[原创]k生素数群的数量公式

独舟星海 · 发表于 2021-7-24 07:43

序126 5 6 7 8 9 （模9的余数类，9与余数0相当）
mod(n,9) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 85 -510 935 -85 340 850 1700
2→→→ 81 -483 882 -80 330 820 1635
3→→→ 72 -420 756 -68 312 760 1500
4→→→ 62 -342 592 -52 308 720 1390
5→→→ 55 -270 425 -35 340 750 1400
6→→→ 55 -225 290 -20 430 900 1625
7→→→ 62 -216 214 -10 560 1140 2020
8→→→ 72 -228 180 -4 696 1400 2460
9→→0同 81 -246 171 -1 804 1610 2820
一周汇总 625 -2940 4445 -355 4120 8950 16550

x+y+z+u=N 正整数解组数及a,b c,d 的值

独舟星海 · 发表于 2021-7-24 07:46

序126 5 6 7 8 9 （模9的余数类，9与余数0相当）
mod(n,9) 24at^4 24bt^3 24ct^2 24dt e 6周 7周 8周
1→→→ 355 -3410 11585 -16210 1920 3725 7625 15250
2→→→ 325 -2970 9695 -13170 1530 3600 7550 15100
3→→→ 306 -2576 7806 -9976 1110 3665 7935 15870
4→→→ 306 -2320 6270 -7160 726 3985 8895 17790
5→→→ 325 -2230 5255 -5030 420 4525 10325 20650
6→→→ 355 -2270 4745 -3670 210 5150 11900 23800
7→→→ 381 -2342 4539 -2938 90 5660 13145 26276
8→→→ 391 -2346 4361 -2526 30 5940 13785 27500
9→→0同 381 -2230 4035 -2210 6 6010 13845 27480
一周汇总 3125 -22694 58291 -62890 6042 42260 95005 189716
x+y+z+u+v=N 的正整数解组数，及系数 a,b,c,d,e 的值

独舟星海 · 发表于 2021-7-24 07:51

mod(n,9) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 13周 14周
1→→→ 1617 -20925 104145 -247275 276558 -5706 1610334 2557269
2→→→ 1617 -19500 89895 -197400 205308 -3996 1751409 2761044
3→→→ 1673 -18855 79825 -158145 146622 -2556 1942996 3045757
4→→→ 1758 -18780 73650 -130620 103512 -1476 2145066 3349632
5→→→ 1833 -18855 69825 -112545 74862 -756 2311716 3600597
6→→→ 1863 -18630 66325 -99870 57032 -336 2410001 3745742
7→→→ 1833 -17805 61425 -88395 45462 -126 2438766 3780777
8→→→ 1758 -16380 54450 -75420 36312 -36 2435466 3761472
9→→0同 1673 -14605 45825 -60395 27622 -6 2457246 3775057
一周汇总 15625 -164335 645365 -1170065 973290 -14994 19503000 30377347
x+y+z+u+v+w=N 的正整数解组数，及系数 a,b,c,d,e,f 的值
序126 5 6 7 8 9 （模9的余数类，9与余数0相当），所列余数类的值，变量可以取，未列出的其它余数类的不能取（模9的余数类）。

白新岭 · 发表于 2021-7-24 17:03

16(15)生素数等比 42952392923.85551 计算到1万以内（9973 0 60 300 1260 5100 20460 81900 327660 1310700 5242860 20971500 83886060 335544300 1342177260 5368709100 21474836460
16(15)生素数等比 0.998822119100593 1万以后到10亿之间 0 60 300 1260 5100 20460 81900 327660 1310700 5242860 20971500 83886060 335544300 1342177260 5368709100 21474836460
16(15)生素数等比 42901800120.646700 10亿右 0 60 300 1260 5100 20460 81900 327660 1310700 5242860 20971500 83886060 335544300 1342177260 5368709100 21474836460
这是蔡家雄先生提供的一种16生素数的素数差等比数列，a=60（首项），q=4（公比）。

白新岭 · 发表于 2021-7-24 17:10

白新岭发表于 2021-7-24 17:03
16(15)生素数等比 42952392923.85551 计算到1万以内（9973 0 60 300 1260 5100 20460 81900 327660 1310700 ...

