一眼千年，2^8191附近的素数分布

时空伴随者

给出2^8191附近100万以内的素数分布，这些素数两两的和能覆盖多少个连续偶数呢？

时空伴随者

2025-09-11 10:00:07
2^8191-999285 is prime
2^8191-998709 is prime
2^8191-991731 is prime
2^8191-990399 is prime
2^8191-989091 is prime
2^8191-985501 is prime
2^8191-967245 is prime
2^8191-962541 is prime
2^8191-960649 is prime
2^8191-934861 is prime
2^8191-934627 is prime
2^8191-925477 is prime
2^8191-922317 is prime
2^8191-920101 is prime
2^8191-912427 is prime
2^8191-907165 is prime
2^8191-899851 is prime
2^8191-880435 is prime
2^8191-876105 is prime
2^8191-866335 is prime
2^8191-864531 is prime
2^8191-864279 is prime
2^8191-858729 is prime
2^8191-852985 is prime
2^8191-847347 is prime
2^8191-846867 is prime
2^8191-842287 is prime
2^8191-827985 is prime
2^8191-816061 is prime
2^8191-813117 is prime
2^8191-810709 is prime
2^8191-804879 is prime
2^8191-797709 is prime
2^8191-796519 is prime
2^8191-796069 is prime
2^8191-792259 is prime
2^8191-783459 is prime
2^8191-779689 is prime
2^8191-776487 is prime
2^8191-771217 is prime
2^8191-771165 is prime
2^8191-763119 is prime
2^8191-735879 is prime
2^8191-733519 is prime
2^8191-723535 is prime
2^8191-709231 is prime
2^8191-701187 is prime
2^8191-696451 is prime
2^8191-695595 is prime
2^8191-692151 is prime
2^8191-675235 is prime
2^8191-674415 is prime
2^8191-665281 is prime
2^8191-662535 is prime
2^8191-657777 is prime
2^8191-657709 is prime
2^8191-656769 is prime
2^8191-654165 is prime
2^8191-654027 is prime
2^8191-646119 is prime
2^8191-643957 is prime
2^8191-630157 is prime
2^8191-629397 is prime
2^8191-617895 is prime
2^8191-617191 is prime
2^8191-613081 is prime
2^8191-600685 is prime
2^8191-583135 is prime
2^8191-582909 is prime
2^8191-576591 is prime
2^8191-552777 is prime
2^8191-549321 is prime
2^8191-546697 is prime
2^8191-538327 is prime
2^8191-534469 is prime
2^8191-522451 is prime
2^8191-521947 is prime
2^8191-512511 is prime
2^8191-512035 is prime
2^8191-509899 is prime
2^8191-500959 is prime
2^8191-494247 is prime
2^8191-481059 is prime
2^8191-463125 is prime
2^8191-461697 is prime
2^8191-453327 is prime
2^8191-452401 is prime
2^8191-449155 is prime
2^8191-447811 is prime
2^8191-441561 is prime
2^8191-436351 is prime
2^8191-436341 is prime
2^8191-435061 is prime
2^8191-424077 is prime
2^8191-421747 is prime
2^8191-412539 is prime
2^8191-411949 is prime
2^8191-402819 is prime
2^8191-402499 is prime
2^8191-396477 is prime
2^8191-388405 is prime
2^8191-385137 is prime
2^8191-382957 is prime
2^8191-379737 is prime
2^8191-376591 is prime
2^8191-376141 is prime
2^8191-374347 is prime
2^8191-358687 is prime
2^8191-356059 is prime
2^8191-354571 is prime
2^8191-353811 is prime
2^8191-352315 is prime
2^8191-348705 is prime
2^8191-347677 is prime
2^8191-333025 is prime
2^8191-332469 is prime
2^8191-332335 is prime
2^8191-327237 is prime
2^8191-325935 is prime
2^8191-315777 is prime
2^8191-315715 is prime
2^8191-307681 is prime
2^8191-303159 is prime
2^8191-303099 is prime
2^8191-302379 is prime
2^8191-301431 is prime

