高精度计算大偶数表为两个素数和的表法数值的实例（以当天日期为随机数选择偶数）

重生888@ · 发表于 2018-11-30 19:39

网站又开通了，祝贺！向愚工好友问好好！

愚工688 · 发表于 2018-11-30 22:35

重生888@ 发表于 2018-11-30 11:39
网站又开通了，祝贺！向愚工好友问好好！

你好！
我还是比较喜欢这里。
在百度吧，常常发的帖子被系统删除，认为是广告帖。要成为高级会员才能避免。
另外在百度吧，不像是谈论学术问题的场所，更多的是谩骂帖子。

愚工688 · 发表于 2018-12-25 20:23

今天是2018-12-25日，在西方是个大节日。
我就计算一下偶数20181225000起连续的20个偶数的表为两个素数和的表法数量以及计算值的精度吧！看看我的高精度计算。
真值：G(M)=s(m)；
精度值：jdz =sp(m)/s(m)；

G(20181225000) = 70758113；Sp( 20181225000 *)≈  70729562.4 , jdz =sp(m)/s(m) ≈ 0.999596
G(20181225002) = 27373524；Sp( 20181225002 *)≈  27361347.6 , jdz =sp(m)/s(m) ≈ 0.999555
G(20181225004) = 25871217；Sp( 20181225004 *)≈  25856555.3 , jdz =sp(m)/s(m) ≈ 0.999433
G(20181225006) = 51806978；Sp( 20181225006 *)≈  51793786.3 , jdz =sp(m)/s(m) ≈ 0.999745
G(20181225008) = 31170616；Sp( 20181225008 *)≈  31158785.6 , jdz =sp(m)/s(m) ≈ 0.999620
G(20181225010) = 34533607；Sp( 20181225010 *)≈  34518127.5 , jdz =sp(m)/s(m) ≈ 0.999552
G(20181225012) = 56439601；Sp( 20181225012 *)≈  56414302.5 , jdz =sp(m)/s(m) ≈ 0.999552
G(20181225014) = 25871444；Sp( 20181225014 *)≈  25858309.6 , jdz =sp(m)/s(m) ≈ 0.999492
G(20181225016) = 25961327；Sp( 20181225016 *)≈  25950579.1 , jdz =sp(m)/s(m) ≈ 0.999586
G(20181225018) = 55747352；Sp( 20181225018 *)≈  55723515.1 , jdz =sp(m)/s(m) ≈ 0.999572
G(20181225020) = 38338233；Sp( 20181225020 *)≈  38321535.7 , jdz =sp(m)/s(m) ≈ 0.999564
G(20181225022) = 32870023；Sp( 20181225022 *)≈  32862605.6 , jdz =sp(m)/s(m) ≈ 0.999774
G(20181225024) = 52012242；Sp( 20181225024 *)≈  51986725.0 , jdz =sp(m)/s(m) ≈ 0.999509
G(20181225026) = 26247894；Sp( 20181225026 *)≈  26236720.5 , jdz =sp(m)/s(m) ≈ 0.999574
G(20181225028) = 27659824；Sp( 20181225028 *)≈  27644615.5 , jdz =sp(m)/s(m) ≈ 0.999450
G(20181225030) = 69129744；Sp( 20181225030 *)≈  69110792.9 , jdz =sp(m)/s(m) ≈ 0.999726
G(20181225032) = 25867462；Sp( 20181225032 *)≈  25858024.9 , jdz =sp(m)/s(m) ≈ 0.999635
G(20181225034) = 25871314；Sp( 20181225034 *)≈  25862025.3 , jdz =sp(m)/s(m) ≈ 0.999641
G(20181225036) = 62089658；Sp( 20181225036 *)≈  62055732.8 , jdz =sp(m)/s(m) ≈ 0.999454
G(20181225038) = 28733673；Sp( 20181225038 *)≈  28720486.1 , jdz =sp(m)/s(m) ≈ 0.999541
time start =19:44:37, time end=19:52:01 ,