10^n 16生素数a=60,q=4
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
12 1
13 2
14 6
15 20
16 69
17 247
18 949
19 3847
20 16394
21 73026
22 338477
23 1626240
24 8072518
25 41282584
26 216961441
27 1169264332
28 6449479591
29 36347905898
30 2.0898614782100000E+11
31 1.2241877455650000E+12
32 7.2969119099010000E+12
33 4.4208949807921000E+13
34 2.7197290076206300E+14
35 1.6974191541768400E+15
36 1.0738385663479600E+16
37 6.8808876640767100E+16
38 4.4627438953853500E+17
39 2.9277386732451200E+18
40 1.9416821197030800E+19
41 1.3010729213769600E+20
42 8.8040533976907400E+20
43 6.0133568665889600E+21
44 4.1439522176298000E+22
45 2.8800445303699900E+23
46 2.0179273291523100E+24
47 1.4248846301767300E+25
48 1.0136258154486800E+26
49 7.2621364558175700E+26
50 5.2385761155040600E+27
51 3.8036908255314600E+28
52 2.7792543365301300E+29
53 2.0430408223467800E+30
54 1.5106087996135800E+31
55 1.1232056800155200E+32
56 8.3967290376806100E+32
57 6.3098725167689100E+33
58 4.7655288474404100E+34
59 3.6166484732334700E+35
60 2.7576213336246400E+36
61 2.1121664861147600E+37
62 1.6248836025758500E+38
63 1.2553230404746600E+39
64 9.7379908176744200E+39
65 7.5841702304463600E+40
66 5.9295051720547100E+41
67 4.6531788205901300E+42
68 3.6648268981802400E+43
69 2.8965650807880200E+44
70 2.2971793530639600E+45
71 1.8278725002058700E+46
72 1.4591356370849300E+47
73 1.1684369606375300E+48
74 9.3850686426953100E+48
75 7.5606018959045900E+49
76 6.1084029599923800E+50
77 4.9490105225652000E+51
78 4.0206544862394700E+52
79 3.2751584730900900E+53
80 2.6748272731952500E+54
81 2.1900740431564800E+55
82 1.7976051523337600E+56
83 1.4790269155782800E+57
84 1.2197726228738400E+58
85 1.0082735710138900E+59
86 8.3531659633420000E+59
87 6.9354462230665400E+60
88 5.7706722398913700E+61
89 4.8115608761684300E+62
90 4.0200617853416500E+63
91 3.3654791754087400E+64
92 2.8229906884485000E+65
93 2.3724763210912200E+66
94 1.9975900726107800E+67
95 1.6850221353245100E+68
96 1.4239110569616500E+69
97 1.2053742481718100E+70
98 1.0221321143022600E+71
99 8.6820643793456800E+71
100 7.3867779040595900E+72
101 6.2948998252638200E+73
102 5.3729208722486300E+74
103 4.5931054066049100E+75
104 3.9324537662317700E+76
105 3.3718586652302500E+77
106 2.8954179689863200E+78
107 2.4898737454407200E+79
108 2.1441534973314200E+80
109 1.8489942451876800E+81
110 1.5966339210212900E+82
111 1.3805575539712600E+83
112 1.1952881427043800E+84
113 1.0362140414402600E+85
114 8.9944623627717500E+85
115 7.8170013417487200E+86
116 6.8019749016296700E+87
117 5.9258490785076100E+88
118 5.1686600276344300E+89
119 4.5134484811188200E+90
120 3.9457875274223300E+91
121 3.4533877068192200E+92
122 3.0257662645895600E+93
123 2.6539697267635500E+94
124 2.3303408616084500E+95
125 2.0483226440029000E+96
126 1.8022931139745700E+97
127 1.5874260670808100E+98
128 1.3995733750698100E+99
129 1.2351654444267500E+100
130 1.0911269055910100E+101
131 9.6480510924213100E+101
132 8.5390940632473300E+102
133 7.5645952026923400E+103
134 6.7074159528417200E+104
135 5.9527073355276100E+105
136 5.2875902476755600E+106
137 4.7008823032968900E+107
138 4.1828641717956800E+108
139 3.7250794710129000E+109
140 3.3201632014821100E+110
141 2.9616944861887900E+111
142 2.6440700328723900E+112
