211
218 3.9688E+212 3.359886 1.006693 3.3294E+212
219 3.9326E+213 3.359886 1.006663 3.299E+213
220 3.8969E+214 3.359886 1.006633 3.269E+214
221 3.8617E+215 3.359886 1.006603 3.2394E+215
222 3.827E+216 3.359886 1.006573 3.2102E+216
223 3.7928E+217 3.359886 1.006543 3.1813E+217
224 3.759E+218 3.359886 1.006514 3.1529E+218
225 3.7257E+219 3.359886 1.006485 3.1249E+219
226 3.6928E+220 3.359886 1.006457 3.0972E+220
227 3.6603E+221 3.359886 1.006428 3.0699E+221
228 3.6283E+222 3.359886 1.006400 3.0429E+222
229 3.5966E+223 3.359886 1.006372 3.0163E+223
230 3.5654E+224 3.359886 1.006344 2.99E+224
231 3.5346E+225 3.359886 1.006317 2.9641E+225
232 3.5042E+226 3.359886 1.006290 2.9386E+226
233 3.4742E+227 3.359886 1.006263 2.9133E+227
234 3.4446E+228 3.359886 1.006236 2.8884E+228
235 3.4153E+229 3.359886 1.006209 2.8638E+229
236 3.3864E+230 3.359886 1.006183 2.8395E+230
237 3.3579E+231 3.359886 1.006157 2.8155E+231
238 3.3298E+232 3.359886 1.006131 2.7918E+232
239 3.302E+233 3.359886 1.006105 2.7684E+233
240 3.2745E+234 3.359886 1.006080 2.7453E+234
241 3.2474E+235 3.359886 1.006055 2.7225E+235
242 3.2206E+236 3.359886 1.006030 2.7E+236
243 3.1942E+237 3.359886 1.006005 2.6778E+237
244 3.168E+238 3.359886 1.005980 2.6558E+238
245 3.1422E+239 3.359886 1.005956 2.6341E+239
246 3.1167E+240 3.359886 1.005932 2.6127E+240
247 3.0915E+241 3.359886 1.005908 2.5915E+241
248 3.0667E+242 3.359886 1.005884 2.5706E+242
249 3.0421E+243 3.359886 1.005860 2.5499E+243
250 3.0178E+244 3.359886 1.005837 2.5295E+244
251 2.9938E+245 3.359886 1.005813 2.5093E+245
252 2.9701E+246 3.359886 1.005790 2.4894E+246
253 2.9466E+247 3.359886 1.005768 2.4697E+247
254 2.9235E+248 3.359886 1.005745 2.4502E+248
255 2.9006E+249 3.359886 1.005722 2.431E+249
256 2.878E+250 3.359886 1.005700 2.412E+250
257 2.8556E+251 3.359886 1.005678 2.3932E+251
258 2.8335E+252 3.359886 1.005656 2.3746E+252
259 2.8117E+253 3.359886 1.005634 2.3563E+253
260 2.7901E+254 3.359886 1.005612 2.3381E+254
261 2.7688E+255 3.359886 1.005591 2.3202E+255
262 2.7477E+256 3.359886 1.005569 2.3025E+256
263 2.7268E+257 3.359886 1.005548 2.285E+257
264 2.7062E+258 3.359886 1.005527 2.2676E+258
265 2.6858E+259 3.359886 1.005506 2.2505E+259
266 2.6657E+260 3.359886 1.005486 2.2336E+260
267 2.6457E+261 3.359886 1.005465 2.2168E+261
268 2.626E+262 3.359886 1.005445 2.2003E+262
269 2.6065E+263 3.359886 1.005424 2.1839E+263
270 2.5873E+264 3.359886 1.005404 2.1677E+264
271 2.5682E+265 3.359886 1.005384 2.1517E+265
272 2.5494E+266 3.359886 1.005365 2.1359E+266
273 2.5307E+267 3.359886 1.005345 2.1202E+267
274 2.5123E+268 3.359886 1.005325 2.1047E+268
275 2.494E+269 3.359886 1.005306 2.0894E+269
276 2.476E+270 3.359886 1.005287 2.0742E+270
277 2.4582E+271 3.359886 1.005268 2.0593E+271
278 2.4405E+272 3.359886 1.005249 2.0444E+272
279 2.423E+273 3.359886 1.005230 2.0298E+273
280 2.4058E+274 3.359886 1.005211 2.0152E+274
281 2.3887E+275 3.359886 1.005193 2.0009E+275
282 2.3718E+276 3.359886 1.005174 1.9867E+276
283 2.355E+277 3.359886 1.005156 1.9726E+277
284 2.3385E+278 3.359886 1.005138 1.9587E+278
285 2.3221E+279 3.359886 1.005120 1.945E+279
286 2.3059E+280 3.359886 1.005102 1.9314E+280
287 2.2898E+281 3.359886 1.005084 1.9179E+281
288 2.274E+282 3.359886 1.005067 1.9046E+282
289 2.2583E+283 3.359886 1.005049 1.8914E+283
290 2.2427E+284 3.359886 1.005032 1.8783E+284
291 2.2273E+285 3.359886 1.005014 1.8654E+285
292 2.2121E+286 3.359886 1.004997 1.8526E+286
293 2.197E+287 3.359886 1.004980 1.84E+287
294 2.1821E+288 3.359886 1.004963 1.8274E+288
295 2.1673E+289 3.359886 1.004946 1.815E+289
296 2.1527E+290 3.359886 1.004930 1.8028E+290
297 2.1382E+291 3.359886 1.004913 1.7906E+291
298 2.1239E+292 3.359886 1.004897 1.7786E+292
299 2.1097E+293 3.359886 1.004880 1.7667E+293
300 2.0957E+294 3.359886 1.004864 1.7549E+294
301 2.0818E+295 3.359886 1.004848 1.7432E+295
302 2.068E+296 3.359886 1.004832 1.7317E+296
303 2.0544E+297 3.359886 1.004816 1.7202E+297
304 2.0409E+298 3.359886 1.004800 1.7089E+298
305 2.0275E+299 3.359886 1.004784 1.6977E+299
306 2.0143E+300 3.359886 1.004769 1.6866E+300
307 2.0012E+301 3.359886 1.004753 1.6756E+301

