[原创]k生素数群的数量公式

白新岭 · 发表于 2025-7-4 11:03

区间范围总量分量应合成量占比
1 19399380 145313 145313 184756 78.651302%
2 38798760 218614 73301 184756 39.674490%
3 58198140 270835 52221 184756 28.264847%
4 77597520 308179 37344 184756 20.212605%
5 96996900 336543 28364 184756 15.352140%
6 116396280 359400 22857 184756 12.371452%
7 135795660 378493 19093 184756 10.334170%
8 155195040 394280 15787 184756 8.544783%
9 174594420 407135 12855 184756 6.957825%
10 193993800 417633 10498 184756 5.682089%
11 213393180 426724 9091 184756 4.920544%
12 232792560 434623 7899 184756 4.275369%
13 252191940 441659 7036 184756 3.808266%
14 271591320 448045 6386 184756 3.456451%
15 290990700 453703 5658 184756 3.062417%
16 310390080 458896 5193 184756 2.810734%
17 329789460 463133 4237 184756 2.293295%
18 349188840 467267 4134 184756 2.237546%
19 368588220 471133 3866 184756 2.092490%
20 387987600 474560 3427 184756 1.854879%
21 407386980 477530 2970 184756 1.607526%
22 426786360 480235 2705 184756 1.464093%
23 446185740 482682 2447 184756 1.324450%
24 465585120 484797 2115 184756 1.144753%
25 484984500 486791 1994 184756 1.079261%
26 504383880 488614 1823 184756 0.986707%
27 523783260 490275 1661 184756 0.899024%
28 543182640 491883 1608 184756 0.870337%
29 562582020 493407 1524 184756 0.824872%
30 581981400 494756 1349 184756 0.730152%
31 601380780 495970 1214 184756 0.657083%
32 620780160 497127 1157 184756 0.626231%
33 640179540 498175 1048 184756 0.567235%
34 659578920 499160 985 184756 0.533136%
35 678978300 500096 936 184756 0.506614%
36 698377680 500947 851 184756 0.460608%
37 717777060 501738 791 184756 0.428132%
38 737176440 502478 740 184756 0.400528%
39 756575820 503144 666 184756 0.360475%
40 775975200 503722 578 184756 0.312845%
41 795374580 504252 530 184756 0.286865%
42 814773960 504739 487 184756 0.263591%
43 834173340 505216 477 184756 0.258178%
44 853572720 505664 448 184756 0.242482%
45 872972100 506108 444 184756 0.240317%
46 892371480 506500 392 184756 0.212172%
47 911770860 506864 364 184756 0.197017%
48 931170240 507203 339 184756 0.183485%
49 950569620 507533 330 184756 0.178614%
50 969969000 507856 323 184756 0.174825%
51 989368380 508114 258 184756 0.139644%
52 1008767760 508410 296 184756 0.160211%
53 1028167140 508661 251 184756 0.135855%
54 1047566520 508907 246 184756 0.133149%
55 1066965900 509145 238 184756 0.128819%
56 1086365280 509346 201 184756 0.108792%
57 1105764660 509561 215 184756 0.116370%
58 1125164040 509733 172 184756 0.093096%
59 1144563420 509897 164 184756 0.088766%
60 1163962800 510061 164 184756 0.088766%
61 1183362180 510199 138 184756 0.074693%
62 1202761560 510366 167 184756 0.090389%
63 1222160940 510501 135 184756 0.073069%
64 1241560320 510649 148 184756 0.080106%
65 1260959700 510773 124 184756 0.067116%
66 1280359080 510887 114 184756 0.061703%
67 1299758460 511024 137 184756 0.074152%
68 1319157840 511140 116 184756 0.062786%
69 1338557220 511250 110 184756 0.059538%
这是最密4生素数中项和合成中没有解的数（特例）统计表，以素数19的素数阶乘2为区间段跨度划分，并进行统计，从结果看，它下降的速度及幅度都很快

