基于偶数哥猜哈-李素对计算公式改进的偶数素对计算式 Xi(M)≈ t1*c1*M/(logM)^2

重生888@ · 发表于 2020-11-24 10:47

谢谢愚工先生的多次点评！另外我想求助您，把您以往发过的：
100  1000  10000.......  10^15素数对真值发到我的求助帖子后面，谢谢！
300  3000  30000.......    能多大就多大；
200  4000  20000.......
500  5000  50000......
400  4000  40000......
........

朱明君 · 发表于 2020-11-24 21:19

重生888@ 发表于 2020-11-24 02:47
谢谢愚工先生的多次点评！另外我想求助您，把您以往发过的：
100 1000 10000....... 10^15素数对真值发 ...

逆向思维，找不全素数，能找全合数！我有八八六十四个公式，能找全合数！在本论坛能搜到（重生888）.利用这一理论，我制成了《新型质数表》（10000以内）。1226个（2.3.5不在内）一个不多，一个不少！

朱明君 · 发表于 2020-11-24 21:23

重生888老师，展示一下你的八八六十四个公式

重生888@ · 发表于 2020-11-25 13:22

朱明君发表于 2020-11-24 21:23
重生888老师，展示一下你的八八六十四个公式

我的电脑水平差，翻不到。请您自己找！

愚工688 · 发表于 2020-11-26 14:30

重生888@ 发表于 2020-11-24 02:47
谢谢愚工先生的多次点评！另外我想求助您，把您以往发过的：
100 1000 10000....... 10^15素数对真值发 ...

Xi(M)=t2*c1*M/(logM)^2  ; 的计算精度：

  G( 10^1 ) = 2                ;Xi(M)≈ 2.12             jdz(M)≈1.06
  G( 10^2 ) = 6                ;Xi(M)≈ 5.15             jdz(M)≈0.85833
  G( 10^3 ) = 28                ;Xi(M)≈ 22.39          jdz(M)≈0.79964
  G( 10^4 ) = 127             ;Xi(M)≈ 123.65          jdz(M)≈0.97362
  G( 10^5 ) = 810             ;Xi(M)≈ 778.34          jdz(M)≈0.96091
  G( 10^6 ) = 5402             ;Xi(M)≈ 5323.31          jdz(M)≈0.98543
  G( 10^7 ) = 38807             ;Xi(M)≈ 38557.1          jdz(M)≈0.99356
  G( 10^8 ) = 291400          ;Xi(M)≈ 291262.27       jdz(M)≈0.99953
  G( 10^9 ) = 2274205          ;Xi(M)≈ 2272089.28       jdz(M)≈0.99907
  G( 10^10 ) = 18200488       ;Xi(M)≈ 18179890.52    jdz(M)≈0.99887
  G( 10^11 ) = 149091160       ;Xi(M)≈ 148486029.78    jdz(M)≈0.99594
  G( 10^12 ) = 1243722370       ;Xi(M)≈ 1233556241.87    jdz(M)≈0.99183
  G( 10^13 ) = 10533150855,    ;Xi(M)≈ 10395227871.57 jdz(M)≈0.98691
  G( 10^14 ) = 90350630388    ;Xi(M)≈ 88673642506.88 jdz(M)≈0.98144
  G( 10^15 ) = 783538341852    ;Xi(M)≈ 764388083252.93 jdz(M)≈0.97556

  G( 200 ) =  8                   ;Xi(M)≈ 7.73          δxi(M)≈-0.03375;
  G( 2000 ) =  37                ;Xi(M)≈ 36.78          δxi(M)≈-0.005946;
  G( 20000 ) = 231                ;Xi(M)≈ 212.8          δxi(M)≈-0.078788;
  G( 200000 ) = 1417             ;Xi(M)≈ 1378.39       δxi(M)≈-0.027241;
  G( 2000000 ) = 9720             ;Xi(M)≈ 9611.44       δxi(M)≈-0.011169;
  G( 20000000 ) = 70730          ;Xi(M)≈ 70594.7       δxi(M)≈-0.001913;
  G( 200000000 ) = 538290       ;Xi(M)≈ 538928.5       δxi(M)≈-0.001186;
  G( 2000000000 ) = 4238417       ;Xi(M)≈ 4238910.11    δxi(M)≈-0.000116;
  G( 20000000000 ) = 34204396    ;Xi(M)≈ 34142796.44    δxi(M)≈-0.001801;
  G( 200000000000 ) = 281856501 ;Xi(M)≈ 280387128.51    δxi(M)≈-0.005213;
  G( 2000000000000 ) = 2362547893  ;Xi(M)≈ 2339960725.71 δxi(M)≈-0.009561;