yangchuanju · 发表于 2023-3-14 20:00

本帖最后由 yangchuanju 于 2023-3-14 20:06 编辑

（接上楼）
指数愚公t2 愚公计算值那宝吉DT 那宝吉计算值哈李计算值
1 1.274784 2.116383978 0.688944 1.73257075 1.660189872
2 1.240315 5.14789693 0.812455 5.107949422 4.150474681
3 1.213866 22.39164808 0.855441 23.90313231 18.44655414
4 1.191569 123.6393818 0.834628 131.1837634 103.761867
5 1.171924 778.246562 0.806778 811.5617195 664.0759489
6 1.154164 5322.587118 0.783410 5472.606387 4611.638534
7 1.137832 38551.36872 0.764682 39245.68131 33881.42596
8 1.122630 291215.5777 0.749410 294474.0745 259404.6675
9 1.108353 2271699.063 0.736659 2287120.143 2049617.126
10 1.094849 18176569.54 0.725792 18252372.07 16601898.72
11 1.082005 148457297.6 0.716373 148888581.3 137205774.6
12 1.069732 1233304727 0.708099 1236627081 1152909634
13 1.057962 10392999937 0.700746 10427532869 9823608711
14 1.046635 88653745075 0.694151 89064594114 84703564910
15 1.035707 7.64209E+11 0.688185 7.69184E+11 7.37862E+11
16 1.025137 6.64813E+12 0.682752 6.70703E+12 6.48512E+12
17 1.014893 5.83016E+13 0.677773 5.89785E+13 5.7446E+13
18 1.004946 5.14938E+14 0.673186 5.22513E+14 5.12404E+14
19 0.995271 4.57712E+15 0.668939 4.66001E+15 4.59886E+15
20 0.985848 4.09174E+16 0.664990 4.18083E+16 4.15047E+16
21 0.976658 3.67673E+17 0.661305 3.77112E+17 3.7646E+17
22 0.967684 3.31929E+18 0.657854 3.41815E+18 3.43014E+18
23 0.958912 3.0094E+19 0.654612 3.11197E+19 3.13836E+19
24 0.950328 2.73911E+20 0.651558 2.84471E+20 2.88227E+20
25 0.941921 2.50203E+21 0.648672 2.61007E+21 2.6563E+21
26 0.933682 2.29303E+22 0.645940 2.403E+22 2.4559E+22
27 0.925599 2.10791E+23 0.643348 2.21935E+23 2.27735E+23
28 0.917664 1.94324E+24 0.640883 2.05575E+24 2.11759E+24
29 0.909870 1.79614E+25 0.638535 1.9094E+25 1.97407E+25
30 0.902209 1.66426E+26 0.636294 1.77796E+26 1.84466E+26
31 0.894675 1.54561E+27 0.634151 1.6595E+27 1.72756E+27
32 0.887261 1.4385E+28 0.632101 1.55236E+28 1.62128E+28
33 0.879962 1.34151E+29 0.630134 1.45517E+29 1.52451E+29
34 0.872773 1.25343E+30 0.628247 1.36672E+30 1.43615E+30
35 0.865689 1.17323E+31 0.626433 1.28601E+31 1.35526E+31
36 0.858706 1.10001E+32 0.624687 1.21217E+32 1.28101E+32
37 0.851819 1.033E+33 0.623004 1.14445E+33 1.2127E+33
38 0.845024 9.71538E+33 0.621382 1.08218E+34 1.14972E+34
39 0.838318 9.15034E+34 0.619816 1.0248E+35 1.09151E+35
40 0.831698 8.62985E+35 0.618302 9.71825E+35 1.03762E+36
41 0.825160 8.14944E+36 0.616839 9.22808E+36 9.8762E+36
42 0.818701 7.70521E+37 0.615422 8.77368E+37 9.41151E+37
43 0.812318 7.29368E+38 0.614049 8.35167E+38 8.97885E+38
44 0.806009 6.91182E+39 0.612718 7.95908E+39 8.57536E+39
45 0.799772 6.55691E+40 0.611427 7.59323E+40 8.19847E+40
46 0.793604 6.22653E+41 0.610173 7.25178E+41 7.84589E+41
47 0.787502 5.91853E+42 0.608955 6.93261E+42 7.51557E+42
48 0.781465 5.63099E+43 0.607771 6.63383E+43 7.20569E+43
49 0.775490 5.36219E+44 0.606619 6.35376E+44 6.91458E+44
50 0.769576 5.11057E+45 0.605497 6.09087E+45 6.64076E+45
51 0.763721 4.87475E+46 0.604405 5.8438E+46 6.38289E+46