白新岭 · 发表于 2025-7-4 11:28

区间范围总量分量应合成量占比
70 1357956600 102 102 184756 0.055208%
71 1377355980 191 89 184756 0.048172%
72 1396755360 282 91 184756 0.049254%
73 1416154740 349 67 184756 0.036264%
74 1435554120 410 61 184756 0.033017%
75 1454953500 465 55 184756 0.029769%
76 1474352880 532 67 184756 0.036264%
77 1493752260 600 68 184756 0.036805%
78 1513151640 664 64 184756 0.034640%
79 1532551020 734 70 184756 0.037888%
80 1551950400 786 52 184756 0.028145%
81 1571349780 842 56 184756 0.030310%
82 1590749160 904 62 184756 0.033558%
83 1610148540 952 48 184756 0.025980%
84 1629547920 995 43 184756 0.023274%
85 1648947300 1037 42 184756 0.022733%
86 1668346680 1094 57 184756 0.030852%
87 1687746060 1136 42 184756 0.022733%
88 1707145440 1179 43 184756 0.023274%
89 1726544820 1219 40 184756 0.021650%
90 1745944200 1251 32 184756 0.017320%
91 1765343580 1283 32 184756 0.017320%
92 1784742960 1320 37 184756 0.020026%
93 1804142340 1353 33 184756 0.017861%
94 1823541720 1392 39 184756 0.021109%
95 1842941100 1426 34 184756 0.018403%
96 1862340480 1454 28 184756 0.015155%
97 1881739860 1479 25 184756 0.013531%
98 1901139240 1503 24 184756 0.012990%
99 1920538620 1527 24 184756 0.012990%
100 1939938000 1544 17 184756 0.009201%
101 1959337380 1577 33 184756 0.017861%
102 1978736760 1590 13 184756 0.007036%
103 1998136140 1612 22 184756 0.011908%
104 2017535520 1633 21 184756 0.011366%
105 2036934900 1646 13 184756 0.007036%
106 2056334280 1669 23 184756 0.012449%
107 2075733660 1689 20 184756 0.010825%
108 2095133040 1700 11 184756 0.005954%
109 2114532420 1717 17 184756 0.009201%
110 2133931800 1734 17 184756 0.009201%
111 2153331180 1748 14 184756 0.007578%
112 2172730560 1766 18 184756 0.009743%
113 2192129940 1778 12 184756 0.006495%
114 2211529320 1796 18 184756 0.009743%
115 2230928700 1813 17 184756 0.009201%
到达素数23阶乘的10倍范围时（2倍的素数19阶乘区间段），特例不足万分之一，即1万个被合成数中不到1个特例，从发展趋势看，很快就会断链，不再出现特例。

白新岭 · 发表于 2025-7-4 11:38

区间范围总量分量应合成量占比
116 2250328080 15 15 184756 0.008119%
117 2269727460 29 14 184756 0.007578%
118 2289126840 42 13 184756 0.007036%
119 2308526220 49 7 184756 0.003789%
120 2327925600 55 6 184756 0.003248%
121 2347324980 70 15 184756 0.008119%
122 2366724360 77 7 184756 0.003789%
123 2386123740 85 8 184756 0.004330%
124 2405523120 97 12 184756 0.006495%
125 2424922500 106 9 184756 0.004871%
126 2444321880 112 6 184756 0.003248%
127 2463721260 120 8 184756 0.004330%
128 2483120640 127 7 184756 0.003789%
129 2502520020 135 8 184756 0.004330%
130 2521919400 143 8 184756 0.004330%
131 2541318780 150 7 184756 0.003789%
132 2560718160 155 5 184756 0.002706%
133 2580117540 159 4 184756 0.002165%
134 2599516920 165 6 184756 0.003248%
135 2618916300 173 8 184756 0.004330%
136 2638315680 177 4 184756 0.002165%
137 2657715060 182 5 184756 0.002706%
138 2677114440 188 6 184756 0.003248%
139 2696513820 193 5 184756 0.002706%
140 2715913200 199 6 184756 0.003248%
141 2735312580 204 5 184756 0.002706%
142 2754711960 207 3 184756 0.001624%
143 2774111340 213 6 184756 0.003248%
144 2793510720 218 5 184756 0.002706%
145 2812910100 221 3 184756 0.001624%
146 2832309480 223 2 184756 0.001083%
147 2851708860 229 6 184756 0.003248%
148 2871108240 231 2 184756 0.001083%
149 2890507620 233 2 184756 0.001083%
150 2909907000 237 4 184756 0.002165%
151 2929306380 242 5 184756 0.002706%
152 2948705760 244 2 184756 0.001083%
153 2968105140 246 2 184756 0.001083%
154 2987504520 246 0 184756 0.000000%
155 3006903900 248 2 184756 0.001083%
156 3026303280 249 1 184756 0.000541%
157 3045702660 252 3 184756 0.001624%
158 3065102040 254 2 184756 0.001083%
159 3084501420 256 2 184756 0.001083%
160 3103900800 257 1 184756 0.000541%
161 3123300180 259 2 184756 0.001083%
个别区间段，已经形成断层，1个特例也未出现