时空伴随者

2^8191-290071 is prime
2^8191-283029 is prime
2^8191-271215 is prime
2^8191-270537 is prime
2^8191-255109 is prime
2^8191-253267 is prime
2^8191-244615 is prime
2^8191-242637 is prime
2^8191-230805 is prime
2^8191-230775 is prime
2^8191-204237 is prime
2^8191-203881 is prime
2^8191-195649 is prime
2^8191-191821 is prime
2^8191-191299 is prime
2^8191-188605 is prime
2^8191-182299 is prime
2^8191-181411 is prime
2^8191-180247 is prime
2^8191-179409 is prime
2^8191-175557 is prime
2^8191-174217 is prime
2^8191-161329 is prime
2^8191-160527 is prime
2^8191-131097 is prime
2^8191-129847 is prime
2^8191-128475 is prime
2^8191-105265 is prime
2^8191-101871 is prime
2^8191-88269 is prime
2^8191-83881 is prime
2^8191-80779 is prime
2^8191-80157 is prime
2^8191-76125 is prime
2^8191-73927 is prime
2^8191-65637 is prime
2^8191-63745 is prime
2^8191-57921 is prime
2^8191-54699 is prime
2^8191-52599 is prime
2^8191-33807 is prime
2^8191-25099 is prime
2^8191-12501 is prime
2^8191-4627 is prime
2^8191-3795 is prime
2^8191-1551 is prime
2^8191+1911 is prime
2^8191+9225 is prime
2^8191+18609 is prime
2^8191+26985 is prime
2^8191+27623 is prime
2^8191+29751 is prime
2^8191+35399 is prime
2^8191+36635 is prime
2^8191+41351 is prime
2^8191+42875 is prime
2^8191+47819 is prime
2^8191+49185 is prime
2^8191+51801 is prime
2^8191+62573 is prime
2^8191+66569 is prime
2^8191+79905 is prime
2^8191+83069 is prime
2^8191+83663 is prime
2^8191+87621 is prime
2^8191+104343 is prime
2^8191+107543 is prime
2^8191+112073 is prime
2^8191+113445 is prime
2^8191+116649 is prime
2^8191+121925 is prime
2^8191+125609 is prime
2^8191+140069 is prime
2^8191+141449 is prime
2^8191+142185 is prime
2^8191+142461 is prime
2^8191+150515 is prime
2^8191+151323 is prime
2^8191+153933 is prime
2^8191+160281 is prime
2^8191+173583 is prime
2^8191+177281 is prime
2^8191+179063 is prime
2^8191+184029 is prime
2^8191+189699 is prime
2^8191+191591 is prime
2^8191+219779 is prime
2^8191+225081 is prime
2^8191+249893 is prime
2^8191+252851 is prime
2^8191+267315 is prime
2^8191+272103 is prime
2^8191+277251 is prime
2^8191+283265 is prime
2^8191+284841 is prime
2^8191+287225 is prime
2^8191+295269 is prime

时空伴随者

2^8191+303579 is prime
2^8191+308751 is prime
2^8191+310053 is prime
2^8191+313379 is prime
2^8191+318783 is prime
2^8191+318825 is prime
2^8191+326213 is prime
2^8191+336261 is prime
2^8191+339153 is prime
2^8191+356559 is prime
2^8191+361385 is prime
2^8191+363875 is prime
2^8191+367851 is prime
2^8191+376581 is prime
2^8191+377159 is prime
2^8191+391901 is prime
2^8191+395361 is prime
2^8191+403493 is prime
2^8191+403991 is prime
2^8191+413871 is prime
2^8191+430205 is prime
2^8191+447045 is prime
2^8191+455813 is prime
2^8191+469685 is prime
2^8191+471851 is prime
2^8191+474999 is prime
2^8191+475125 is prime
2^8191+480201 is prime
2^8191+487803 is prime
2^8191+503513 is prime
2^8191+504185 is prime
2^8191+508619 is prime
2^8191+511479 is prime
2^8191+521663 is prime
2^8191+538199 is prime
2^8191+542159 is prime
2^8191+542759 is prime
2^8191+543263 is prime
2^8191+546843 is prime
2^8191+557103 is prime
2^8191+560535 is prime
2^8191+564915 is prime
2^8191+580383 is prime
2^8191+580625 is prime
2^8191+597015 is prime
2^8191+603273 is prime
2^8191+614763 is prime
2^8191+614873 is prime
2^8191+617903 is prime
2^8191+618423 is prime
2^8191+619103 is prime
2^8191+623405 is prime
2^8191+623979 is prime
2^8191+624543 is prime
2^8191+638621 is prime
2^8191+643325 is prime
2^8191+648215 is prime
2^8191+648861 is prime
2^8191+651443 is prime
2^8191+660663 is prime
2^8191+676143 is prime
2^8191+677013 is prime
2^8191+678539 is prime
2^8191+680459 is prime
2^8191+685391 is prime
2^8191+688503 is prime
2^8191+704795 is prime
2^8191+705771 is prime
2^8191+710471 is prime
2^8191+713349 is prime
2^8191+717749 is prime
2^8191+721419 is prime
2^8191+723393 is prime
2^8191+729339 is prime
2^8191+730169 is prime
2^8191+732371 is prime
2^8191+735143 is prime
2^8191+744101 is prime
2^8191+751253 is prime
2^8191+762369 is prime
2^8191+766815 is prime
2^8191+768993 is prime
2^8191+774405 is prime
2^8191+776769 is prime
2^8191+779351 is prime
2^8191+785001 is prime
2^8191+792219 is prime
2^8191+794135 is prime
2^8191+795123 is prime
2^8191+795951 is prime
2^8191+806945 is prime
2^8191+816081 is prime
2^8191+821865 is prime
2^8191+834495 is prime
2^8191+836181 is prime
2^8191+848409 is prime
2^8191+862581 is prime
2^8191+865649 is prime
2^8191+874859 is prime
2^8191+875415 is prime
2^8191+880799 is prime
2^8191+885231 is prime
2^8191+888009 is prime
2^8191+891585 is prime
2^8191+892655 is prime
2^8191+897641 is prime
2^8191+909141 is prime
2^8191+912933 is prime
2^8191+918191 is prime
2^8191+924221 is prime
2^8191+926943 is prime
2^8191+940913 is prime
2^8191+942605 is prime
2^8191+945659 is prime
2^8191+946191 is prime
2^8191+956703 is prime
2^8191+958155 is prime
2^8191+958691 is prime
2^8191+958913 is prime
2^8191+964421 is prime
2^8191+969741 is prime
2^8191+972215 is prime
2^8191+973829 is prime
2^8191+975039 is prime
2^8191+975435 is prime
2^8191+984615 is prime
2^8191+999933 is prime
用时 14798.18981 秒

