请天山草网友帮忙计算和画图

qingjiao · 发表于 2011-7-1 00:07

下面引用由天山草在 2011/06/30 07:00pm 发表的内容： 楼主，请您给出一个等比数列来，我按您的这个数列再算一算。从计算结果看，/x 大概不会收敛到零。/√x 就更不会了。

我估计│ψ(x)-x│/√x<=A，A是某个小于1的常数，x很大时可能-->1-γ。电脑中能画出的图一般不超过400个数据点，再多就看不清了。可取1.5*a^400=40*10^8，lna=(ln4+9ln10-ln1.5)/400，a=1.055759314810350 即x0=1.5，x1=1.5a，x2=1.5a^2，.... 纵坐标取(ψ(x)-x)/√x，结果请以excel文件上传，谢谢！

qingjiao · 发表于 2011-7-1 00:10

这样看不出波动，可能[ψ(x)-x]/√x更好一些。
============================================
注意这里有点笔误，应为(ψ(x)-x)/√x，即不需要取整。

qingjiao · 发表于 2011-7-1 00:18

[这个贴子最后由qingjiao在 2011/07/01 00:22am 第 1 次编辑]

另外，请将θ(x)也按21楼的等比数列整一整，纵坐标取(θ(x)-x)/√x。

天山草 · 发表于 2011-7-1 10:09

先算到 x = 14 亿  以内，因为一次直接算到 40 亿，内存不够用了。14 亿以后的数字将分段计算。

      x                         ψ(x)                [ψ(x)-x]/√x
----------------------------------------------------------------------------
2.58071756274035          .693147180559945          -1.17498660477507
2.72461660575779          .693147180559945          -1.23071527460455
2.87653936081575          .693147180559945          -1.28734985979105
3.03693322459983          1.79175946922805          -.714516623087798
3.20627054032831          1.79175946922805          -.789962123557277
3.38504998875362          1.79175946922805          -.865989106059169
3.57379805672531          1.79175946922805          -.942653533180774
3.77307058763887          1.79175946922805          -1.02001183672504
3.9834544183367          1.79175946922805          -1.09812095924939
4.20556910728141          2.484906649788          -.839041218107442
4.440068759091             2.484906649788          -.927871689905235
4.68764395080875          2.484906649788          -1.01738515738089
4.94902376558073          2.484906649788          -1.10764751036817
5.22497793972965          4.0943445622221          -.494628995671799
5.51631912954817          4.0943445622221          -.605434461389744
5.823905304487             4.0943445622221          -.716685580450556
6.14864227378556          4.0943445622221          -.828464243523283
6.4914863539858          4.0943445622221          -.940852729596049
6.85344718518478          4.0943445622221          -1.05393376654068
7.23559070431961          6.04025471127741          -.444378461227743
7.6390422842406          6.04025471127741          -.578457301055175
8.06499004781715          6.73340189183736          -.468886798867968
8.51468836683572          6.73340189183736          -.610449006940387
8.98946155599414          6.73340189183736          -.752460559504972
9.49070777287036          7.83201418050547          -.538414647506039
10.0199031353509          7.83201418050547          -.691183742217234
10.5786060686441          7.83201418050547          -.844461609330561
11.1684618946803          10.2299094533038          -.280841872708315
11.7912076774132          10.2299094533038          -.454680910933078
12.4486773382923          10.2299094533038          -.628854634546299
13.1428070569706          12.7948588107654          -9.59777546635989E-02
13.8756409731519          12.7948588107654          -.290142695384448
14.6493372063693          12.7948588107654          -.484521206805931
15.4661742114222          12.7948588107654          -.679256368714417
16.3285574881886          13.4880059913253          -.702956995660895
17.2390266655714          16.3212193353815          -.221052357618864
18.200262980441          16.3212193353815          -.440451441891949
19.2150971735986          19.265658314548          1.15344150013351E-02
20.2865178260127          19.265658314548          -.226653393633554
21.4176801598792          19.265658314548          -.465008039224358
22.6119153304212          19.265658314548          -.703704971883964
23.8727402357952          22.4011525304771          -.301186162164429
25.2038678739886          24.0105904429112          -.237688313742074
26.6092182772128          24.0105904429112          -.50376504302318
28.0929300559892          25.1092027315793          -.562938060550365
29.6593725869262          28.4764985615658          -.217198846958088
31.3131588800781          31.910485766051          .106745265611879