白新岭 · 发表于 2025-7-4 17:29

区间范围总量分量应合成量占比
162 3142699560 1 1 184756 0.000541%
163 3162098940 3 2 184756 0.001083%
164 3181498320 3 0 184756 0.000000%
165 3200897700 7 4 184756 0.002165%
166 3220297080 8 1 184756 0.000541%
167 3239696460 9 1 184756 0.000541%
168 3259095840 13 4 184756 0.002165%
169 3278495220 14 1 184756 0.000541%
170 3297894600 15 1 184756 0.000541%
171 3317293980 18 3 184756 0.001624%
172 3336693360 18 0 184756 0.000000%
173 3356092740 19 1 184756 0.000541%
174 3375492120 21 2 184756 0.001083%
175 3394891500 22 1 184756 0.000541%
176 3414290880 23 1 184756 0.000541%
177 3433690260 23 0 184756 0.000000%
178 3453089640 23 0 184756 0.000000%
179 3472489020 24 1 184756 0.000541%
180 3491888400 25 1 184756 0.000541%
181 3511287780 27 2 184756 0.001083%
182 3530687160 29 2 184756 0.001083%
183 3550086540 32 3 184756 0.001624%
184 3569485920 33 1 184756 0.000541%
185 3588885300 34 1 184756 0.000541%
186 3608284680 35 1 184756 0.000541%
187 3627684060 35 0 184756 0.000000%
188 3647083440 36 1 184756 0.000541%
189 3666482820 36 0 184756 0.000000%
190 3685882200 38 2 184756 0.001083%
191 3705281580 39 1 184756 0.000541%
192 3724680960 40 1 184756 0.000541%
193 3744080340 40 0 184756 0.000000%
194 3763479720 41 1 184756 0.000541%
195 3782879100 41 0 184756 0.000000%
196 3802278480 43 2 184756 0.001083%
197 3821677860 44 1 184756 0.000541%
198 3841077240 44 0 184756 0.000000%
199 3860476620 44 0 184756 0.000000%
200 3879876000 44 0 184756 0.000000%
201 3899275380 44 0 184756 0.000000%
202 3918674760 44 0 184756 0.000000%
203 3938074140 44 0 184756 0.000000%
204 3957473520 46 2 184756 0.001083%
205 3976872900 46 0 184756 0.000000%
206 3996272280 46 0 184756 0.000000%
207 4015671660 47 1 184756 0.000541%
在分段区间内，少的无，多的最多4个特例，已经有16个区间段没有特例了，占总分段46的34.782%，超过了1/3.