愚工688 · 发表于 2018-12-31 16:49

本帖最后由愚工688 于 2018-12-31 08:57 编辑

今天是2018年的最后一天12月31日，就以今天的日期为随机数，计算偶数201,812,310,000起的连续21个偶数的表为两个素数和的表法数量（单记）。
前面都是使用概率连乘式的公式计算的，今天换一换，用类似哈李公式的方法来计算吧！
看看我的计算的精度怎么样？
使用计算式： Xi(M)=t2*c1*M/(logM)^2 ;  (t2=  1.078409 ，t2计算式略 )
      计算式中的C1，是对拉曼纽扬系数C（N）的改进：
   C1(M)=C2A(M)× C2B(M),
   式中：C2A(M)= PI(1-1/（P-1）^2）[这里P为大于“2”，√M以内的全部素数]
            C2B(M)= PI((P1-1)/(P1-2))[这里P1为大于“2”，能整除M的全部√M内的素数,即偶数的奇素因子]

  S( 201812310000 ) = 682127679 ;Xi(M)≈ 678544861.66 δxi( 201812310000 )≈-0.005252
  S( 201812310002 ) = 217334731 ;Xi(M)≈ 216196953.86 δxi( 201812310002 )≈-0.005235
  S( 201812310004 ) = 213152620 ;Xi(M)≈ 212042148.73 δxi( 201812310004 )≈-0.005210
  S( 201812310006 ) = 426318894 ;Xi(M)≈ 424086671.37 δxi( 201812310006 )≈-0.005236
  S( 201812310008 ) = 213243299 ;Xi(M)≈ 212112408.86 δxi( 201812310008 )≈-0.005303
  S( 201812310010 ) = 288586346 ;Xi(M)≈ 287068616.86 δxi( 201812310010 )≈-0.005259
  S( 201812310012 ) = 426329843 ;Xi(M)≈ 424102140.1 δxi( 201812310012 )≈-0.005225
  S( 201812310014 ) = 255790652 ;Xi(M)≈ 254447182.26 δxi( 201812310014 )≈-0.005252
  S( 201812310016 ) = 216912176 ;Xi(M)≈ 215779872.89 δxi( 201812310016 )≈-0.005220
  S( 201812310018 ) = 506190497 ;Xi(M)≈ 503538513.17 δxi( 201812310018 )≈-0.005239
  S( 201812310020 ) = 285176297 ;Xi(M)≈ 283684911.9 δxi( 201812310020 )≈-0.005230
  S( 201812310022 ) = 213146857 ;Xi(M)≈ 212039315.37 δxi( 201812310022 )≈-0.005196
  S( 201812310024 ) = 476986202 ;Xi(M)≈ 474493587.31 δxi( 201812310024 )≈-0.005226
  S( 201812310026 ) = 223400056 ;Xi(M)≈ 222234232.8 δxi( 201812310026 )≈-0.005219
  S( 201812310028 ) = 255796809 ;Xi(M)≈ 254447182.28 δxi( 201812310028 )≈-0.005276
  S( 201812310030 ) = 569839076 ;Xi(M)≈ 566866975.7 δxi( 201812310030 )≈-0.005216
  S( 201812310032 ) = 226806637 ;Xi(M)≈ 225623834.27 δxi( 201812310032 )≈-0.005215
  S( 201812310034 ) = 213496723 ;Xi(M)≈ 212384087.78 δxi( 201812310034 )≈-0.005211
  S( 201812310036 ) = 426331597 ;Xi(M)≈ 424078630.77 δxi( 201812310036 )≈-0.005285
  S( 201812310038 ) = 213165008 ;Xi(M)≈ 212039315.38 δxi( 201812310038 )≈-0.005281
  S( 201812310040 ) = 315934625 ;Xi(M)≈ 314274029.15 δxi( 201812310040 )≈-0.005256

  time start =21:44:14  , time end =22:08:11

愚工688 · 发表于 2019-1-1 13:26

本帖最后由愚工688 于 2019-1-1 05:28 编辑

今天是20190101元旦节，新的一年开始了！
使用我新的素对计算式 Xi(M)=t2*c1*M/(logM)^2 ，计算一下日期的10倍、100倍、1000倍的各3个连续偶数，看看计算值的精度如何？（精度值=相对误差值+1 ，参数t2的解析式暂不公布）