yangchuanju

猜想朱容仟是想要梅森素数的是——                               
2n        A        B        B增        A/B
14        7        7        ——        1
18        7        11        4        0.636363636
20        7        13        2        0.538461538
62        31        31        ——        1
68        31        37        6        0.837837838
72        31        41        4        0.756097561
92        31        61        20        0.508196721
254        127        127        ——        1
258        127        131        4        0.969465649
264        127        137        6        0.927007299
266        127        139        2        0.913669065
284        127        157        18        0.808917197
16382        8191        8191        ——        1
16400        8191        8209        18        0.997807285
16410        8191        8219        10        0.99659326
16412        8191        8221        2        0.996350809
16422        8191        8231        10        0.995140323
16424        8191        8233        2        0.994898579
16434        8191        8243        10        0.993691617
16460        8191        8269        26        0.990567179
16568        8191        8377        108        0.977796347

2n        A        B        A增        A/B
12        5        7        ——        0.714285714
14        7        7        2        1
44        13        31        ——        0.419354839
50        19        31        6        0.612903226
54        23        31        4        0.741935484
60        29        31        6        0.935483871
62        31        31        2        1
224        97        127        ——        0.763779528
228        101        127        4        0.795275591
230        103        127        2        0.811023622
234        107        127        4        0.842519685
236        109        127        2        0.858267717
240        113        127        4        0.88976378
254        127        127        14        1
16208        8017        8191        ——        0.978757173
16244        8053        8191        36        0.98315224
16292        8101        8191        48        0.989012331
16352        8161        8191        60        0.996337444
16362        8171        8191        10        0.997558296
16370        8179        8191        8        0.998534977
16382        8191        8191        12        1

等A异B的B增（差）和等B异A的A增（差）与普通素数没有明显的差异。
等A异B的A/B总是由1逐渐下降；最小比值从7,31,127到8191逐渐增大；
等B异A的A/B总是由一个纯小数逐渐增大到1；最小比值从31,127到8191逐渐增大。

yangchuanju

朱容仟不关心梅森素数附近的素数密度（几率），素数密度（几率）肯定越往后越小。               
2的8192次方附近的哥德巴赫猜想最大素数对能覆盖多少个连续偶数，恐怕更不是朱所关心的。               
也许他关心的只是梅森素数前后A或B的个数问题——               
素数        A个数        B个数
5        3        2
7        3        2
11        3        3
               
29        5        3
31        4        5
37        4        4
               
113        6        3
127        5        7
131        5        5
               
8179        6        13
8191        9        7
8209        6        11
等A异B的B个数和等B异A的A个数与普通素数没有明显的差异。               

yangchuanju

时空伴随者 发表于 2025-9-11 14:12
2^8191+303579 is prime
2^8191+308751 is prime
2^8191+310053 is prime

经对时空伴随者的统计数据进行统计，
2^8191前后200万内共350个素数，其中前172个，后178个。
按哈李素数公式公式估算，2^8191以内约有2^8191/ln(2^8191)=2^8191/(8191*ln(2))个素数，
数字太大，取常用对数计算之——
8191*log(2)-log(8191)-log(ln(2))=2461.983
其中ln(2)=0.693147181, log(ln(2))=-0.15917
以2462为指数，得2^8191以内约有10^2462个素数；
素数分率为10^2462/2^8191，取常用对数计算得10^(-3.7367),
200万间约有10^(-3.7367)*2*10^6=367个，与时空伴随者所求得数350吻合。

350*350=122500，仅12万个素数和，不可能全覆盖2*2^8191-2000000至2*2^8191+2000000间的200万个偶数；
其中的连续偶数无法估计。