白新岭 · 发表于 2025-7-4 17:39

区间范围总量分量应合成量占比
208 4035071040 0 0 184756 0.000000%
209 4054470420 2 2 184756 0.001083%
210 4073869800 3 1 184756 0.000541%
211 4093269180 6 3 184756 0.001624%
212 4112668560 7 1 184756 0.000541%
213 4132067940 7 0 184756 0.000000%
214 4151467320 7 0 184756 0.000000%
215 4170866700 7 0 184756 0.000000%
216 4190266080 7 0 184756 0.000000%
217 4209665460 7 0 184756 0.000000%
218 4229064840 8 1 184756 0.000541%
219 4248464220 8 0 184756 0.000000%
220 4267863600 8 0 184756 0.000000%
221 4287262980 8 0 184756 0.000000%
222 4306662360 8 0 184756 0.000000%
223 4326061740 8 0 184756 0.000000%
224 4345461120 8 0 184756 0.000000%
225 4364860500 8 0 184756 0.000000%
226 4384259880 9 1 184756 0.000541%
227 4403659260 10 1 184756 0.000541%
228 4423058640 10 0 184756 0.000000%
229 4442458020 10 0 184756 0.000000%
230 4461857400 10 0 184756 0.000000%
231 4481256780 11 1 184756 0.000541%
232 4500656160 11 0 184756 0.000000%
233 4520055540 11 0 184756 0.000000%
234 4539454920 11 0 184756 0.000000%
235 4558854300 11 0 184756 0.000000%
236 4578253680 11 0 184756 0.000000%
237 4597653060 11 0 184756 0.000000%
238 4617052440 11 0 184756 0.000000%
239 4636451820 11 0 184756 0.000000%
240 4655851200 11 0 184756 0.000000%
241 4675250580 11 0 184756 0.000000%
242 4694649960 11 0 184756 0.000000%
243 4714049340 11 0 184756 0.000000%
244 4733448720 11 0 184756 0.000000%
245 4752848100 11 0 184756 0.000000%
246 4772247480 11 0 184756 0.000000%
247 4791646860 11 0 184756 0.000000%
248 4811046240 12 1 184756 0.000541%
249 4830445620 12 0 184756 0.000000%
250 4849845000 12 0 184756 0.000000%
251 4869244380 12 0 184756 0.000000%
252 4888643760 13 1 184756 0.000541%
253 4908043140 13 0 184756 0.000000%
到这个范围，绝大分区间段已经没有特例了，46个分区，36个分区无，只剩下10个分区还有特例。

白新岭 · 发表于 2025-7-4 17:46

区间范围总量分量应合成量占比
254 4927442520 0 0 184756 0.000000%
255 4946841900 0 0 184756 0.000000%
256 4966241280 0 0 184756 0.000000%
257 4985640660 1 1 184756 0.000541%
258 5005040040 1 0 184756 0.000000%
259 5024439420 1 0 184756 0.000000%
260 5043838800 1 0 184756 0.000000%
261 5063238180 1 0 184756 0.000000%
262 5082637560 1 0 184756 0.000000%
263 5102036940 1 0 184756 0.000000%
264 5121436320 1 0 184756 0.000000%
265 5140835700 1 0 184756 0.000000%
266 5160235080 1 0 184756 0.000000%
267 5179634460 2 1 184756 0.000541%
268 5199033840 2 0 184756 0.000000%
269 5218433220 2 0 184756 0.000000%
270 5237832600 2 0 184756 0.000000%
271 5257231980 2 0 184756 0.000000%
272 5276631360 2 0 184756 0.000000%
273 5296030740 2 0 184756 0.000000%
274 5315430120 2 0 184756 0.000000%
275 5334829500 2 0 184756 0.000000%
276 5354228880 2 0 184756 0.000000%
277 5373628260 3 1 184756 0.000541%
278 5393027640 3 0 184756 0.000000%
279 5412427020 3 0 184756 0.000000%
280 5431826400 3 0 184756 0.000000%
281 5451225780 3 0 184756 0.000000%
282 5470625160 3 0 184756 0.000000%
283 5490024540 3 0 184756 0.000000%
284 5509423920 5 2 184756 0.001083%
285 5528823300 6 1 184756 0.000541%
286 5548222680 7 1 184756 0.000541%
287 5567622060 7 0 184756 0.000000%
288 5587021440 7 0 184756 0.000000%
289 5606420820 8 1 184756 0.000541%
290 5625820200 9 1 184756 0.000541%
291 5645219580 9 0 184756 0.000000%
292 5664618960 9 0 184756 0.000000%
293 5684018340 9 0 184756 0.000000%
294 5703417720 9 0 184756 0.000000%
295 5722817100 9 0 184756 0.000000%
296 5742216480 9 0 184756 0.000000%
297 5761615860 9 0 184756 0.000000%
298 5781015240 9 0 184756 0.000000%
299 5800414620 9 0 184756 0.000000%