  G( 300 ) =  21       ;          Xi(M)≈ 20.2          ;jdz=0.9619
  G( 3000 ) =  104       ;          Xi(M)≈ 99.46       ;jdz=0.9564
  G( 30000 ) =  602    ;          Xi(M)≈ 587.9       ;jdz=0.9766
  G( 300000 ) =  3915    ;       Xi(M)≈ 3863.55       ;jdz=0.9869
  G( 3000000 ) = 27502    ;       Xi(M)≈ 27216.98    ;jdz=0.9896
  G( 30000000 ) = 202166    ;       Xi(M)≈ 201417.42    ;jdz=0.9963
  G( 300000000 ) =  1547388 ;    Xi(M)≈ 1546564.56    ;jdz=0.99995
  G( 3000000000 ) = 12224533 ;    Xi(M)≈ 12219977.77 ;jdz=0.99963
  G( 30000000000 ) =  99039834 ;    Xi(M)≈ 98790288.7    ;jdz=0.99748
  G( 300000000000 ) = 818772509 ;    Xi(M)≈ 813751776.9 ;jdz=0.99387
  G( 3000000000000 ) = 6881609867 ; Xi(M)≈ 6808454018.63  ;jdz=0.9894
  G( 30000000000000 ) = 58651540055;  Xi(M)≈ 57722112492.79 ;jdz=0.98415

G( 400 ) = 14                   ;Xi(M)≈ 12                      δxi(M)≈-0.142857;
  G( 4000 ) = 65                ;Xi(M)≈ 61.43                   δxi(M)≈-0.054923;
  G( 40000 ) = 389                ;Xi(M)≈ 369.88                   δxi(M)≈-0.049152;
  G( 400000 ) = 2487                ;Xi(M)≈ 2457.12                   δxi(M)≈-0.012014;
  G( 4000000 ) = 17638             ;Xi(M)≈ 17434.77                δxi(M)≈-0.011522;
  G( 40000000 ) = 130164             ;Xi(M)≈ 129702.13                δxi(M)≈-0.003549;
  G( 400000000 ) =999700             ;Xi(M)≈ 999873.56                δxi(M)≈ 0.000174;
  G( 4000000000 ) =7930427          ;Xi(M)≈ 7925260.39                δxi(M)≈-0.000652;
  G( 40000000000 ) =64411146          ;Xi(M)≈ 64234176.38             δxi(M)≈-0.002748;
  G( 400000000000 ) = 533673299       ;Xi(M)≈ 530227062.24             δxi(M)≈-0.006458;
  G( 4000000000000 ) =4493879898    ;Xi(M)≈ 4444178047.31             δxi(M)≈-0.011060;

愚工688 · 发表于 2020-11-26 14:34

继续：（以n*10^12为主，）
Xi(M)=t2*c1*M/(logM)^2

  G( 500 ) = 13                ;Xi(M)≈ 13.92                   δxi(M)≈ 0.07077;
  G( 5000 ) = 76                ;Xi(M)≈ 72.69                   δxi(M)≈-0.043553;
  G( 50000 ) = 450                ;Xi(M)≈ 442.77                δxi(M)≈-0.016067;
  G( 500000 ) =3052                ;Xi(M)≈ 2963.5                δxi(M)≈-0.028997;
  G( 5000000 ) =21290                ;Xi(M)≈ 21138.58             δxi(M)≈-0.007112;
  G( 50000000 ) = 158467             ;Xi(M)≈ 157867.81          δxi(M)≈-0.003781;
  G( 500000000 ) = 1219610          ;Xi(M)≈ 1220646.74          δxi(M)≈ 0.000850;
  G( 5000000000 ) = 9703556          ;Xi(M)≈ 9698149.31          δxi(M)≈-0.000557;
  G( 50000000000 ) = 79004202       ;Xi(M)≈ 78755206.45          δxi(M)≈-0.003152;
  G( 500000000000 ) = 655630055       ;Xi(M)≈ 651132862.99       δxi(M)≈-0.006859;
  G( 5000000000000 ) = 5528644312    ;Xi(M)≈ 5464927127.99       δxi(M)≈-0.011525;

