计算哥德巴赫猜想的好公式

qdxy

      计算哥德巴赫猜想的好公式
   比N/LnN好的,N数内素数个数的最大下界公式:  
{2/(1+√(1-(4/LnN))}{N/LnN}
还有:{(1-√(1-(4/LnN))/2}N
其他公式:
N数内素数个数与数的比例:{(1-√(1-(4/LnN))/2}
N数内合数个数与数的比例:{(1+√(1-(4/LnN))/2}
两种比例的和等于1。有(0.5-(..)+0.5+(..)=1)
两种比例的积等于1/LnN.
{(1-√(1-(4/LnN))/2}{(1+√(1-(4/LnN))/2}
==(0.25){1-1+(4/LnN)}==1/LnN
由N数内素数个数与数的比例:{(1-√(1-(4/LnN))/2}可推出
N数内素数个数约为0.5)N{1-√(1-(4/LnN)}。
减小了两倍N数内素数个数的邻近数{N-[2π(N)]}，数内的素数个数约为:
N-N{1-[√(1-(4/LnN)]}==N[√(1-(4/LnN)]。
  用此公式简化一下liudan提供的最新的哥德巴赫猜想的好公式
计算公式如下：
h≈1.32×Π[(k-1)/(k-2),其中k是整除N的奇素数。
N < 1000的较小偶数时：
D(N)≈(0.5)N{√[0.5+(4h/(LnN)^2)]-√0.5}
N > 1000的较大偶数时：
```````N`````````4`````4h``````````````4
D(N)≈---{√[1-(---)+(-------)]-√[1-(---)]}
.......2........LnN...(LnN)^2.........LnN
检验数据:
N，````````````实际D(N)，````````计算 D(N)，                     
2^37，.........299422268，.........299516484，   
2^40，.........2036739786，........2036880234，   
10^6，.........10804，.............10801，      
10^10,.........36400976，..........36373303，      
2310，.........228，...............228，         
223092870，....4089694，...........4028109，     
21000，........1092，..............1085，         
21002，........340，...............354，         
很准,欢迎电脑高手继续提供验证数,
    青岛 王新宇
     2009.5.21

qdxy

==============================================================================
---- N --- D(N) -- GSHA(N) ----------- GS2Li(N) ----------- XinYu(N) ---------
==============================================================================
1*10^3 ``````28 ``````0.00 -1.000000 `````24.05 -0.141157 `````26.30 -0.060726
2*10^3 ``````37 `````42.08 +0.137165 `````39.35 +0.063555 `````41.74 +0.128094
3*10^3 `````104 ````111.50 +0.072068 ````105.68 +0.016163 ````105.90 +0.018270
4*10^3 ``````65 `````68.38 +0.052011 `````65.32 +0.004894 `````67.93 +0.045014
5*10^3 ``````76 `````80.31 +0.056741 `````77.11 +0.014660 `````79.81 +0.050109
6*10^3 `````178 ````183.45 +0.030607 ````176.81 -0.006686 ````175.86 -0.012005
7*10^3 `````119 ````123.27 +0.035908 ````119.16 +0.001335 ````121.68 +0.022525
8*10^3 `````106 ````113.40 +0.069795 ````109.87 +0.036504 ````112.77 +0.063840
9*10^3 `````242 ````247.58 +0.023054 ````240.34 -0.006876 ````238.37 -0.014980
1*10^4 `````127 ````133.94 +0.054657 ````130.23 +0.025460 ````133.24 +0.049104
2*10^4 `````231 ````226.88 -0.017826 ````222.52 -0.036718 ````225.87 -0.022205
3*10^4 `````602 ````621.45 +0.032303 ````611.80 +0.016283 ````604.14 +0.003554
4*10^4 `````389 ````389.36 +0.000921 ````384.18 -0.012402 ````387.87 -0.002896