33.0591591637789          32.6036329466109          -7.92259536492114E-02
34.9025152269575          32.6036329466109          -.389124315877438
36.8486555611705          32.6036329466109          -.69930910803858
38.9033113469439          36.2145508592551          -.431080951664683
41.0725333315032          39.9281229259594          -.178568994267695
43.3627096475931          43.689323041653          4.95993270829798E-02
45.7805846258631          43.689323041653          -.309077714733789
48.3332786562184          47.5394706433631          -.114180607760215
51.0283091566269          49.4853807924184          -.215993247336727
53.8736127111311          53.4556727059705          -5.69411053911769E-02
56.8775684422619          53.4556727059705          -.45372871142261
60.0490226866812          57.5332101498762          -.324657399171262
63.3973150467217          61.6440840140495          -.22019310545334
66.9323058945428          62.3372311946095          -.561661534685835
70.6644054098992          66.5419238140004          -.490408931348208
74.604604237036          75.0950631321901          5.67831917145413E-02
78.7645058509905          75.0950631321901          -.413461271875405
83.1563607286175          84.9819638811219          .200197495349924
87.7931024249675          84.9819638811219          -.300021274539813
92.6883856612586          89.470600250854          -.334229222862457
97.8566265366078          94.0453112293574          -.385282922129342
103.313044981941          103.295160734428          -1.75951547502422E-03
109.073709581105          112.659337451119          .343324797841536
115.155584891171          117.386725269832          .20791431573747
121.576581401288          119.78462054263          -.162518780779145
128.355608277208          126.931392722083          -.125709558230206
135.512629046811          131.806590045284          -.31836117573835
143.06872039061          141.661044904243          -.117687463140834
151.046134210384          151.682271047003          5.17601751851393E-02
159.468363158707          156.738516852351          -.216172740439421
168.360209822365          166.950260865575          -.108663493002311
177.747859763387          174.668501817534          -.230971281700162
187.658958632799          185.054384654641          -.190130612072383
198.122693584188          200.85255200033          .193942509612373
209.169879226823          206.145856825055          -.209091044081859
220.833048371474          211.497714958531          -.628199808569807
233.146547836149          233.214597204592          4.45666104047115E-03
246.146639593891          245.274469978683          -5.55909373530279E-02
259.871607560516          257.04214618327          -.175519087991403
274.361870336755          273.811130415929          -3.32494664331903E-02
289.660100236818          293.552162833149          .228683841033523
305.811348953921          299.232335442166          -.376213156475783
322.86318023282          322.20408106635          -3.66810283229714E-02
340.865809940093          333.82628237208          -.381286819800898
359.872253944627          359.226379668706          -3.40466044911227E-02
379.938484243836          379.935295120653          -1.63611810945284E-04
401.123593795355          403.824807161446          .134871375340953
423.489970539649          421.919026071093          -7.63377347764295E-02
447.103481125995          446.23394107232          -.041123073512366
472.033664882903          476.883101705708          .223205462708174
498.353938604192          495.439510553996          -.130552258907515
526.141812753801          527.313633522776          5.10869273561777E-02
555.479119726028          543.046995819974          -.527486635350252
586.452254833408          574.751952598331          -.48314862744124
619.152430731903          625.985896373393          .274626362129624
653.675946032677          659.925737753304          .244446763944142
690.124468891466          692.466126589786          8.91373456819714E-02
728.605336410711          725.287417662375          -.12291915685413