G( 600 ) = 32                   ;Xi(M)≈ 31.48                   δxi(M)≈  -0.01625;
  G( 6000 ) = 178                ;Xi(M)≈ 166.97                   δxi(M)≈ -0.06197;
  G( 60000 ) = 1084                ;Xi(M)≈ 1026.4                   δxi(M)≈-0.053137;
  G( 600000 ) = 6993                ;Xi(M)≈ 6910.6                   δxi(M)≈-0.011783;
  G( 6000000 ) = 49783             ;Xi(M)≈ 49499.21                δxi(M)≈-0.005705;
  G( 60000000 ) = 371226             ;Xi(M)≈ 370818.25                δxi(M)≈-0.001099;
  G( 600000000 ) = 2874881             ;Xi(M)≈ 2874060.71                δxi(M)≈-0.000285;
  G( 6000000000 ) = 22899781          ;Xi(M)≈ 22878144.49             δxi(M)≈-0.004919;
  G( 60000000000 ) = 186693890       ;Xi(M)≈ 186073260.34             δxi(M)≈-0.003324;
  G( 600000000000 ) = 1551585485       ;Xi(M)≈ 1540398009.6             δxi(M)≈-0.007210;
  G( 6000000000000 ) = 13098988138    ;Xi(M)≈ 12942526631.34          δxi(M)≈-0.011945;

G( 700 ) =  24                ;Xi(M)≈ 20.98             δxi(M)≈ -0.12583
  G( 7000 ) = 119                ;Xi(M)≈ 112.71             δxi(M)≈-0.52941
  G( 70000 ) =  719                ;Xi(M)≈ 698.01             δxi(M)≈-0.02921
  G( 700000 ) =  4878             ;Xi(M)≈ 4722.53             δxi(M)≈-0.03187
  G( 7000000 ) =  34284             ;Xi(M)≈ 33943.26          δxi(M)≈ -0.009946
  G( 70000000 ) = 255175             ;Xi(M)≈ 254935.83          δxi(M)≈-0.0009374
  G( 700000000 ) = 1979689          ;Xi(M)≈ 1979831.6          δxi(M)≈ 0.000072
  G( 7000000000 ) = 15799407          ;Xi(M)≈ 15784853.81       δxi(M)≈-0.000921
  G( 70000000000 ) = 129009540       ;Xi(M)≈ 128547778.47       δxi(M)≈-0.003579
  G( 700000000000 ) = 1073350237    ;Xi(M)≈ 1065319456.38       δxi(M)≈-0.007482
  G( 7000000000000 ) = 9070480173    ;Xi(M)≈ 8959005515.17       δxi(M)≈



  G( 800 ) = 21                ;Xi(M)≈ 19.17                   δxi(M)≈-0.087143;
  G( 8000 ) = 106                ;Xi(M)≈ 104.07                   δxi(M)≈-0.018208;
  G( 80000 ) = 652                ;Xi(M)≈ 648.53                   δxi(M)≈-0.005322;
  G( 800000 ) = 4433                ;Xi(M)≈ 4405.92                   δxi(M)≈-0.006113;
  G( 8000000 ) =31753                ;Xi(M)≈ 31760.41                δxi(M)≈ 0.000233;
  G( 80000000 ) =239209             ;Xi(M)≈ 239063.18                δxi(M)≈-0.000610;
  G( 800000000 ) = 1859646             ;Xi(M)≈ 1859713.97                δxi(M)≈ 0.0000365;
  G( 8000000000 ) = 14862150          ;Xi(M)≈ 14847253.41             δxi(M)≈-0.001002;
  G( 80000000000 ) = 121504043       ;Xi(M)≈ 121045896.57             δxi(M)≈-0.003771;
  G( 800000000000 ) = 1011911933       ;Xi(M)≈ 1004071908.7             δxi(M)≈-0.007748;
  G( 8000000000000 ) = 8558144934    ;Xi(M)≈ 8450501739.32             δxi(M)≈-0.012578;


  G( 900 ) = 48                   ;Xi(M)≈ 41.6                      δxi(M)≈-0.133333;
  G( 9000 ) = 242                ;Xi(M)≈ 227.94                   δxi(M)≈-0.058099;
  G( 90000 ) = 1471             ;Xi(M)≈ 1428.05                   δxi(M)≈-0.029198;
  G( 900000 ) = 9853             ;Xi(M)≈ 9736.36                   δxi(M)≈-0.011838;
  G( 9000000 ) =70619             ;Xi(M)≈ 70363.59                δxi(M)≈-0.003617;
  G( 90000000 ) =531538             ;Xi(M)≈ 530639.45                δxi(M)≈-0.001690;
  G( 900000000 ) =4132595             ;Xi(M)≈ 4134032.32                δxi(M)≈ 0.0003477;
  G( 9000000000 ) = 33076258          ;Xi(M)≈ 33043510.31             δxi(M)≈-0.000990;
  G( 90000000000 ) = 270719498       ;Xi(M)≈ 269655377.56             δxi(M)≈-0.003931;
  G( 900000000000 ) = 2256592982    ;Xi(M)≈ 2238581637.62             δxi(M)≈-0.007982;
  G( 9000000000000 ) = 19098578267    ;Xi(M)≈ 18853233583.44          δxi(M)≈-0.012846;