143 2.3623952843954400E+113
144 2.1123906841579100E+114
145 1.8903108722496900E+115
146 1.6928749558726400E+116
147 1.5172062743941600E+117
148 1.3607803134284600E+118
149 1.2213796204282700E+119
150 1.0970547421225100E+120
151 9.8609034653105300E+120
152 8.8697581322284400E+121
153 7.9837967830549400E+122
154 7.1912740815209100E+123
155 6.4818205044208800E+124
156 5.8462737470048100E+125
157 5.2765316883200800E+126
158 4.7654240457088100E+127
159 4.3066002448800000E+128
160 3.8944313721854600E+129
161 3.5239243674046600E+130
162 3.1906468656543000E+131
163 2.8906613120601500E+132
164 2.6204671577114900E+133
165 2.3769501045389900E+134
166 2.1573375038312400E+135
167 1.9591591312978200E+136
168 1.7802126635908000E+137
169 1.6185332693089100E+138
170 1.4723668036886600E+139
171 1.3401461621081500E+140
172 1.2204704046228300E+141
173 1.1120863132433800E+142
174 1.0138720866020700E+143
175 9.2482291393513900E+143
176 8.4403820270656200E+144
177 7.7071026237539000E+145
178 7.0411427133479200E+146
179 6.4359937541573700E+147
180 5.8858078497431100E+148
181 5.3853275383259700E+149
182 4.9298233753272400E+150
183 4.5150384076296500E+151
184 4.1371387465777700E+152
185 3.7926695416278200E+153
186 3.4785157396608500E+154
187 3.1918670878075600E+155
188 2.9301869015126800E+156
189 2.6911841756326200E+157
190 2.4727886656029400E+158
191 2.2731286089924500E+159
192 2.0905107958262300E+160
193 1.9234027295630000E+161
194 1.7704166501180700E+162
195 1.6302952163277600E+163
196 1.5018986681837800E+164
197 1.3841933094037200E+165
198 1.2762411687745000E+166
199 1.1771907144960300E+167
200 1.0862685097142800E+168
201 1.0027717097847500E+169
202 9.2606131274289400E+169
203 8.5555608414409800E+170
204 7.9072708602217900E+171
205 7.3109274732960200E+172
206 6.7621441998045500E+173
207 6.2569237061743900E+174
208 5.7916216355533100E+175
209 5.3629139509272600E+176
210 4.9677674359947600E+177
211 4.6034130353922600E+178
212 4.2673217492755600E+179
213 3.9571828270321700E+180
214 3.6708840314389000E+181
215 3.4064937682521200E+182
216 3.1622448973449800E+183
217 2.9365200603719500E+184
218 2.7278383767955200E+185
219 2.5348433751766600E+186
220 2.3562920401055300E+187
221 2.1910448672064900E+188
222 2.0380568294464900E+189
223 1.8963691676454900E+190
224 1.7651019267529300E+191
225 1.6434471672246600E+192
226 1.5306627878045500E+193
227 1.4260669022710000E+194
228 1.3290327183263400E+195
229 1.2389838718532000E+196
230 1.1553901742986300E+197
231 1.0777637350250500E+198
232 1.0056554241372300E+199
233 9.3865164459714400E+199
234 8.7637138541310500E+200
235 8.1846353036876600E+201
236 7.6460439917306800E+202
237 7.1449550008957100E+203
238 6.6786147506832600E+204
239 6.2444822017642900E+205
240 5.8402116572419900E+206
241 5.4636370193006400E+207
242 5.1127573727390000E+208
243 4.7857237787008200E+209
244 4.4808271725994300E+210
245 4.1964872699022900E+211
246 3.9312423921925700E+212
247 3.6837401338510100E+213
248 3.4527287968803800E+214
249 3.2370495279030500E+215
250 3.0356290972616400E+216
251 2.8474732655045700E+217
252 2.6716606873941700E+218
253 2.5073373079834000E+219
254 2.3537112093095600E+220
255 2.2100478698907900E+221
256 2.0756658025151900E+222
上楼提到的k生素数的理论值。