769.231870736137          772.729662851165          .126114597921172
812.123712778668          806.123091798134          -.210564474316082
857.407174544443          856.586299960965          -2.80338827311575E-02
905.21561111052          897.231218375255          -.265378584503802
955.689813341674          951.915839002464          -.122078859817545
1008.97842250484          996.680912247175          -.387147317220337
1065.23836800213          1073.73998924419          .260482380648622
1124.63532951163          1136.75667473703          .361447278631664
1187.34422489671          1186.1619439571          -3.43109202163661E-02
1253.54972532098          1250.13121945716          -9.65529497246237E-02
1323.44679908558          1336.11453131804          .348213521190172
1397.24128579054          1378.20568593637          -.509249794116665
1475.15050251095          1465.44549186335          -.252684062397449
1557.40388377311          1553.2966925213          -.104074491971776
1644.24365721527          1656.57758795717          .304171428804091
1735.92555692286          1742.07148910152          .147510255388466
1832.71957653865          1831.90597214818          -1.90048862287555E-02
1934.91076436596          1933.73117225564          -.026816456419876
2042.80006280618          2040.11956049832          -5.93066310289073E-02
2156.70519460279          2163.24511194203          .140824061926799
2276.96159850177          2270.97208871098          -.125520143208237
2403.9234170837          2420.34949521003          .335022187576034
2537.96453967685          2521.86192521211          -.319634478646226
2679.47970342219          2663.45777056119          -.309520680597111
2828.88565573325          2841.59589252308          .238971409266258
2986.62238157377          2993.0886158665          .11832084942242
3153.15439916757          3131.14946680472          -.391874874787052
3328.9721279564          3308.98291046161          -.346450118243522
3514.593332834             3492.0432542195          -.380373733944548
3710.56464890985          3721.38542971574          .17763911399302
3917.46319129257          3923.44022439689          9.54955642074617E-02
4135.89825463381          4148.25111590113          .192080218376385
4366.51310743751          4373.84421590084          .110943601705092
4609.98688641864          4605.12250184558          -.071643708384101
4867.03659649004          4842.03726678396          -.358340634550407
5138.41922226722          5138.69574081851          3.85753172146607E-03
5424.93395730917          5408.74825070182          -.219752809460361
5727.42455766013          5727.89141131596          6.16880547211209E-03
6046.78182662323          6031.63361900884          -.194804551251428
6383.94623808342          6420.38414058405          .456046113496608
6739.91070610506          6746.77743097314          8.36416468638255E-02
7115.72350896042          7125.53960764668          .116366878211397
7512.49137619996          7481.42982679865          -.358369567052688
7931.38274785553          7933.39902661274          .022639984251752
8373.63121537458          8357.40202108066          -.17735361476014
8840.53915441842          8846.76513531008          6.62168332837958E-02
9333.48156022287          9320.73896886023          -.131897304185757
9853.91009681593          9884.57476039206          .308911379271749
10403.3573720172          10433.3758990183          .294308373796292
10983.4414508081          10985.3873120605          1.85670390356114E-02
11595.8706203647          11568.6038950711          -.253210261752411
12242.4484207857          12214.7111723308          -.250685511974878
12925.0789563298          12946.3202628995          .186837748279163
13645.7725028044          13629.846129805          -.136338282732929
14406.6514276187          14345.8100111565          -.506894748834706
15209.9564399342          15193.1561612023          -.136223646652768
16058.0531893202          16073.4095164216          .121182779180164
16953.4392323449          16945.1461224048          -6.36925322730654E-02