52 0.757923 4.65346E+47 0.603341 5.6113E+47 6.13976E+47
53 0.752181 4.44558E+48 0.602303 5.39226E+48 5.91025E+48
54 0.746492 4.25006E+49 0.601291 5.18567E+49 5.69338E+49
55 0.740856 4.06599E+50 0.600303 4.9906E+50 5.48823E+50
56 0.735271 3.8925E+51 0.599339 4.80622E+51 5.29397E+51
57 0.729735 3.72884E+52 0.598397 4.63177E+52 5.10985E+52
58 0.724248 3.57428E+53 0.597477 4.46655E+53 4.93517E+53
59 0.718808 3.4282E+54 0.596577 4.30992E+54 4.76929E+54
60 0.713414 3.29001E+55 0.595696 4.16131E+55 4.61164E+55
61 0.708065 3.15916E+56 0.594835 4.02017E+56 4.46168E+56
62 0.702759 3.03515E+57 0.593993 3.88602E+57 4.31891E+57
63 0.697496 2.91755E+58 0.593167 3.7584E+58 4.18289E+58
64 0.692274 2.80593E+59 0.592359 3.63691E+59 4.0532E+59
65 0.687094 2.6999E+60 0.591567 3.52115E+60 3.92944E+60
66 0.681952 2.59911E+61 0.590791 3.41078E+61 3.81127E+61
67 0.676850 2.50323E+62 0.590030 3.30546E+62 3.69835E+62
68 0.671786 2.41196E+63 0.589284 3.2049E+63 3.59038E+63
69 0.666758 2.32503E+64 0.588552 3.10881E+64 3.48706E+64
70 0.661767 2.24216E+65 0.587833 3.01693E+65 3.38814E+65
71 0.656812 2.16313E+66 0.587128 2.92903E+66 3.29337E+66
72 0.651891 2.0877E+67 0.586435 2.84487E+67 3.20253E+67
73 0.647005 2.01567E+68 0.585755 2.76425E+68 3.11539E+68
74 0.642151 1.94685E+69 0.585087 2.68698E+69 3.03176E+69
75 0.637331 1.88105E+70 0.584431 2.61287E+70 2.95145E+70
76 0.632542 1.81811E+71 0.583786 2.54176E+71 2.87429E+71
77 0.627785 1.75787E+72 0.583152 2.47348E+72 2.80012E+72
78 0.623059 1.70019E+73 0.582528 2.40788E+73 2.72878E+73
79 0.618363 1.64493E+74 0.581915 2.34484E+74 2.66013E+74
80 0.613696 1.59196E+75 0.581312 2.28421E+75 2.59405E+75
81 0.609059 1.54116E+76 0.580718 2.22588E+76 2.53039E+76
82 0.604450 1.49242E+77 0.580134 2.16974E+77 2.46905E+77
83 0.599869 1.44563E+78 0.579559 2.11567E+78 2.40991E+78
84 0.595315 1.4007E+79 0.578992 2.06358E+79 2.35288E+79
85 0.590789 1.35754E+80 0.578435 2.01337E+80 2.29784E+80
86 0.586289 1.31605E+81 0.577886 1.96495E+81 2.24471E+81
87 0.581816 1.27616E+82 0.577345 1.91824E+82 2.19341E+82
88 0.577368 1.23778E+83 0.576812 1.87316E+83 2.14384E+83
89 0.572945 1.20085E+84 0.576286 1.82964E+84 2.09593E+84
90 0.568547 1.1653E+85 0.575769 1.7876E+85 2.04962E+85
91 0.564173 1.13106E+86 0.575258 1.74698E+86 2.00482E+86
92 0.559823 1.09808E+87 0.574755 1.70771E+87 1.96147E+87
93 0.555497 1.06629E+88 0.574259 1.66974E+88 1.91952E+88
94 0.551194 1.03563E+89 0.573770 1.63301E+89 1.87889E+89
95 0.546914 1.00607E+90 0.573287 1.59747E+90 1.83955E+90
96 0.542656 9.77552E+90 0.572811 1.56306E+91 1.80142E+91
97 0.538420 9.50027E+91 0.572341 1.52974E+92 1.76447E+92
98 0.534207 9.23453E+92 0.571877 1.49747E+93 1.72864E+93
99 0.530014 8.9779E+93 0.571419 1.4662E+94 1.6939E+94
100 0.525843 8.72999E+94 0.570968 1.43588E+95 1.66019E+95
101 0.521693 8.49043E+95 0.570522 1.40649E+96 1.62748E+96
102 0.517563 8.25886E+96 0.570081 1.37798E+97 1.59572E+97
103 0.513453 8.03496E+97 0.569646 1.35032E+98 1.56489E+98