  S( 201901010 ) = 584329 ;Xi(M)≈ 584077.87    δxi( 201901010 )≈-0.0004298  (t2=  1.118359 )
  S( 201901012 ) = 413500 ;Xi(M)≈ 412880.03    δxi( 201901012 )≈-0.0014994  (t2=
1.118359 )
  S( 201901014 ) = 978724 ;Xi(M)≈ 978271.31    δxi( 201901014 )≈-0.0004625  (t2=
1.118359 )
  time start =12:58:10 time end =12:58:12
  S( 2019010100 ) = 4596216 ;Xi(M)≈ 4594529.21    δxi( 2019010100 )≈-0.0003670  (t2=
1.104341 )
  S( 2019010102 ) = 3391625 ;Xi(M)≈ 3389795.77    δxi( 2019010102 )≈-0.0005393  (t2=
1.104341 )
  S( 2019010104 ) = 6718402 ;Xi(M)≈ 6718181.02    δxi( 2019010104 )≈-0.0000329  (t2=
1.104341 )
  time start =12:58:24  ，  time end =12:58:32
  S( 20190101000 ) = 37084574  ;Xi(M)≈ 37010416.04 δxi( 20190101000 )≈-0.0019997  (t2=
1.091059 )
  S( 20190101002 ) = 25991412  ;Xi(M)≈ 25940436.35 δxi( 20190101002 )≈-0.0019612  (t2=
1.091059 )
  S( 20190101004 ) = 51916057  ;Xi(M)≈ 51814261.58 δxi( 20190101004 )≈-0.0019608  (t2=
1.091059 )
  time start =12:58:40 ， time end =12:59:22

愚工688 · 发表于 2019-1-3 13:07

同样的以偶数素对计算式  Xi(M)=t2*c1*M/(logM)^2 ，计算今天日期 20190103 的十倍、百倍、千倍、万倍的连续3个偶数，看看计算值的计算精度怎么样？

  S( 201901030 ) = 576460 ;Xi(M)≈ 576573.05    δxi( M )≈0.000196  (t2=  1.118359 )
  S( 201901032 ) = 817627 ;Xi(M)≈ 817158.28    δxi( M )≈-0.000573  (t2=  1.118359 )
  S( 201901034 ) = 409741 ;Xi(M)≈ 410118.36    δxi( M )≈0.000922  (t2=  1.118359 )
  time start =12:34:38, time end =12:34:40

  S( 2019010300 ) = 4536208 ;Xi(M)≈ 4535494.46    δxi( M )≈-0.000157  (t2=  1.104341 )
  S( 2019010302 ) = 6881425 ;Xi(M)≈ 6880478.05    δxi( M )≈-0.000138  (t2=  1.104341 )
  S( 2019010304 ) = 3503400 ;Xi(M)≈ 3503908.8    δxi( M )≈0.000145  (t2=  1.104341 )
  time start =12:34:48, time end =12:34:57

  S( 20190103000 ) = 36605865  ;Xi(M)≈ 36534872.07 δxi( M )≈-0.001939  (t2=  1.091059 )
  S( 20190103002 ) = 51898940  ;Xi(M)≈ 51806123.38 δxi( M )≈-0.001788  (t2=  1.091059 )
  S( 20190103004 ) = 25876755  ;Xi(M)≈ 25828626.71 δxi( M )≈-0.001860  (t2=  1.091059 )
  time start =12:35:04, time end =12:35:46

  S( 201901030000 ) = 301633893 ;Xi(M)≈ 300052996.23 δxi( M )≈-0.005241  (t2=  1.078407 )
  S( 201901030002 ) = 515598032 ;Xi(M)≈ 512870919.15 δxi( M )≈-0.005289  (t2=  1.078407 )
  S( 201901030004 ) = 217002765 ;Xi(M)≈ 215862315.01 δxi( M )≈-0.005255  (t2=  1.078407 )
  time start =12:36:02, time end =12:39:27