17898.7513876194          17877.6906270175          -.157421006076184
18896.7735009538          18854.4813077702          -.307656700809541
19950.4446434934          19907.1934311293          -.306211851792189
21062.8677669764          21038.9758015879          -.16462399106184
22237.318841604          22251.905484961          9.78169580996319E-02
23477.2565034311          23481.3619726551          2.67940971930269E-02
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26168.401142036          26150.8171273846          -.108699974612657
27627.5332593983          27573.4720384405          -.325248119819965
29168.0255838425          29180.7048934485          7.42407055456721E-02
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2635090.55398076          2635097.968658             4.56766746165002E-03
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2937145.00465933          2937210.99887979          3.85073124894663E-02
3100918.19761778          3100416.80448537          -.284729998796326
3273823.27159989          3274458.16531544          .350891956110691
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5335062.70214223          5335884.25779567          .355686371089303
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6628255.10999322          6627908.16960237          -.134758216877213
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8234910.86346747          8234882.70042992          -9.81409014762324E-03
8694083.85073872          8694615.6960872          .180373799257105
9178860.00915964          9178669.72341094          -6.28075554174835E-02
9690666.9540105          9691230.86800785          .181149041579579
10231011.9034214          10229659.3445488          -.422860269929737
10801486.1169727          10801159.5228843          -9.93725795633037E-02
11403769.5817886          11403458.5786714          -9.20959485432991E-02
12039635.9599243          12040063.0328507          .123082231987032
12710957.8116157          12711752.9896294          .223036132075971
13419712.1097747          13419418.2245055          -8.02243520926093E-02
14167986.0619679          14167731.1926018          -6.77116782938799E-02
14957983.2570258          14958043.2879693          1.55216772103907E-02
15792030.1543822          15791068.2046627          -.242065774964027
16672582.935255          16671704.8367381          -.215051165391614
17602234.7358435          17603883.8627299          .393070243791317
18583723.2838451          18583649.0423108          -1.72218805896439E-02
19619938.9607774          19619590.9568856          -7.85661143738661E-02
20713933.3138513          20714674.7393938          .16290569115759
21868928.0424589          21869373.4984655          9.52557216623501E-02
23088324.4857433          23088375.4677233          1.06101247348365E-02
24375713.6391873          24376012.5705558          6.05470266502099E-02
25734886.7297217          25732915.1344001          -.388648189059092
27169846.380493          27170534.7965577          .132070981367222
28684818.3981717          28685775.1555074          .178638781765881
30284264.2175131          30286447.935772          .396815010579855
31972894.0398172          31973704.5688582          .143343368481152
33755680.7039814          33757754.5590458          .35694801111523
35637874.3309923          35635659.7230517          -.370971850775519
37625017.7849858          37622837.4285044          -.355458700011448
39722962.9964038          39725569.5777252          .413571364659365
41937888.1953202          41937907.2925864          2.94895349547663E-03
44276316.1056843          44274765.6608798          -.233007859541754
46745133.1540637          46746705.3257766          .229949133504744
49351609.7494529          49350299.8436476          -.186461599492003
52103421.6938702          52105432.3783612          .278554902070921
55008672.7867951          55006220.5012808          -.330640043498618
58075918.6900135          58075906.6094088          -1.58522396468871E-03
61314192.1231503          61313273.7261478          -.117287020105081