104 0.509363 7.81841E+98 0.569217 1.3235E+99 1.5349E+99
105 0.505293 7.6089E+99 0.568793 1.2974E+100 1.5058E+100
106 0.501242 7.4062E+100 0.568373 1.2721E+101 1.4776E+101
107 0.497210 7.2099E+101 0.567959 1.2475E+102 1.4501E+102
108 0.493197 7.0199E+102 0.567550 1.2237E+103 1.4233E+103
109 0.489203 6.8359E+103 0.567146 1.2005E+104 1.3973E+104
110 0.485226 6.6576E+104 0.566746 1.1779E+105 1.3721E+105
111 0.481268 6.4848E+105 0.566351 1.156E+106 1.3474E+106
112 0.477328 6.3174E+106 0.565961 1.1346E+107 1.3235E+107
113 0.473405 6.1551E+107 0.565575 1.1139E+108 1.3002E+108
114 0.469499 5.9977E+108 0.565193 1.0937E+109 1.2775E+109
115 0.465611 5.845E+109 0.564816 1.074E+110 1.2553E+110
116 0.461739 5.6969E+110 0.564442 1.0549E+111 1.2338E+111
117 0.457885 5.5532E+111 0.564073 1.0363E+112 1.2128E+112
118 0.454046 5.4137E+112 0.563708 1.0181E+113 1.1923E+113
119 0.450224 5.2783E+113 0.563347 1.0004E+114 1.1724E+114
120 0.446418 5.1468E+114 0.562989 9.8321E+114 1.1529E+115
121 0.442627 5.0191E+115 0.562636 9.6642E+115 1.1339E+116
122 0.438853 4.895E+116 0.562286 9.5005E+116 1.1154E+117
123 0.435093 4.7745E+117 0.561939 9.3409E+117 1.0974E+118
124 0.431349 4.6574E+118 0.561597 9.1852E+118 1.0797E+119
125 0.427620 4.5436E+119 0.561257 9.0334E+119 1.0625E+120
126 0.423906 4.4329E+120 0.560922 8.8852E+120 1.0457E+121
127 0.420207 4.3253E+121 0.560589 8.7407E+121 1.0293E+122
128 0.416522 4.2206E+122 0.560260 8.5996E+122 1.0133E+123
129 0.412851 4.1188E+123 0.559934 8.4618E+123 9.9765E+123
130 0.409195 4.0198E+124 0.559611 8.3274E+124 9.8236E+124
131 0.405553 3.9234E+125 0.559292 8.196E+125 9.6742E+125
132 0.401924 3.8296E+126 0.558975 8.0677E+126 9.5282E+126
133 0.398310 3.7383E+127 0.558662 7.9424E+127 9.3854E+127
134 0.394709 3.6494E+128 0.558352 7.82E+128 9.2459E+128
135 0.391121 3.5629E+129 0.558044 7.7003E+129 9.1094E+129
136 0.387546 3.4786E+130 0.557739 7.5833E+130 8.9759E+130
137 0.383985 3.3965E+131 0.557438 7.469E+131 8.8454E+131
138 0.380437 3.3165E+132 0.557139 7.3572E+132 8.7177E+132
139 0.376901 3.2386E+133 0.556842 7.2479E+133 8.5927E+133
140 0.373379 3.1626E+134 0.556549 7.1409E+134 8.4704E+134
141 0.369868 3.0886E+135 0.556258 7.0363E+135 8.3506E+135
142 0.366370 3.0165E+136 0.555969 6.934E+136 8.2334E+136
143 0.362885 2.9461E+137 0.555684 6.8338E+137 8.1187E+137
144 0.359412 2.8776E+138 0.555400 6.7358E+138 8.0063E+138
145 0.355950 2.8107E+139 0.555119 6.6398E+139 7.8963E+139
146 0.352501 2.7454E+140 0.554841 6.5459E+140 7.7885E+140
147 0.349063 2.6818E+141 0.554565 6.4539E+141 7.6829E+141
148 0.345637 2.6197E+142 0.554292 6.3639E+142 7.5794E+142
149 0.342223 2.5591E+143 0.554020 6.2757E+143 7.478E+143
150 0.338820 2.5E+144 0.553751 6.1893E+144 7.3786E+144
151 0.335428 2.4423E+145 0.553485 6.1046E+145 7.2812E+145
152 0.332048 2.386E+146 0.553220 6.0217E+146 7.1857E+146
153 0.328679 2.331E+147 0.552958 5.9404E+147 7.0921E+147
154 0.325320 2.2773E+148 0.552698 5.8608E+148 7.0003E+148