5*10^4 `````450 ````464.43 +0.032062 ````458.94 +0.019877 ````462.74 +0.028312
6*10^4 ````1084 ```1073.65 -0.009547 ```1062.17 -0.020143 ```1047.93 -0.033277
7*10^4 `````719 ````728.53 +0.013251 ````721.36 +0.003284 ````723.08 +0.005678
8*10^4 `````652 ````675.65 +0.036270 ````669.47 +0.026794 ````673.42 +0.032859
9*10^4 ````1471 ```1485.44 +0.009816 ```1472.71 +0.001162 ```1452.70 -0.012441
1*10^5 `````810 ````808.53 -0.001821 ````801.99 -0.009891 ````805.98 -0.004961
2*10^5 ````1417 ```1420.51 +0.002474 ```1412.74 -0.003008 ```1416.60 -0.000280
3*10^5 ````3915 ```3965.34 +0.012859 ```3948.23 +0.008487 ```3895.90 -0.004879
4*10^5 ````2487 ```2515.75 +0.011559 ```2506.61 +0.007883 ```2509.67 +0.009114
5*10^5 ````3052 ```3028.64 -0.007655 ```3019.04 -0.010801 ```3021.60 -0.009961
6*10^5 ````6993 ```7052.50 +0.008508 ```7032.54 +0.005655 ```6943.16 -0.007128
7*10^5 ````4878 ```4814.00 -0.013119 ```4801.65 -0.015651 ```4790.76 -0.017884
8*10^5 ````4433 ```4487.00 +0.012182 ```4476.44 +0.009800 ```4477.39 +0.010014
9*10^5 ````9853 ```9907.55 +0.005536 ```9885.95 +0.003345 ```9764.05 -0.009028
==============================================================================
---- N --- D(N) -- GSHA(N) ----------- GS2Li(N) ----------- XinYu(N) ---------
==============================================================================
1*10^6 ````5402 ```5413.13 +0.002060 ```5402.13 +0.000023 ```5401.96 -0.000008
2*10^6 ````9720 ```9733.67 +0.001406 ```9721.54 +0.000158 ```9715.72 -0.000441
3*10^6 ```27502 ``27509.29 +0.000265 ``27484.36 -0.000641 ``27179.81 -0.011715
4*10^6 ```17630 ``17597.91 -0.001820 ``17585.45 -0.002527 ``17568.74 -0.003475
5*10^6 ```21290 ``21316.63 +0.001251 ``21304.37 +0.000675 ``21282.45 -0.000355
6*10^6 ```49783 ``49880.78 +0.001964 ``49856.93 +0.001485 ``49341.26 -0.008873
7*10^6 ```34284 ``34185.51 -0.002873 ``34171.71 -0.003275 ``34070.53 -0.006227
8*10^6 ```31753 ``31972.11 +0.006900 ``31961.09 +0.006553 ``31924.24 +0.005393
9*10^6 ```70619 ``70804.55 +0.002627 ``70783.57 +0.002330 ``70081.43 -0.007612
1*10^7 ```38807 ``38785.50 -0.000554 ``38775.57 -0.000810 ``38729.24 -0.002004
2*10^7 ```70730 ``70874.44 +0.002042 ``70871.20 +0.001996 ``70780.99 +0.000721
3*10^7 ``202166 `202057.46 -0.000537 `202065.68 -0.000496 `200301.65 -0.009222
4*10^7 ``130164 `130021.56 -0.001094 `130033.16 -0.001005 `129865.09 -0.002296
5*10^7 ``158467 `158194.18 -0.001722 `158213.27 -0.001601 `158009.16 -0.002889
6*10^7 ``371226 `371475.95 +0.000673 `371529.02 +0.000816 `368518.47 -0.007293
