Thomas R. Nicely
Last updated 1000 GMT 18 January 2010.
This is an extended table of values of pi_3b(x), the counts of prime triplets (q, q+4, q+6) such that q <= x, for 1e16 <= x <= 2e16. Also provided are the values of the related functions delta_3b(x), S_3b(x), and F_3b(x); see Enumeration of the prime triplets (q, q+4, q+6) to 1e16 for an explanation of these symbols and additional notes.
Complete counts and reciprocal sums of the prime constellations from Nicely's computations (1993-2009), including the prime triplets, are also available. These data files are very large (over 60MB each, even for the zipped versions), including more than two million data points from 0 to 2e16 at intervals of 1e10 or better.
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x pi_3b(x) delta_3b(x) S_3b(x) F_3b(x)
========================================================================================
1.000000e+16 624025508307 -320804.2443 0.83395442856513697017 0.837113212460369
1.000100e+16 624082675203 -327832.3293 0.83395444571434839020 0.837113212462478
1.000200e+16 624139834121 -327347.8187 0.83395446285945195960 0.837113212462332
1.000300e+16 624196987917 -322206.6608 0.83395448000130528892 0.837113212460790
1.000400e+16 624254141616 -317433.8041 0.83395449714141592912 0.837113212459359
1.000500e+16 624311291766 -309577.1970 0.83395451427874903241 0.837113212457003
1.000600e+16 624368446951 -307220.7880 0.83395453141587911476 0.837113212456296
1.000700e+16 624425598621 -301814.5255 0.83395454855024282930 0.837113212454676
1.000800e+16 624482752290 -298872.3580 0.83395456568349359900 0.837113212453794
1.000900e+16 624539904887 -295323.2340 0.83395458281471108258 0.837113212452730
1.001000e+16 624597055249 -290004.1020 0.83395459994354726013 0.837113212451135
1.001100e+16 624654218349 -297887.9105 0.83395461707448984065 0.837113212453498
1.001200e+16 624711363485 -288272.6080 0.83395463419833817924 0.837113212450617
1.001300e+16 624768514511 -285012.1430 0.83395465132224114966 0.837113212449640
1.001400e+16 624825682934 -299613.4640 0.83395466844964620373 0.837113212454015
1.001500e+16 624882831002 -294324.5197 0.83395468556924323907 0.837113212452430
1.001600e+16 624939977250 -287680.2585 0.83395470268658583668 0.837113212450440
1.001700e+16 624997133237 -291239.6291 0.83395471980513640452 0.837113212451506
1.001800e+16 625054290987 -297026.5800 0.83395473692250600194 0.837113212453239
1.001900e+16 625111444157 -298698.0597 0.83395475403679554381 0.837113212453740
1.002000e+16 625168594897 -298404.0170 0.83395477114864947210 0.837113212453652
1.002100e+16 625225744968 -297905.4005 0.83395478825859536102 0.837113212453502
1.002200e+16 625282894227 -297059.1586 0.83395480536659083876 0.837113212453249
1.002300e+16 625340030259 -283450.2402 0.83395482246892023402 0.837113212449175
1.002400e+16 625397177336 -281350.5937 0.83395483957284925305 0.837113212448547
1.002500e+16 625454330946 -286248.1680 0.83395485667702707122 0.837113212450013
1.002600e+16 625511487982 -295035.9116 0.83395487378052397431 0.837113212452643
1.002700e+16 625568639434 -298703.7732 0.83395489088064425642 0.837113212453740
1.002800e+16 625625768955 -280904.7015 0.83395490797249792311 0.837113212448415
1.002900e+16 625682913517 -278610.6453 0.83395492506714682240 0.837113212447729
1.003000e+16 625740057931 -276632.5531 0.83395494216004699018 0.837113212447137
1.003100e+16 625797204841 -277614.3738 0.83395495925198967536 0.837113212447431
1.003200e+16 625854344380 -271689.0561 0.83395497634002402914 0.837113212445659
1.003300e+16 625911496372 -278680.5487 0.83395499343007903669 0.837113212447749
1.003400e+16 625968637100 -274871.8004 0.83395501051506278718 0.837113212446611
1.003500e+16 626025775293 -268991.7599 0.83395502759758605464 0.837113212444853
1.003600e+16 626082920191 -270280.3760 0.83395504468041149767 0.837113212445238
1.003700e+16 626140061957 -268900.5974 0.83395506176059862705 0.837113212444826
1.003800e+16 626197210101 -274362.3731 0.83395507884099035927 0.837113212446458
1.003900e+16 626254349560 -271602.6518 0.83395509591708501720 0.837113212445633