155 0.321973 2.2249E+149 0.552440 5.7827E+149 6.9103E+149
156 0.318636 2.1737E+150 0.552184 5.7061E+150 6.822E+150
157 0.315310 2.1237E+151 0.551930 5.6311E+151 6.7353E+151
158 0.311995 2.0749E+152 0.551678 5.5575E+152 6.6503E+152
159 0.308690 2.0272E+153 0.551428 5.4853E+153 6.5669E+153
160 0.305395 1.9805E+154 0.551180 5.4145E+154 6.4851E+154
161 0.302111 1.935E+155 0.550934 5.3451E+155 6.4048E+155
162 0.298837 1.8904E+156 0.550690 5.277E+156 6.326E+156
163 0.295573 1.8469E+157 0.550448 5.2101E+157 6.2486E+157
164 0.292319 1.8044E+158 0.550208 5.1445E+158 6.1726E+158
165 0.289075 1.7628E+159 0.549970 5.0802E+159 6.098E+159
166 0.285841 1.7221E+160 0.549733 5.017E+160 6.0248E+160
167 0.282616 1.6824E+161 0.549498 4.955E+161 5.9528E+161
168 0.279401 1.6435E+162 0.549265 4.8941E+162 5.8822E+162
169 0.276196 1.6055E+163 0.549034 4.8343E+163 5.8128E+163
170 0.273000 1.5683E+164 0.548804 4.7756E+164 5.7446E+164
171 0.269813 1.5319E+165 0.548576 4.7179E+165 5.6776E+165
172 0.266636 1.4963E+166 0.548350 4.6613E+166 5.6118E+166
173 0.263468 1.4615E+167 0.548126 4.6057E+167 5.5471E+167
174 0.260309 1.4274E+168 0.547903 4.5511E+168 5.4835E+168
175 0.257160 1.3941E+169 0.547681 4.4974E+169 5.421E+169
176 0.254019 1.3614E+170 0.547462 4.4446E+170 5.3596E+170
177 0.250887 1.3295E+171 0.547243 4.3928E+171 5.2992E+171
178 0.247764 1.2982E+172 0.547027 4.3419E+172 5.2398E+172
179 0.244650 1.2676E+173 0.546812 4.2918E+173 5.1815E+173
180 0.241544 1.2377E+174 0.546598 4.2426E+174 5.124E+174
181 0.238447 1.2084E+175 0.546386 4.1942E+175 5.0676E+175
182 0.235359 1.1796E+176 0.546175 4.1466E+176 5.012E+176
183 0.232279 1.1515E+177 0.545966 4.0999E+177 4.9574E+177
184 0.229207 1.124E+178 0.545758 4.0539E+178 4.9037E+178
185 0.226144 1.097E+179 0.545552 4.0087E+179 4.8508E+179
186 0.223089 1.0706E+180 0.545347 3.9642E+180 4.7988E+180
187 0.220042 1.0447E+181 0.545143 3.9204E+181 4.7476E+181
188 0.217004 1.0193E+182 0.544941 3.8774E+182 4.6972E+182
189 0.213973 9.9447E+182 0.544740 3.8351E+183 4.6477E+183
190 0.210951 9.7013E+183 0.544540 3.7934E+184 4.5989E+184
191 0.207936 9.4628E+184 0.544342 3.7524E+185 4.5508E+185
192 0.204929 9.2291E+185 0.544145 3.7121E+186 4.5036E+186
193 0.201930 9.0001E+186 0.543950 3.6724E+187 4.457E+187
194 0.198939 8.7756E+187 0.543755 3.6334E+188 4.4112E+188
195 0.195956 8.5555E+188 0.543562 3.5949E+189 4.366E+189
196 0.192980 8.3399E+189 0.543370 3.5571E+190 4.3216E+190
197 0.190012 8.1284E+190 0.543179 3.5198E+191 4.2778E+191
198 0.187051 7.9211E+191 0.542990 3.4831E+192 4.2347E+192
199 0.184098 7.7179E+192 0.542802 3.447E+193 4.1923E+193
200 0.181152 7.5187E+193 0.542614 3.4114E+194 4.1505E+194
201 0.178214 7.3233E+194 0.542428 3.3764E+195 4.1093E+195
202 0.175283 7.1317E+195 0.542244 3.3419E+196 4.0687E+196
203 0.172359 6.9438E+196 0.542060 3.308E+197 4.0287E+197
204 0.169442 6.7596E+197 0.541877 3.2745E+198 3.9893E+198
205 0.166532 6.5788E+198 0.541696 3.2416E+199 3.9505E+199
206 0.163630 6.4016E+199 0.541516 3.2091E+200 3.9122E+200