7*10^7 ``255175 `255329.72 +0.000606 `255370.42 +0.000766 `254698.13 -0.001869
8*10^7 ``239209 `239388.57 +0.000751 `239429.79 +0.000923 `239124.60 -0.000353
9*10^7 ``531538 `531281.28 -0.000483 `531378.21 -0.000301 `527255.86 -0.008056
1*10^8 ``291400 `291577.49 +0.000609 `291633.12 +0.000800 `291264.66 -0.000464
2*10^8 ``538290 `539158.96 +0.001614 `539282.87 +0.001844 `538626.48 +0.000625
3*10^8 `1547388 1547090.01 -0.000193 1547465.21 +0.000050 1536902.61 -0.006776
4*10^8 ``999700 `999935.93 +0.000236 1000184.03 +0.000484 `999023.96 -0.000676
5*10^8 `1219610 1220647.30 +0.000851 1220953.48 +0.001102 1219561.50 -0.000040
6*10^8 `2874881 2873970.40 -0.000317 2874695.07 -0.000065 2856441.23 -0.006414
7*10^8 `1979689 1979741.63 +0.000027 1980241.91 +0.000279 1975992.20 -0.001867
8*10^8 `1859646 1859623.67 -0.000012 1860093.79 +0.000241 1858052.76 -0.000857
9*10^8 `4132595 4133849.32 +0.000304 4134893.67 +0.000556 4109709.26 -0.005538
1*10^9 `2274205 2272009.33 -0.000965 2272582.52 -0.000713 2270135.71 -0.001789
==============================================================================  
   青岛 王新宇
    2009.5.21

zhaojunjie

00000000000000

qdxy

   我在论述哈代的哥解渐近公式解大于一时，指出：只要{一半的平方根内素数个数}大于一，N/{(lnN)平方数}大于一。由：r(N)==(大于1的数)(大于1的数)(大于1的数)==大于1的数， 可证明偶数N表示为两个素数之和的表示法个数r(N)大于1。
   现补充点内容：
只要{一半的平方根内素数个数}大于一，r(N)》1。
换句话说就是：
偶数选取大于第二个素数的平方数的数后，偶数一定有哥解。
若第二个素数选奇数型素数5，偶数选取大于25，满足条件。
若第二个素数选常规素数3，偶数选取大于9，满足条件。
若第二个素数选素数筛选法解的数2，偶数选取大于4，满足条件。
偶数选取大于6，满足偶数选取大于4，同样满足条件。
青岛 王新宇
2009.5.27

申一言

啊!
  万里长征只是走了一步,而且还是不精确的一步!(偏西了?不能到延安!)

qdxy

  重写一点
N数内素数个数约为0.5)N{1-√(1-(4/LnN)}。继续推出：
减小了两倍N数内素数个数的邻近数{N-[2π(N)]}，邻近数为；
N-N{1-[√(1-(4/LnN)]}==N[√(1-(4/LnN)]。
补充liudan的原公式：
`````````````(k-1)
设h≈1.32×Π───   
.............(k-2)  
``{√[(F-s)^2+4h(N/lnN)^2]}-(F-s)
x=────────────────
................2
公式中的(F-s)=N-s-s=N-2s={N-[2π(N)]}.
即F-s)=N[√(1-(4/LnN)]
有：√[(F-s)^2+4h(N/lnN)^2]
==N√{√[(1-(4/LnN)+4h/((lnN)^2)]}
得到满足哥德巴赫猜想的素数个数的公式为:  
```````N`````````4`````4h``````````````4
D(N)≈---{[√1-(---)+(-------)]-[√1-(---)]
.......2........LnN...(LnN)^2.........LnN
N > 1000的较大偶数时，新公式误差很小，
给偶数N|实际数D|GSHA的解..|GS2Li的解|新公式解XinYu
10^3```|28`````| `````````|24.05````|26.30
10^4```|127````|133.94 ```|130.23```|133.24
10^5```|1417```|1420.51```|1412.74``|1416.60
10^6```|5402```|5413.13```|5402.13``|5401.96
10^7``|38807 ..|38785.50..|38775.57.|38729.24
10^8``|291400..|291577.490|291633.12|291264.66
10^9``|2274205.|2272009.33|2272582.52|2270135.71
新公式解很不错啊。
    青岛 王新宇
        2009.5.28