重生888@ · 发表于 2020-11-26 18:16

谢谢愚工先生！太感谢了！

愚工688 · 发表于 2020-12-14 21:23

本帖最后由愚工688 于 2020-12-14 13:45 编辑

以今天日期的百倍开始的偶数的素对计算：
Xi(M)=t2*c1*M/(logM)^2

  G( 2020121400 ) = ?    ;Xi(M)≈ 9545920.32          δxi(M)≈?
  G( 2020121402 ) = ?    ;Xi(M)≈ 3543082.76          δxi(M)≈?
  G( 2020121404 ) = ?    ;Xi(M)≈ 3849594.64          δxi(M)≈?
  G( 2020121406 ) = ?    ;Xi(M)≈ 6460875.5          δxi(M)≈?
  G( 2020121408 ) = ?    ;Xi(M)≈ 3253178.64          δxi(M)≈?
  G( 2020121410 ) = ?    ;Xi(M)≈ 4293715.6          δxi(M)≈?
  G( 2020121412 ) = ?    ;Xi(M)≈ 6606137.5          δxi(M)≈?
  G( 2020121414 ) = ?    ;Xi(M)≈ 3347975.59          δxi(M)≈?
  G( 2020121416 ) = ?    ;Xi(M)≈ 3237976.83          δxi(M)≈?
  G( 2020121418 ) = ?    ;Xi(M)≈ 8151098.44          δxi(M)≈?
  time start =21:24:16, time end =21:24:47

同样这些偶数，使用连乘式计算它们的素对下界值：
G(2020121400) = 9548099；
inf( 2020121400 )≈  9484907.4 , Δ≈-0.006618 ,infS(m) = 3187491.42 , k(m)= 2.97567
G(2020121402) = 3543669；
inf( 2020121402 )≈  3520437 , Δ≈-0.006556 ,infS(m) = 3187491.43 , k(m)= 1.10445
G(2020121404) = 3849708；
inf( 2020121404 )≈  3824989.7 , Δ≈-0.006421 ,infS(m) = 3187491.43 , k(m)= 1.2
G(2020121406) = 6463449；
inf( 2020121406 )≈  6419580.5 , Δ≈-0.006787 ,infS(m) = 3187491.43 , k(m)= 2.01399
G(2020121408) = 3252718；
inf( 2020121408 )≈  3232385.7 , Δ≈-0.006251 ,infS(m) = 3187491.44 , k(m)= 1.01408
G(2020121410) = 4295374；
inf( 2020121410 )≈  4266272.1 , Δ≈-0.006775 ,infS(m) = 3187491.44 , k(m)= 1.33844
G(2020121412) = 6607402；
inf( 2020121412 )≈  6563914.3 , Δ≈-0.006582 ,infS(m) = 3187491.44 , k(m)= 2.05927
G(2020121414) = 3347483；
inf( 2020121414 )≈  3326576.8 , Δ≈-0.006245 ,infS(m) = 3187491.45 , k(m)= 1.04363
G(2020121416) = 3236595；
inf( 2020121416 )≈  3217281.1 , Δ≈-0.005967 ,infS(m) = 3187491.45 , k(m)= 1.00935
G(2020121418) = 8151883；
inf( 2020121418 )≈  8099000.6 , Δ≈-0.006487 ,infS(m) = 3187491.45 , k(m)= 2.54087