207 0.160735 6.2277E+200 0.541337 3.1771E+201 3.8745E+201
208 0.157846 6.0571E+201 0.541158 3.1456E+202 3.8373E+202
209 0.154965 5.8898E+202 0.540981 3.1146E+203 3.8007E+203
210 0.152090 5.7256E+203 0.540805 3.084E+204 3.7646E+204
211 0.149222 5.5645E+204 0.540630 3.0538E+205 3.729E+205
212 0.146361 5.4064E+205 0.540456 3.0241E+206 3.6939E+206
213 0.143507 5.2514E+206 0.540283 2.9948E+207 3.6593E+207
214 0.140659 5.0992E+207 0.540112 2.9659E+208 3.6252E+208
215 0.137818 4.9498E+208 0.539941 2.9375E+209 3.5915E+209
216 0.134984 4.8032E+209 0.539771 2.9094E+210 3.5584E+210
217 0.132156 4.6594E+210 0.539602 2.8818E+211 3.5256E+211
218 0.129335 4.5181E+211 0.539434 2.8545E+212 3.4934E+212
219 0.126520 4.3795E+212 0.539267 2.8276E+213 3.4615E+213
220 0.123712 4.2435E+213 0.539101 2.8011E+214 3.4301E+214
221 0.120910 4.1099E+214 0.538936 2.775E+215 3.3992E+215
222 0.118114 3.9788E+215 0.538771 2.7492E+216 3.3686E+216
223 0.115325 3.8501E+216 0.538608 2.7238E+217 3.3385E+217
224 0.112541 3.7237E+217 0.538446 2.6987E+218 3.3087E+218
225 0.109764 3.5996E+218 0.538284 2.674E+219 3.2794E+219
226 0.106994 3.4778E+219 0.538124 2.6496E+220 3.2504E+220
227 0.104229 3.3581E+220 0.537964 2.6255E+221 3.2219E+221
228 0.101470 3.2406E+221 0.537805 2.6017E+222 3.1937E+222
229 0.098718 3.1252E+222 0.537647 2.5783E+223 3.1658E+223
230 0.095971 3.0119E+223 0.537490 2.5552E+224 3.1384E+224
231 0.093231 2.9006E+224 0.537334 2.5324E+225 3.1112E+225
232 0.090496 2.7913E+225 0.537179 2.5099E+226 3.0845E+226
233 0.087767 2.684E+226 0.537024 2.4876E+227 3.0581E+227
234 0.085045 2.5785E+227 0.536870 2.4657E+228 3.032E+228
235 0.082327 2.475E+228 0.536717 2.4441E+229 3.0062E+229
236 0.079616 2.3732E+229 0.536565 2.4227E+230 2.9808E+230
237 0.076911 2.2732E+230 0.536414 2.4017E+231 2.9557E+231
238 0.074211 2.1751E+231 0.536263 2.3808E+232 2.9309E+232
239 0.071516 2.0786E+232 0.536114 2.3603E+233 2.9064E+233
240 0.068828 1.9838E+233 0.535965 2.34E+234 2.8823E+234
241 0.066145 1.8907E+234 0.535816 2.32E+235 2.8584E+235
242 0.063467 1.7992E+235 0.535669 2.3002E+236 2.8348E+236
243 0.060796 1.7093E+236 0.535522 2.2807E+237 2.8115E+237
244 0.058129 1.621E+237 0.535376 2.2614E+238 2.7885E+238
245 0.055468 1.5342E+238 0.535231 2.2424E+239 2.7658E+239
246 0.052813 1.4489E+239 0.535087 2.2236E+240 2.7434E+240
247 0.050163 1.365E+240 0.534943 2.2051E+241 2.7212E+241
248 0.047518 1.2827E+241 0.534800 2.1867E+242 2.6993E+242
249 0.044878 1.2017E+242 0.534658 2.1686E+243 2.6777E+243
250 0.042244 1.1221E+243 0.534516 2.1507E+244 2.6563E+244
251 0.039615 1.0439E+244 0.534375 2.1331E+245 2.6352E+245
252 0.036992 9.6708E+244 0.534235 2.1156E+246 2.6143E+246
253 0.034373 8.9153E+245 0.534095 2.0984E+247 2.5937E+247
254 0.031760 8.1728E+246 0.533957 2.0814E+248 2.5733E+248
255 0.029152 7.4429E+247 0.533819 2.0645E+249 2.5532E+249
256 0.026549 6.7255E+248 0.533681 2.0479E+250 2.5332E+250
257 0.023951 6.0202E+249 0.533544 2.0315E+251 2.5136E+251