64733029.4640873          64731632.1310426          -.173674862389077
68342498.832603          68343836.9922189          .161868555905253
72153229.7399361          72154923.5147973          .199401212551347
76176444.3915886          76180339.3107288          .446260139802667
80423990.7355524          80422946.9922085          -.116386044685679
84908377.3532807          84907342.2071021          -.112337928827376
89642810.2961583          89641277.3707123          -.161906133622278
94641231.9759462          94638379.2750771          -.293235159522964
99918362.2237324          99916291.003128          -.207206657157357
105489741.6383             105491441.13823          .165468769277706
111371777.351572          111376132.108759          .41264479295831
117581791.345907          117582498.515713          .065215927224869
124138071.465528          124135724.586968          -.210638678041113
131059925.272324          131062401.336255          .216285246424795
138367736.904605          138364996.667714          -.232954277761811
146083027.106264          146084526.456769          .124051862881649
154228516.603131          154225648.233769          -.230968489575132
162828193.013139          162824123.10102          -.31894825465539
171907381.487359          171909970.485803          .197462452575762
181492819.289935          181496681.513306          .28668677818896
191612734.536541          191612272.442841          -.033382423522653
202296929.323236          202295059.764627          -.131445111472926
213576867.490537          213574822.412103          -.139937097839512
225485767.28115          225482402.97343          -.224045458501782
238058699.164233          238060249.247895          .100464611853001
251332689.114274          251336123.511495          .216633708840822
265346827.648729          265350020.383344          .195999909535807
280142384.945522          280144160.049065          .106055764774811
295762932.379422          295761466.443412          -8.52399411864258E-02
312254470.835198          312257691.716311          .182272169171791
329665566.175437          329666363.239589          4.38991876419276E-02
348047492.261945          348044310.411739          -.170553437010019
367454381.951932          367452064.463284          -.120897104655018
387943386.513632          387949949.607604          .333214925521435
409574843.930839          409573087.094861          -8.68089652371198E-02
432412456.591979          432411123.937832          -6.40867660963629E-02
456523478.887008          456530014.639472          .305889124380213
481978915.264585          481984007.735833          .231960782836239
508853729.332774          508850263.647407          -.153635879773259
537227064.61906          537222571.937785          -.193832531472205
567182477.639795          567179231.436376          -.136305797510883
598808183.965426          598812952.14973          .194853930312439
632197318.006168          632201854.223731          .180412884900033
667448207.283133          667455013.11673          .263434433462926
704664661.992637          704672702.124961          .302880943871384
743956280.716413          743957205.159436          3.38927213828334E-02
785438773.178017          785431614.68832          -.25542607863419
829234300.995905          829238161.331916          .134056068644591
875471837.436676          875474649.645604          9.50443911038572E-02
924287547.227903          924287796.41384          8.1963402258849E-03
975825187.54907          975821457.303485          -.119412946096428
1030236531.38149          1030241981.64586          .169804461113604
1087681814.46391          1087697406.25278          .472764667369968
1148330207.1701          1148320256.5812          -.2936401175325
1212360312.69793          1212355583.95778          -.135809326125693
1279960693.03723          1279958899.02941          -5.01448127516178E-02
1351330424.26516          1351328612.04439          -4.92981165353855E-02
[br][br]-=-=-=-=- 以下内容由 天山草 在时添加 -=-=-=-=-
取整时，没有先加上 0.5 再取整。[br][br]-=-=-=-=- 以下内容由 天山草 在时添加 -=-=-=-=-
另外，x 的初始值是 1.5 * a ^ 10，而不是 1.5