白新岭 · 发表于 2021-7-24 20:02

序125 4 6 7 8 9
mod(n,9) 120at^5 120bt^4 120ct^3 120dt^2 120et 6f 10周 11周
1→→→ 1713 -20805 97125 -216795 229482 -4536 340830 639576
2→→→ 1713 -19680 86175 -179220 176532 -3276 370440 688626
3→→→ 1713 -18635 76305 -146125 130662 -2196 399210 735996
4→→→ 1737 -17880 68295 -119100 93588 -1332 434952 795474
5→→→ 1746 -17160 61710 -98400 66504 -720 462672 840852
6→→→ 1763 -16450 55765 -81950 47592 -336 498660 899271
7→→→ 1758 -15630 50250 -68970 35112 -126 526680 943416
8→→→ 1749 -14610 44175 -56850 26256 -36 562932 999828
9→→0同 1733 -13495 37785 -44945 19042 -6 598590 1054866
一周汇总 15625 -154345 577585 -1012355 824770 -12564 4194966 7597905
x+y+z+u+v+w=N 的正整数解组数，及系数 a,b,c,d,e,f 的值

白新岭 · 发表于 2021-7-24 20:03

mod(n,9) 24at^4 24bt^3 24ct^2 24dt e 6周 7周 8周
1→→→ 350 -3120 9970 -13320 1530 3975 8425 16850
2→→→ 346 -2892 8714 -11088 1230 4185 9070 18126
3→→→ 336 -2636 7416 -8836 930 4265 9435 18870
4→→→ 336 -2420 6180 -6640 636 4610 10345 20620
5→→→ 340 -2280 5240 -4860 390 4875 11100 22130
6→→→ 345 -2150 4455 -3490 210 5300 12075 23940
7→→→ 355 -2090 3965 -2590 90 5750 13075 25800
8→→→ 356 -1996 3556 -2036 30 6115 13785 27010
9→→0同 361 -1890 3155 -1650 6 6810 15070 29160
一周汇总 3125 -21474 52651 -54510 5052 45885 102380 202506
x+y+z+u+v=N 的正整数解组数，及系数 a,b,c,d,e 的值
序125 4 6 7 8 9

白新岭 · 发表于 2021-7-24 20:31

mod(n,9) 6at^3 6bt^2 6ct d 5周 6周 7周
1→→→ 75 -438 789 -71 324 790 1560
2→→→ 74 -414 724 -64 356 840 1630
3→→→ 72 -384 648 -56 384 880 1680
4→→→ 66 -330 528 -44 396 880 1650
5→→→ 67 -294 413 -31 484 1030 1880
6→→→ 63 -249 306 -20 510 1060 1905
7→→→ 67 -228 221 -10 620 1255 2216
8→→→ 68 -216 172 -4 656 1320 2320
9→→0同 73 -210 143 -1 764 1510 2624
一周汇总 625 -2763 3944 -301 4494 9565 17465

x+y+z+u=N 正整数解组数及a,b c,d 的值
一个比较有规律的现象，系数从高位正负交叉出现（一周内的累计和）

白新岭 · 发表于 2021-7-24 22:47

截止2021年7月23日星期五六月十四22：07分，浏览量43622人次，回复3205，热度119°
截止2021年7月24日星期六六月十五22：45分，浏览量43934人次，回复3216，热度119°
浏览量 ↑ 312人次，回复 ↑ 11，热度→0。
今天，心里默念，应是312，还真是312.312的确是一个特殊数字。

独舟星海 · 发表于 2021-7-25 06:45

mod(n,9) 2at^2 2bt c 10周 11周 12周 13周 14周
1→→→ 15 -45 15 540 675 825 990 1170
2→→→ 15 -45 15 540 675 825 990 1170
3→→→ 17 -49 16 621 775 946 1134 1339
4→→→ 15 -45 15 540 675 825 990 1170
5→→→ 15 -39 12 567 705 858 1026 1209
6→→→ 13 -33 10 495 615 748 894 1053
7→→→ 12 -24 6 486 600 726 864 1014
8→→→ 12 -18 3 513 630 759 900 1053
9→→0同 11 -13 1 486 595 715 846 988
一周汇总 125 -311 93 4788 5945 7227 8634 10166

x+y+z=N 正整数解组数及系数 a,b,c 的值
序125 4 6 7 8 9

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