愚工688 · 发表于 2019-1-6 13:34

同样的以计算式 Xi(M)=t2*c1*M/(logM)^2 计算今天日期 20190106 的十倍、百倍、千倍的连续3个偶数，看看计算值的计算精度怎么样？

  S( 201901060 ) = 543450 ;Xi(M)≈ 543484.14    δxi( 201901060 )≈0.0000628  (t2=  1.118359 )
  S( 201901062 ) = 923544 ;Xi(M)≈ 923567.83    δxi( 201901062 )≈0.0000258  (t2=  1.118359 )
  S( 201901064 ) = 415205 ;Xi(M)≈ 415464.25    δxi( 201901064 )≈0.0006244  (t2=  1.118359 )
  time start =11:23:34, time end =11:23:36
  S( 2019010600 ) = 4276169 ;Xi(M)≈ 4275207.29    δxi( 2019010600 )≈-0.0002249  (t2=  1.104341 )
  S( 2019010602 ) = 7696691 ;Xi(M)≈ 7695373.06    δxi( 2019010602 )≈-0.0001712  (t2=  1.104341 )
  S( 2019010604 ) = 3740877 ;Xi(M)≈ 3741251.01    δxi( 2019010604 )≈ 0.00009998  (t2=  1.104341 )
  time start =11:23:52, time end =11:24:01
  S( 20190106000 ) = 34506827  ;Xi(M)≈ 34438174.83 δxi( 20190106000 )≈-0.0019895  (t2=  1.091059 )
  S( 20190106002 ) = 62986085  ;Xi(M)≈ 62868879.66 δxi( 20190106002 )≈-0.0018608  (t2=  1.091059 )
  S( 20190106004 ) = 25883241  ;Xi(M)≈ 25830276.94 δxi( 20190106004 )≈-0.0020463  (t2=  1.091059 )
  time start =11:24:11, time end =11:24:54

愚工688 · 发表于 2019-1-21 23:20

本帖最后由愚工688 于 2019-1-27 05:03 编辑

同样的以计算式 Xi(M)=t2*c1*M/(logM)^2 计算今天日期 20190121 的十倍、百倍、千倍的连续3个偶数，看看计算值的计算精度怎么样？

  S( 201901210 ) = 661915    ;Xi(M)≈ 661367       δxi( M)≈-0.0008279  (t2=  1.118359 )
  S( 201901212 ) = 815809 ;Xi(M)≈ 815226.74    δxi( M )≈-0.0007138  (t2=  1.118359 )
  S( 201901214 ) = 436296 ;Xi(M)≈ 435855.86    δxi( M )≈-0.0010088  (t2=  1.118359 )
  time start =23:00:40, time end =23:00:42
  S( 2019012100 ) = 5201632 ;Xi(M)≈ 5202640.9    δxi( M )≈ 0.0001940  (t2=  1.104341 )
  S( 2019012102 ) = 6412146 ;Xi(M)≈ 6412815.13    δxi( M )≈ 0.0001043 (t2=  1.104341 )
  S( 2019012104 ) = 3332970 ;Xi(M)≈ 3332239.8    δxi( M )≈-0.0002191  (t2=  1.104341 )
  time start =23:00:54, time end =23:01:03
  S( 20190121000 ) = 41992225  ;Xi(M)≈ 41908950.24 δxi( M )≈-0.0019831  (t2=  1.091059 )
  S( 20190121002 ) = 53631039  ;Xi(M)≈ 53526795.97 δxi( M )≈-0.0019437  (t2=  1.091059 )
  S( 20190121004 ) = 27117253  ;Xi(M)≈ 27064780.73 δxi( M )≈-0.0019350  (t2=  1.091059 )
  time start =23:01:25, time end =23:02:08

很明显，上述三组偶数的素对计算值的相对误差绝对值都比较小。

看亚洲杯足球，闲着无事，再计算一组今天日期万倍的千万亿级的偶数，相对误差绝对值也不错。
  S( 201901210000 ) = 346010073 ;Xi(M)≈ 344189143.32 δxi(M)≈-0.0052627  ( t2=  1.078407 )
  S( 201901210002 ) = 426463302 ;Xi(M)≈ 424250180.94 δxi(M)≈-0.0051895  ( t2=  1.078407 )
  S( 201901210004 ) = 233425466 ;Xi(M)≈ 232204404.39 δxi(M)≈-0.0052311  ( t2=  1.078407 )
  time start =23:25:33, time end =23:29:00