qingjiao · 发表于 2011-7-1 11:34

请将结果以excel文件贴上来，或先压缩成rar。
这个论坛copy网页时自动插入乱码，整起来很麻烦，讨厌得很。

天山草 · 发表于 2011-7-1 12:33

不好啦，只能算到 14 亿，而不能算到 40 亿了，因为计算机内存不够，无法一次性地把 40 亿以内的素数全都调入内存中去。想了想，还没有解决的办法。
我试试把文件放到这里。时间长了，都不会了。

天山草 · 发表于 2011-7-1 12:35

上传文件成功。是 TXT 格式的文件。应该能转换成 excel 格式吧。我不会玩 excel，请楼主自行转换吧。

天山草 · 发表于 2011-7-1 12:45

下面再算 θ(x)，算完会发上来。

天山草 · 发表于 2011-7-1 13:39

下面是 θ(x) 的计算结果，也是只算到 14 亿。文件也已另行上传。
      x                         θ(x)                [θ(x)-x]/√x
----------------------------------------------------------------------------
2.58071756274035          .693147180559945          -1.17498660477507
2.72461660575779          .693147180559945          -1.23071527460455
2.87653936081575          .693147180559945          -1.28734985979105
3.03693322459983          1.79175946922805          -.714516623087798
3.20627054032831          1.79175946922805          -.789962123557277
3.38504998875362          1.79175946922805          -.865989106059169
3.57379805672531          1.79175946922805          -.942653533180774
3.77307058763887          1.79175946922805          -1.02001183672504
3.9834544183367          1.79175946922805          -1.09812095924939
4.20556910728141          1.79175946922805          -1.17703839598042
4.440068759091             1.79175946922805          -1.25682223713555
4.68764395080875          1.79175946922805          -1.33753121068253
4.94902376558073          1.79175946922805          -1.4192247255684
5.22497793972965          3.40119738166216          -.797866721174745
5.51631912954817          3.40119738166216          -.900555906997076
5.823905304487             3.40119738166216          -1.00390798166368
6.14864227378556          3.40119738166216          -1.10799902144788
6.4914863539858          3.40119738166216          -1.21290564656673
6.85344718518478          3.40119738166216          -1.31870507758026
7.23559070431961          5.34710753071747          -.702063061452698
7.6390422842406          5.34710753071747          -.829244869135642
8.06499004781715          5.34710753071747          -.957037074428159
8.51468836683572          5.34710753071747          -1.0855337437026
8.98946155599414          5.34710753071747          -1.21482946187916
9.49070777287036          5.34710753071747          -1.34501940204873
10.0199031353509          5.34710753071747          -1.47619939552873
10.5786060686441          5.34710753071747          -1.60846600240341
11.1684618946803          7.74500280351584          -1.02439738038812
11.7912076774132          7.74500280351584          -1.1783348558761
12.4486773382923          7.74500280351584          -1.3331396900974
13.1428070569706          10.3099521609774          -.781412336950961
13.8756409731519          10.3099521609774          -.957231344919706
14.6493372063693          10.3099521609774          -1.13375495987065
15.4661742114222          10.3099521609774          -1.31111311880626
16.3285574881886          10.3099521609774          -1.48943637302721
17.2390266655714          13.1431655050336          -.986481297582491
18.200262980441          13.1431655050336          -1.18539336789105
19.2150971735986          16.0876044842             -.713468840216094
20.2865178260127          16.0876044842             -.932251644625941
21.4176801598792          16.0876044842             -1.15172066874794
22.6119153304212          16.0876044842             -1.37203746120625
23.8727402357952          19.2230987001292          -.95163046314314
25.2038678739886          19.2230987001292          -1.19130631552443
26.6092182772128          19.2230987001292          -1.43185907478127
28.0929300559892          19.2230987001292          -1.67346580903274
29.6593725869262          22.5903945301157          -1.29800287282785
31.3131588800781          26.0243817346008          -.945130605056491
33.0591591637789          26.0243817346008          -1.22350136947451
34.9025152269575          26.0243817346008          -1.50277273917697
36.8486555611705          26.0243817346008          -1.78315028260671
38.9033113469439          29.635299647245          -1.48591268052286
41.0725333315032          33.3488717139493          -1.20516772691807
43.3627096475931          37.1100718296429          -.949522076877984
45.7805846258631          37.1100718296429          -1.28145723177815
48.3332786562184          40.960219431353          -1.06053399526544
51.0283091566269          40.960219431353          -1.40942343448007
53.8736127111311          44.9305113449051          -1.21842865275028