愚工688 · 发表于 2022-8-5 20:29

以今天日期的百倍为随机数的连续偶数的素对计算：

  Xi(M)=t2*c1*M/(logM)^2
式中：t2=1.358-(log(M))^(.5)*0.05484;c1:只计算√M内素数的类似拉曼扭杨系数。

  G(2022080500) = 4756934  ;Xi(M)≈ 4756739.96 δxi(M)≈?-0.00004079；
  G(2022080502) = 7114160  ;Xi(M)≈ 7113155.68 δxi(M)≈?-0.00014117；
  G(2022080504) = 3508456  ;Xi(M)≈ 3508385.81 δxi(M)≈?-0.00002001；
  G(2022080506) = 3332760  ;Xi(M)≈ 3332181.68 δxi(M)≈?-0.0001735；
  G(2022080508) = 7707403  ;Xi(M)≈ 7705918.82 δxi(M)≈?-0.00019257；
  G(2022080510) = 4531527  ;Xi(M)≈ 4532893.46 δxi(M)≈? 0.00030155；
  G(2022080512) = 3366081  ;Xi(M)≈ 3364949.31 δxi(M)≈?-0.00033630；
  G(2022080514) = 6423807  ;Xi(M)≈ 6421598.94 δxi(M)≈?-0.00034372；
  G(2022080516) = 3210619  ;Xi(M)≈ 3210799.47 δxi(M)≈? 0.00006064；
  G(2022080518) = 3210904  ;Xi(M)≈ 3211330.56 δxi(M)≈? 0.00013286；
  G(2022080520) = 8602085  ;Xi(M)≈ 8603098.84 δxi(M)≈? 0.00011788；
  G(2022080522) = 4279966  ;Xi(M)≈ 4281066.07 δxi(M)≈? 0.0002570；
  G(2022080524) = 3363701  ;Xi(M)≈ 3364653.35 δxi(M)≈? 0.0002830；
  G(2022080526) = 6475586  ;Xi(M)≈ 6477795.57 δxi(M)≈? 0.0003413；
  G(2022080528) = 3543227  ;Xi(M)≈ 3545933.54 δxi(M)≈? 0.0007637；
  time start =20:02:57, time end =20:03:44

  count = 15, algorithm = 2, working threads = 2, time use 0.605 sec

愚工688 · 发表于 2022-8-8 14:33

本帖最后由愚工688 于 2022-8-8 06:45 编辑

以今天日期的十倍为随机数的连续偶数的素对计算：

  计算式： Xi(M)=t2*c1*M/(logM)^2 ；
  式中；相对误差动态修正系数 t2=1.358-log(M)^(0.5)*.05484;
   C1--类似拉曼扭杨系数，略作改进；（只计算√M内的素数）

  G(202208080) = 550043 ;Xi(M)≈ 549305.62 infS(m)= 408164.59 δxi(M)≈?-0.001341；
  G(202208082) = 815332 ;Xi(M)≈ 816329.21 infS(m)= 408164.61 δxi(M)≈? 0.001223；
  G(202208084) = 451378 ;Xi(M)≈ 451053.23 infS(m)= 408164.62 δxi(M)≈?-0.000720；
  G(202208086) = 413072 ;Xi(M)≈ 413203.69 infS(m)= 408164.62 δxi(M)≈? 0.000319；
  G(202208088) = 858918 ;Xi(M)≈ 858545.48 infS(m)= 408164.63 δxi(M)≈?-0.000434；
  G(202208090) = 655329 ;Xi(M)≈ 655374.07 infS(m)= 408164.62 δxi(M)≈? 0.000087；
  G(202208092) = 407926 ;Xi(M)≈ 408164.62 infS(m)= 408164.62 δxi(M)≈? 0.000571；
  G(202208094) = 908026 ;Xi(M)≈ 907032.51 infS(m)= 408164.63 δxi(M)≈?-0.001095；
  G(202208096) = 407932 ;Xi(M)≈ 408164.63 infS(m)= 408164.63 δxi(M)≈? 0.000571；
  G(202208098) = 435806 ;Xi(M)≈ 435375.61 infS(m)= 408164.63 δxi(M)≈?-0.000987；
  G(202208100) = 1113302 ;Xi(M)≈ 1112626.55 infS(m)= 408164.63  δxi(M)≈?-0.000607；
  G(202208102) = 439055 ;Xi(M)≈ 439052.87 infS(m)= 408164.65 δxi(M)≈?-0.000005；
  G(202208104) = 498772 ;Xi(M)≈ 498790.19 infS(m)= 408164.65 δxi(M)≈? 0.000061；
  G(202208106) = 817816 ;Xi(M)≈ 816329.3    infS(m)= 408164.65 δxi(M)≈?-0.001818；
  G(202208108) = 444888 ;Xi(M)≈ 444522.17 infS(m)= 408164.65 δxi(M)≈?-0.000823；
  time start =14:12:09, time end =14:12:19

		自动登录	找回密码
密码			注册