1.004000e+16 626311497878 -278165.3823 0.83395511299412609998 0.837113212447594
1.004100e+16 626368630773 -269768.5134 0.83395513006485816989 0.837113212445085
1.004200e+16 626425769170 -267336.9940 0.83395514713553406530 0.837113212444359
1.004300e+16 626482908114 -265915.7730 0.83395516420467341361 0.837113212443934
1.004400e+16 626540050623 -268522.7991 0.83395518127317820475 0.837113212444713
1.004500e+16 626597191816 -270277.0213 0.83395519833959053883 0.837113212445237
1.004600e+16 626654338588 -278073.3885 0.83395521540597010487 0.837113212447565
1.004700e+16 626711467961 -268933.8494 0.83395523246545545981 0.837113212444836
1.004800e+16 626768613613 -276536.3532 0.83395524952810339039 0.837113212447106
1.004900e+16 626825741194 -266530.8485 0.83395526658365830456 0.837113212444119
1.005000e+16 626882867022 -255235.2845 0.83395528363699277249 0.837113212440747
1.005100e+16 626939991393 -242945.6100 0.83395530068819540755 0.837113212437079
1.005200e+16 626997122101 -237455.7739 0.83395531773959306894 0.837113212435440
1.005300e+16 627054264169 -243788.7253 0.83395533479268465000 0.837113212437330
1.005400e+16 627111399400 -243747.4131 0.83395535184203993169 0.837113212437317
1.005500e+16 627168531598 -241135.7862 0.83395536888879465380 0.837113212436538
1.005600e+16 627225657982 -233172.7937 0.83395538593211928888 0.837113212434163
1.005700e+16 627282792813 -234119.3845 0.83395540297626922841 0.837113212434445
1.005800e+16 627339921802 -229686.5077 0.83395542001698189708 0.837113212433123
1.005900e+16 627397042797 -217722.1123 0.83395543705361599236 0.837113212429554
1.006000e+16 627454177195 -219623.1473 0.83395545409255373817 0.837113212430121
1.006100e+16 627511308766 -219159.5618 0.83395547112895476347 0.837113212429983
1.006200e+16 627568444460 -223281.3048 0.83395548816489185672 0.837113212431212
1.006300e+16 627625580227 -227938.3254 0.83395550519915792254 0.837113212432600
1.006400e+16 627682710768 -227831.5727 0.83395552223017333395 0.837113212432568
1.006500e+16 627739826740 -213617.9956 0.83395553925515382508 0.837113212428332
1.006600e+16 627796970548 -227702.5435 0.83395555628673924316 0.837113212432529
1.006700e+16 627854093222 -221115.1653 0.83395557331033467017 0.837113212430566
1.006800e+16 627911219285 -218378.8101 0.83395559033324890810 0.837113212429751
1.006900e+16 627968345522 -216278.4272 0.83395560735452429810 0.837113212429125
1.007000e+16 628025472693 -215573.9655 0.83395562437438751939 0.837113212428915
1.007100e+16 628082597157 -212624.3744 0.83395564139175427488 0.837113212428037
1.007200e+16 628139727041 -215556.6029 0.83395565840904581095 0.837113212428910
1.007300e+16 628196860060 -222085.6002 0.83395567542558167464 0.837113212430855
1.007400e+16 628253979786 -215783.3155 0.83395569243646944571 0.837113212428978
1.007500e+16 628311089903 -200333.6981 0.83395570944280745317 0.837113212424377
1.007600e+16 628368224389 -209714.6969 0.83395572645471331624 0.837113212427170
1.007700e+16 628425347184 -207866.2615 0.83395574346145025160 0.837113212426620
1.007800e+16 628482471764 -208264.3408 0.83395576046703095122 0.837113212426738
1.007900e+16 628539597014 -209793.8842 0.83395577747112376626 0.837113212427194
1.008000e+16 628596725995 -215515.8409 0.83395579447464010765 0.837113212428897
1.008100e+16 628653849353 -216076.1602 0.83395581147479632994 0.837113212429063
1.008200e+16 628710970461 -214847.7913 0.83395582847259662038 0.837113212428698
1.008300e+16 628768103895 -226406.6835 0.83395584547237857823 0.837113212432137
1.008400e+16 628825223896 -224993.7861 0.83395586246647822995 0.837113212431717
1.008500e+16 628882355705 -235850.0485 0.83395587946240532644 0.837113212434946
1.008600e+16 628939472696 -232349.4198 0.83395589645223948639 0.837113212433905
1.008700e+16 628996609168 -248790.8494 0.83395591344618348888 0.837113212438795
1.008800e+16 629053738345 -258398.2868 0.83395593043627339689 0.837113212441652
1.008900e+16 629110851573 -252517.6811 0.83395594741993636793 0.837113212439904
1.009000e+16 629167978277 -260573.9817 0.83395596440592310735 0.837113212442299