56.8775684422619          44.9305113449051          -1.58412857662079
60.0490226866812          49.0080487888108          -1.42480165654658
63.3973150467217          53.1189226529841          -1.29089155853896
66.9323058945428          53.1189226529841          -1.68842652999091
70.6644054098992          57.3236152723751          -1.58701560758758
74.604604237036          65.8767545905648          -1.01047236501951
78.7645058509905          65.8767545905648          -1.45215130364307
83.1563607286175          74.6650430508284          -.931166518299393
87.7931024249675          74.6650430508284          -1.40110387454452
92.6883856612586          79.1536794205605          -1.40584090345895
97.8566265366078          83.7283903990639          -1.42821248434921
103.313044981941          92.9782399041348          -1.01677464777247
109.073709581105          102.342416620826          -.644523045496903
115.155584891171          107.069804439538          -.753493382076475
121.576581401288          107.069804439538          -1.31566696530683
128.355608277208          111.913991525997          -1.45123283547007
135.512629046811          116.789188849198          -1.60840628841809
143.06872039061          126.643643708157          -1.37320399862883
151.046134210384          136.664869850917          -1.17015195439098
159.468363158707          141.721115656265          -1.4053798995669
168.360209822365          151.932859669489          -1.26604104339183
177.747859763387          157.086151263987          -1.54975854646883
187.658958632799          167.472034101093          -1.47362000436862
198.122693584188          183.270201446783          -1.05519377198943
209.169879226823          188.563506271507          -1.42479368983762
220.833048371474          193.915364404983          -1.81136368321314
233.146547836149          215.632246651045          -1.14703935580892
246.146639593891          226.593507136467          -1.24629079314644
259.871607560516          237.668036160494          -1.37734716353543
274.361870336755          254.437020393153          -1.20291012932648
289.660100236818          271.344839466318          -1.07613998461305
305.811348953921          277.025012075335          -1.6461128467238
322.86318023282          299.996757699519          -1.27259134172709
340.865809940093          311.618959005248          -1.58411749572644
359.872253944627          335.073146152819          -1.30725970393558
379.938484243836          352.8376226256          -1.3903574097229
401.123593795355          376.727134666393          -1.21811332546975
423.489970539649          394.82135357604          -1.3931092549611
447.103481125995          419.136268577266          -1.32265067344052
472.033664882903          449.785429210655          -1.02402153468868
498.353938604192          468.341838058943          -1.34439672321931
526.141812753801          499.522813847163          -1.16048708082456
555.479119726028          512.120681928431          -1.83966928263637
586.452254833408          543.825638706789          -1.7602101775028
619.152430731903          595.059582481851          -.968254121024652
653.675946032677          627.389985949328          -1.02811712242064
690.124468891466          659.93037478581          -1.14936585555645
728.605336410711          692.751665858399          -1.32827332092643
769.231870736137          739.09529875852          -1.08658877734616
812.123712778668          772.488727705489          -1.390809355154
857.407174544443          819.584640038334          -1.29168635292239
905.21561111052          860.229558452624          -1.49520888721292
955.689813341674          914.914179079832          -1.31899225898394
1008.97842250484          956.245265120059          -1.66013282219911
1065.23836800213          1032.61119493651          -.999668589318734
1124.63532951163          1095.62788042936          -.864975242917797
1187.34422489671          1145.03314964942          -1.22790774885881
1253.54972532098          1209.00242514949          -1.25820267835597
1323.44679908558          1294.98573701036          -.782344184433156
1397.24128579054          1331.06807844325          -1.77029841327853
1475.15050251095          1418.30788437023          -1.47998020719907
1557.40388377311          1506.15908502818          -1.29852156098806
1644.24365721527          1609.43998046405          -.858305783174936
1735.92555692286          1691.2203095417          -1.07298327848396
1832.71957653865          1781.05479258836          -1.2068314189381