258 0.021358 5.3269E+250 0.533408 2.0152E+252 2.4941E+252
259 0.018770 4.6454E+251 0.533273 1.9992E+253 2.4749E+253
260 0.016187 3.9754E+252 0.533138 1.9834E+254 2.4559E+254
261 0.013609 3.3167E+253 0.533004 1.9677E+255 2.4371E+255
262 0.011036 2.6692E+254 0.532870 1.9522E+256 2.4186E+256
263 0.008468 2.0325E+255 0.532737 1.9369E+257 2.4002E+257
264 0.005905 1.4066E+256 0.532605 1.9218E+258 2.382E+258
265 0.003346 7.9114E+256 0.532473 1.9068E+259 2.3641E+259
266 0.000793 1.8605E+257 0.532342 1.8921E+260 2.3464E+260
267 -0.001756 -4.0889E+258 0.532212 1.8775E+261 2.3288E+261
268 -0.004300 -9.9388E+259 0.532082 1.863E+262 2.3115E+262
269 -0.006839 -1.5691E+261 0.531952 1.8487E+263 2.2943E+263
270 -0.009374 -2.1347E+262 0.531824 1.8346E+264 2.2774E+264
271 -0.011903 -2.6908E+263 0.531696 1.8207E+265 2.2606E+265
272 -0.014429 -3.2377E+264 0.531568 1.8069E+266 2.244E+266
273 -0.016949 -3.7755E+265 0.531441 1.7932E+267 2.2276E+267
274 -0.019465 -4.3044E+266 0.531315 1.7797E+268 2.2113E+268
275 -0.021976 -4.8244E+267 0.531189 1.7664E+269 2.1953E+269
276 -0.024483 -5.3359E+268 0.531064 1.7532E+270 2.1794E+270
277 -0.026985 -5.8388E+269 0.530939 1.7402E+271 2.1637E+271
278 -0.029483 -6.3335E+270 0.530815 1.7273E+272 2.1482E+272
279 -0.031976 -6.8199E+271 0.530692 1.7145E+273 2.1328E+273
280 -0.034465 -7.2983E+272 0.530569 1.7019E+274 2.1176E+274
281 -0.036949 -7.7688E+273 0.530446 1.6894E+275 2.1025E+275
282 -0.039429 -8.2315E+274 0.530324 1.6771E+276 2.0877E+276
283 -0.041905 -8.6866E+275 0.530203 1.6649E+277 2.0729E+277
284 -0.044376 -9.1342E+276 0.530082 1.6528E+278 2.0584E+278
285 -0.046843 -9.5744E+277 0.529962 1.6408E+279 2.0439E+279
286 -0.049305 -1.0007E+279 0.529842 1.629E+280 2.0297E+280
287 -0.051763 -1.0433E+280 0.529723 1.6173E+281 2.0156E+281
288 -0.054217 -1.0852E+281 0.529604 1.6057E+282 2.0016E+282
289 -0.056667 -1.1264E+282 0.529486 1.5943E+283 1.9878E+283
290 -0.059112 -1.1669E+283 0.529368 1.583E+284 1.9741E+284
291 -0.061554 -1.2068E+284 0.529251 1.5717E+285 1.9605E+285
292 -0.063991 -1.246E+285 0.529134 1.5607E+286 1.9471E+286
293 -0.066423 -1.2845E+286 0.529018 1.5497E+287 1.9338E+287
294 -0.068852 -1.3225E+287 0.528902 1.5388E+288 1.9207E+288
295 -0.071277 -1.3598E+288 0.528787 1.5281E+289 1.9077E+289
296 -0.073697 -1.3964E+289 0.528672 1.5174E+290 1.8948E+290
297 -0.076113 -1.4325E+290 0.528558 1.5069E+291 1.8821E+291
298 -0.078526 -1.468E+291 0.528444 1.4965E+292 1.8695E+292
299 -0.080934 -1.503E+292 0.528330 1.4862E+293 1.857E+293
300 -0.083338 -1.5373E+293 0.528217 1.476E+294 1.8447E+294
301 -0.085739 -1.5711E+294 0.528105 1.4659E+295 1.8324E+295
302 -0.088135 -1.6043E+295 0.527993 1.4559E+296 1.8203E+296
303 -0.090527 -1.637E+296 0.527882 1.446E+297 1.8083E+297
304 -0.092915 -1.6692E+297 0.527770 1.4362E+298 1.7964E+298
305 -0.095300 -1.7008E+298 0.527660 1.4265E+299 1.7847E+299
306 -0.097680 -1.7319E+299 0.527550 1.4169E+300 1.773E+300
307 -0.100057 -1.7625E+300 0.527440 1.4074E+301 1.7615E+301