白新岭 · 发表于 2025-7-4 17:59

区间范围总量分量应合成量占比
300 5819814000 0 0 184756 0.000000%
301 5839213380 0 0 184756 0.000000%
302 5858612760 0 0 184756 0.000000%
303 5878012140 0 0 184756 0.000000%
304 5897411520 0 0 184756 0.000000%
305 5916810900 0 0 184756 0.000000%
306 5936210280 0 0 184756 0.000000%
307 5955609660 1 1 184756 0.000541%
308 5975009040 1 0 184756 0.000000%
309 5994408420 2 1 184756 0.000541%
310 6013807800 2 0 184756 0.000000%
311 6033207180 2 0 184756 0.000000%
312 6052606560 2 0 184756 0.000000%
313 6072005940 2 0 184756 0.000000%
314 6091405320 2 0 184756 0.000000%
315 6110804700 2 0 184756 0.000000%
316 6130204080 2 0 184756 0.000000%
317 6149603460 3 1 184756 0.000541%
318 6169002840 3 0 184756 0.000000%
319 6188402220 3 0 184756 0.000000%
320 6207801600 3 0 184756 0.000000%
321 6227200980 3 0 184756 0.000000%
322 6246600360 3 0 184756 0.000000%
323 6265999740 3 0 184756 0.000000%
324 6285399120 3 0 184756 0.000000%
325 6304798500 4 1 184756 0.000541%
326 6324197880 4 0 184756 0.000000%
327 6343597260 4 0 184756 0.000000%
328 6362996640 4 0 184756 0.000000%
329 6382396020 4 0 184756 0.000000%
330 6401795400 4 0 184756 0.000000%
331 6421194780 4 0 184756 0.000000%
332 6440594160 4 0 184756 0.000000%
333 6459993540 4 0 184756 0.000000%
334 6479392920 4 0 184756 0.000000%
335 6498792300 4 0 184756 0.000000%
336 6518191680 4 0 184756 0.000000%
337 6537591060 4 0 184756 0.000000%
338 6556990440 4 0 184756 0.000000%
339 6576389820 4 0 184756 0.000000%
340 6595789200 4 0 184756 0.000000%
341 6615188580 4 0 184756 0.000000%
342 6634587960 4 0 184756 0.000000%
343 6653987340 4 0 184756 0.000000%
344 6673386720 4 0 184756 0.000000%
345 6692786100 4 0 184756 0.000000%

区间范围总量分量应合成量占比
307 5955609660 1 1 184756 0.000541%
309 5994408420 2 1 184756 0.000541%
317 6149603460 3 1 184756 0.000541%
325 6304798500 4 1 184756 0.000541%