1934.91076436596          1879.11879258013          -1.26835621134075
2042.80006280618          1985.50718082281          -1.26761607420094
2156.70519460279          2107.93958508595          -1.05007003273462
2276.96159850177          2208.15285260706          -1.44200175646624
2403.9234170837          2355.58434895706          -.985911562372355
2537.96453967685          2457.09677895914          -1.60521290458154
2679.47970342219          2598.69262430822          -1.56069008201099
2828.88565573325          2772.86045435655          -1.05335734878935
2986.62238157377          2924.35317769998          -1.13941820875289
3153.15439916757          3060.80459072576          -1.64461171809069
3328.9721279564          3238.63803438266          -1.56565695521652
3514.593332834             3417.62084069664          -1.63572773092176
3710.56464890985          3646.96301619287          -1.04411482748105
3917.46319129257          3844.90693700985          -1.15923742073613
4135.89825463381          4069.02468133353          -1.03984739123594
4366.51310743751          4294.61778133324          -1.08801096910026
4609.98688641864          4521.6913746586          -1.30043539961933
4867.03659649004          4758.60613959697          -1.55424322109747
5138.41922226722          5048.16872041042          -1.2590264637715
5424.93395730917          5313.93077085258          -1.50708663357369
5727.42455766013          5633.07393146673          -1.24670901018031
6046.78182662323          5936.8161391596          -1.4141485873915
6383.94623808342          6321.19721288234          -.785348417575894
6739.91070610506          6646.49189098276          -1.13790834714014
7115.72350896042          7017.89078806934          -1.15977728840129
7512.49137619995          7373.78100722131          -1.6003572208957
7931.38274785553          7821.26157066568          -1.23650646441603
8373.63121537458          8244.57141795303          -1.41037325565149
8840.53915441842          8733.93453218245          -1.13380054014342
9333.48156022287          9207.9083657326          -1.29979572913391
9853.91009681593          9767.16944628593          -.873812749571676
10403.3573720172          10311.3554643954          -.902007344240727
10983.4414508081          10858.7321484493          -1.18995251184423
11595.8706203647          11437.2759026254          -1.47277715086192
12242.4484207857          12075.556337787          -1.50834814560303
12925.0789563298          12802.4380405369          -1.07874496695646
13645.7725028044          13485.9639074425          -1.36804716670014
14406.6514276187          14201.927788794          -1.70563644827495
15209.9564399342          15046.8760435669          -1.32232367362129
16058.0531893202          15925.5199608738          -1.04587150631065
16953.4392323449          16789.773322441          -1.25698276326443
17898.7513876194          17717.4426297305          -1.35521254986394
18896.7735009538          18689.3133295573          -1.50917952171695
19950.4446434934          19735.9923666947          -1.51828874175533
21062.8677669764          20867.7747371533          -1.34425915472714
22237.318841604          22075.7004742204          -1.08380089123427
23477.2565034311          23300.1396820777          -1.155942248482
24786.3322396893          24601.6731901196          -1.17290938843749
26168.401142036          25961.1712951718          -1.28104301205817
27627.5332593983          27378.732456027          -1.4968584148224
29168.0255838425          28978.282367865          -1.11099662871515
30794.4147047683          30514.1465461163          -1.59712086428019
32511.490168692          32275.7948993321          -1.30717107103528
34324.3085839617          34140.3721203054          -.992811807685079
36238.2085119424          35993.6499883243          -1.28469325553495
38258.8261885229          38014.319030912          -1.25004531372513
40392.1121222432          40119.5513892463          -1.35617272870932
42644.3486179223          42469.7594412415          -.845447364058011
45022.1682773913          44821.1671069296          -.947295300851309
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天山草 · 发表于 2011-7-1 13:48

下面引用由wangyangkee在 2011/06/30 07:26pm 发表的内容：
借用宝楼：关于结论验算，求助天山草或诸师长------
http://www.mathchina.com/cgi-bin/topic.cgi?forum=5&topic=7469

您的文章我下载了，但是要看明白，估计很困难，因为数论这东西很艰深。既然您对素数间距有研究，我只提个我最关心的问题：据网友说，以及本人的小范围验证，我觉得——间距为 2 的孪生素数的个数，跟间距为 4 的那些素数的个数，是一样多的。
这个猜想有可能是真的吗？还是肯定是错的？

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