愚工688 · 发表于 2019-1-27 13:45

以计算式 Xi(M)=t2*c1*M/(logM)^2 计算今天日期 20190127 的十倍、百倍、千倍的连续3个偶数，看看计算值的相对误差值怎么样？
  S( 201901270 ) = 543722 ;Xi(M)≈ 543730.06    δxi(M)≈ 0.0000147  ( t2=  1.118359 )
  S( 201901272 ) = 815241 ;Xi(M)≈ 815226.98    δxi(M)≈-0.0000172  ( t2=  1.118359 )
  S( 201901274 ) = 415400 ;Xi(M)≈ 415605.93    δxi(M)≈ 0.0004957  ( t2=  1.118359 )
  time start =13:07:32, time end =13:07:34
  S( 2019012700 ) = 4278759 ;Xi(M)≈ 4277141.82    δxi(M)≈-0.0003780  ( t2=  1.104341 )
  S( 2019012702 ) = 7958499 ;Xi(M)≈ 7960738.35    δxi(M)≈ 0.0002813  ( t2=  1.104341 )
  S( 2019012704 ) = 3241756 ;Xi(M)≈ 3243263.91    δxi(M)≈ 0.0004651  ( t2=  1.104341 )
  time start =13:07:42, time end =13:07:51
  S( 20190127000 ) = 34521277  ;Xi(M)≈ 34453756.69 δxi(M)≈-0.0019559  ( t2=  1.091059 )
  S( 20190127002 ) = 53252504  ;Xi(M)≈ 53155567.02 δxi(M)≈-0.0018203  ( t2=  1.091059 )
  S( 20190127004 ) = 26837816  ;Xi(M)≈ 26785270.76 δxi(M)≈-0.0019579  ( t2=  1.091059 )
  time start =13:08:02, time end =13:08:47

而使用素数连乘式Sp(m*)的计算精度如下：
G(20190127000 )= 34521277；Sp( 20190127000 *)≈ 34505217.6 , jdz =sp(m)/s(m) ≈ 0.999535;
G(20190127002 )= 53252504；Sp( 20190127002 *)≈ 53234959.9 , jdz =sp(m)/s(m) ≈ 0.999671;
G(20190127004 )= 26837816；Sp( 20190127004 *)≈ 26825278.0 , jdz =sp(m)/s(m) ≈ 0.999533;
G(20190127006 )= 31761238；Sp( 20190127006 *)≈ 31742468.1 , jdz =sp(m)/s(m) ≈ 0.999409;
G(20190127008 )= 51810287；Sp( 20190127008 *)≈ 51793187.2 , jdz =sp(m)/s(m) ≈ 0.999670;
start time =13:24:32,end time=13:26:27 ,

我的两个偶数素对数量的计算式的计算精度都不错！

愚工688 · 发表于 2019-1-30 22:01

今天2019-01-30，计算一下20190130000的连续偶数的素对数值与精度：
G(20190130000) = 34508653 ；Sp( 20190130000 *)≈  34489648.3 , jdz =sp(m)/s(m) ≈0.999449；
G(20190130002) = 66244126 ；Sp( 20190130002 *)≈  66220124.7 , jdz =sp(m)/s(m) ≈0.999638；
G(20190130004) = 28747671 ；Sp( 20190130004 *)≈  28741373.6 , jdz =sp(m)/s(m) ≈0.999781；
G(20190130006) = 25937826 ；Sp( 20190130006 *)≈  25927830.1 , jdz =sp(m)/s(m) ≈0.999615；
G(20190130008) = 52790541 ；Sp( 20190130008 *)≈  52764809.7 , jdz =sp(m)/s(m) ≈0.999513；
start time =21:42:04,end time=21:43:48 ,
计算公式如下：
Sp( 20190130000 *) = 1/(1+ .1533 )*( 20190130000 /2 -2)*p(m) ≈ 34489648.3 , k(m)= 1.333333
Sp( 20190130002 *) = 1/(1+ .1533 )*( 20190130002 /2 -2)*p(m) ≈ 66220124.7 , k(m)= 2.56
Sp( 20190130004 *) = 1/(1+ .1533 )*( 20190130004 /2 -2)*p(m) ≈ 28741373.6 , k(m)= 1.111111
Sp( 20190130006 *) = 1/(1+ .1533 )*( 20190130006 /2 -2)*p(m) ≈ 25927830.1 , k(m)= 1.002342
Sp( 20190130008 *) = 1/(1+ .1533 )*( 20190130008 /2 -2)*p(m) ≈ 52764809.7 , k(m)= 2.039832

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