在46个分区中，还有4个分区各有1个特例，其余42个分区已经没有特例了

白新岭 · 发表于 2025-7-4 18:12

区间范围总量分量应合成量占比
346 6712185480 0 0 184756 0.000000%
347 6731584860 0 0 184756 0.000000%
348 6750984240 0 0 184756 0.000000%
349 6770383620 0 0 184756 0.000000%
350 6789783000 0 0 184756 0.000000%
351 6809182380 0 0 184756 0.000000%
352 6828581760 0 0 184756 0.000000%
353 6847981140 0 0 184756 0.000000%
354 6867380520 0 0 184756 0.000000%
355 6886779900 0 0 184756 0.000000%
356 6906179280 0 0 184756 0.000000%
357 6925578660 0 0 184756 0.000000%
358 6944978040 0 0 184756 0.000000%
359 6964377420 0 0 184756 0.000000%
360 6983776800 0 0 184756 0.000000%
361 7003176180 0 0 184756 0.000000%
362 7022575560 0 0 184756 0.000000%
363 7041974940 0 0 184756 0.000000%
364 7061374320 1 1 184756 0.000541%
365 7080773700 1 0 184756 0.000000%
366 7100173080 1 0 184756 0.000000%
367 7119572460 1 0 184756 0.000000%
368 7138971840 1 0 184756 0.000000%
369 7158371220 1 0 184756 0.000000%
370 7177770600 1 0 184756 0.000000%
371 7197169980 1 0 184756 0.000000%
372 7216569360 1 0 184756 0.000000%
373 7235968740 1 0 184756 0.000000%
374 7255368120 1 0 184756 0.000000%
375 7274767500 1 0 184756 0.000000%
376 7294166880 1 0 184756 0.000000%
377 7313566260 1 0 184756 0.000000%
378 7332965640 1 0 184756 0.000000%
379 7352365020 1 0 184756 0.000000%
380 7371764400 1 0 184756 0.000000%
381 7391163780 1 0 184756 0.000000%
382 7410563160 1 0 184756 0.000000%
383 7429962540 1 0 184756 0.000000%
384 7449361920 1 0 184756 0.000000%
385 7468761300 1 0 184756 0.000000%
386 7488160680 1 0 184756 0.000000%
387 7507560060 1 0 184756 0.000000%
388 7526959440 1 0 184756 0.000000%
389 7546358820 1 0 184756 0.000000%
390 7565758200 1 0 184756 0.000000%
391 7585157580 1 0 184756 0.000000%
从此以后再无特例

白新岭 · 发表于 2025-7-4 18:21

区间范围总量累分量
154 2987504520 513309 0
164 3181498320 513325 0
172 3336693360 513340 0
177 3433690260 513345 0
178 3453089640 513345 0
187 3627684060 513357 0
189 3666482820 513358 0
193 3744080340 513362 0
195 3782879100 513363 0
198 3841077240 513366 0
199 3860476620 513366 0
200 3879876000 513366 0
201 3899275380 513366 0
202 3918674760 513366 0
203 3938074140 513366 0
205 3976872900 513368 0
206 3996272280 513368 0
208 4035071040 513369 0
213 4132067940 513376 0
214 4151467320 513376 0
215 4170866700 513376 0
216 4190266080 513376 0
217 4209665460 513376 0
219 4248464220 513377 0
220 4267863600 513377 0
221 4287262980 513377 0
222 4306662360 513377 0
223 4326061740 513377 0
224 4345461120 513377 0
225 4364860500 513377 0
228 4423058640 513379 0
229 4442458020 513379 0
230 4461857400 513379 0
232 4500656160 513380 0
233 4520055540 513380 0
234 4539454920 513380 0
235 4558854300 513380 0
236 4578253680 513380 0
237 4597653060 513380 0
238 4617052440 513380 0
239 4636451820 513380 0
240 4655851200 513380 0
241 4675250580 513380 0
242 4694649960 513380 0
243 4714049340 513380 0
244 4733448720 513380 0
245 4752848100 513380 0
246 4772247480 513380 0
247 4791646860 513380 0
249 4830445620 513381 0
250 4849845000 513381 0
251 4869244380 513381 0
253 4908043140 513382 0
254 4927442520 513382 0
255 4946841900 513382 0
256 4966241280 513382 0
258 5005040040 513383 0
259 5024439420 513383 0
260 5043838800 513383 0
261 5063238180 513383 0
262 5082637560 513383 0
263 5102036940 513383 0
264 5121436320 513383 0
265 5140835700 513383 0
266 5160235080 513383 0
268 5199033840 513384 0
269 5218433220 513384 0
270 5237832600 513384 0
271 5257231980 513384 0
272 5276631360 513384 0
273 5296030740 513384 0
274 5315430120 513384 0
275 5334829500 513384 0
276 5354228880 513384 0
278 5393027640 513385 0
279 5412427020 513385 0
280 5431826400 513385 0
281 5451225780 513385 0
282 5470625160 513385 0
283 5490024540 513385 0
287 5567622060 513389 0
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分区内无特例的区段编码

白新岭 · 发表于 2025-7-4 18:23

截止到2025年7月4日最密4生素数中项和合成，其中特例共计513396个。

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