假定偶数达到10的307次方时，哈李计算式值已经近似等于真实值，
则按重生计算式的计算精度仍可得到95%（重生/哈李=0.95），那宝吉计算式的计算精度降到80%，已无实用价值，
愚公计算式早已变为负值，对于大偶数愚公计算式不再有用。

yangchuanju · 发表于 2023-3-14 20:03

本帖最后由 yangchuanju 于 2023-3-14 20:06 编辑

（接上楼）
重生、愚公、那宝吉计算式精度对比：
在万以内，不进行对比；
除10^5-10^15间，那宝吉计算式稍大于1外，三人的计算值都比哥猜真实值小一些，
在10^5-10^15之间，总的来说，那宝吉的精度最高，愚公次之，重生最低；
重生在10^6-10^8时精度最高为0.992-0.993；愚公在10^8-10^10精度最高为0.999；那宝吉在10^5-10^12间精度最高为1.002-0.994；
当偶数超过10^12时，三人的计算式的精度都有所降低。
指数真实素数对重生/真实值愚公/真实值那宝吉/真实值哈李/真实值
1 2 1.127186 1.058192 0.866285 0.830095
2 6 0.939322 0.857983 0.851325 0.691746
3 28 0.849446 0.799702 0.853683 0.658806
4 127 1.011456 0.973538 1.032943 0.817023
5 810 0.980681 0.960798 1.001928 0.819847
6 5402 0.992987 0.985299 1.013070 0.853691
7 38807 0.992484 0.993413 1.011304 0.873075
8 291400 0.992986 0.999367 1.010549 0.890201
9 2274205 0.989620 0.998898 1.005679 0.901246
10 18200488 0.988493 0.998686 1.002851 0.912168
11 149091160 0.986215 0.995748 0.998641 0.920281
12 1243722370 0.983969 0.991624 0.994295 0.926983
13 10533150855 0.981866 0.986694 0.989973 0.932637
14 90350630388 0.979955 0.981219 0.985766 0.937498
15 783538341852 0.978208 0.975331 0.981680 0.941705

yangchuanju · 发表于 2023-3-14 20:31

本帖最后由 yangchuanju 于 2023-3-14 20:40 编辑

计算2的幂数之素数对，与10的幂数完全相同，唯波动系数由4/3改为1即可。
计算整数阶乘、素数阶乘的素数对，需逐个计算它们的波动系数，比较繁杂，
但最终结论回是一样的，愚公计算式、那宝吉计算式都不适合很大的偶数，重生计算式可适合较大的偶数，但不可能扩展至无穷。

要计算非常大偶数的素数对，还得用大傻公式，哈李公式。

大傻8888888 · 发表于 2023-3-14 21:11

yangchuanju 发表于 2023-3-14 20:00
（接上楼）
指数愚公t2 愚公计算值那宝吉DT 那宝吉计算值哈李计算值
1 1.274784 2.116383978 0.68894 ...

根据yangchuanju先生的数据，可以看出不论是愚公用连乘积计算或者那宝吉用类似哈李公式计算，用一个固定的纠正系数求偶数所有的素数对个数只能在一定的数值范围内精确度比较高，超过和小于这个范围精确度就不尽人意了。重生用不固定的纠正系数计算精度即使得到95%，也不过是重生/哈李=0.95，还是不如哈李公式，只要哈李公式的计算值与实际值之比大于某一个值，比如0.97，那么大于这个偶数直至无限大的偶数用哈李公式的计算值与实际值之比都会大于0.97，当然当用哈李公式的计算值与实际值之比大于0.999，那么大于这个偶数直至无限大的偶数用哈李公式的计算值与实际值之比都会大于0.999，并且随着数值不断增大计算值与实际值之比都会接近0.999........。这时就不需要用纠正系数来提高求偶数的素数对个数的精确度了。（有种说法是偶数无限大时哈李公式计算值接近真值，不如说偶数无限大时哈李公式计算值与实际值之比趋近1比较合理）

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