1.009100e+16 629225095061 -259171.1381 0.83395598138727709959 0.837113212441882
1.009200e+16 629282212556 -258940.0996 0.83395599836715966923 0.837113212441814
1.009300e+16 629339323613 -252731.8155 0.83395601534344608190 0.837113212439968
1.009400e+16 629396435746 -248060.2353 0.83395603231837051159 0.837113212438580
1.009500e+16 629453548194 -244164.3084 0.83395604929170692070 0.837113212437422
1.009600e+16 629510670010 -250096.9841 0.83395606626614585278 0.837113212439185
1.009700e+16 629567773802 -238466.2120 0.83395608323354812411 0.837113212435729
1.009800e+16 629624892704 -242405.9414 0.83395610020375908246 0.837113212436899
1.009900e+16 629681999367 -234567.1218 0.83395611716865373850 0.837113212434571
1.010000e+16 629739119508 -240666.7027 0.83395613413587220366 0.837113212436383
1.010100e+16 629796228787 -236364.6334 0.83395615109818469355 0.837113212435105
1.010200e+16 629853341787 -236243.8636 0.83395616805992302605 0.837113212435069
1.010300e+16 629910461601 -243397.3427 0.83395618502200585077 0.837113212437193
1.010400e+16 629967581138 -250734.0201 0.83395620198232762174 0.837113212439372
1.010500e+16 630024685599 -243454.8455 0.83395621893649494590 0.837113212437210
1.010600e+16 630081795232 -241807.7682 0.83395623589051994246 0.837113212436721
1.010700e+16 630138901283 -237038.7379 0.83395625284180413977 0.837113212435306
1.010800e+16 630196009804 -235199.7041 0.83395626979214430313 0.837113212434760
1.010900e+16 630253121920 -237415.6164 0.83395628674187454579 0.837113212435418
1.011000e+16 630310222941 -228996.4242 0.83395630368663570435 0.837113212432919
1.011100e+16 630367327570 -224645.0773 0.83395632063079151831 0.837113212431628
1.011200e+16 630424449796 -238350.5251 0.83395633757849249636 0.837113212435694
1.011300e+16 630481569918 -250411.7172 0.83395635452389338625 0.837113212439273
1.011400e+16 630538677128 -250020.6034 0.83395637146378859403 0.837113212439157
1.011500e+16 630595788418 -254169.1331 0.83395638840321913199 0.837113212440387
1.011600e+16 630652910567 -269636.2560 0.83395640534419561696 0.837113212444974
1.011700e+16 630710027850 -280696.9217 0.83395642228205441068 0.837113212448254
1.011800e+16 630767128692 -275776.0800 0.83395643921336409359 0.837113212446795
1.011900e+16 630824229515 -271295.6804 0.83395645614299487072 0.837113212445467
1.012000e+16 630881334933 -271869.6726 0.83395647307231484341 0.837113212445637
1.012100e+16 630938447991 -280543.0063 0.83395649000222679237 0.837113212448208
1.012200e+16 630995537388 -266014.6312 0.83395650692345295213 0.837113212443902
1.012300e+16 631052639873 -265033.4970 0.83395652384688650283 0.837113212443611
1.012400e+16 631109743696 -265849.5534 0.83395654076904480007 0.837113212443853
1.012500e+16 631166855526 -275131.7501 0.83395655769190414222 0.837113212446603
1.012600e+16 631223976597 -294114.0368 0.83395657461583013568 0.837113212452227
1.012700e+16 631281090205 -306092.3633 0.83395659153587388601 0.837113212455776
1.012800e+16 631338184941 -299657.6794 0.83395660844865671093 0.837113212453869
1.012900e+16 631395290850 -304854.9348 0.83395662536307907971 0.837113212455409
1.013000e+16 631452378587 -292339.0792 0.83395664227044974280 0.837113212451702
1.013100e+16 631509471723 -285681.0625 0.83395665917775035843 0.837113212449730
1.013200e+16 631566579712 -294334.8345 0.83395667608778027840 0.837113212452293
1.013300e+16 631623682481 -298227.3449 0.83395669299459566354 0.837113212453445
1.013400e+16 631680778164 -295492.5436 0.83395670989764489493 0.837113212452636
1.013500e+16 631737886578 -305947.3804 0.83395672680279475891 0.837113212455731
1.013600e+16 631794987357 -309225.8052 0.83395674370401698609 0.837113212456701
1.013700e+16 631852094133 -318959.7677 0.83395676060534652753 0.837113212459582
1.013800e+16 631909198568 -326811.2178 0.83395677750431622336 0.837113212461905
1.013900e+16 631966291798 -323916.1055 0.83395679439830350209 0.837113212461049
1.014000e+16 632023393161 -329612.3805 0.83395681129303098680 0.837113212462734
1.014100e+16 632080477991 -319233.9929 0.83395682818120116102 0.837113212459664
1.014200e+16 632137565106 -311598.8923 0.83395684506838200930 0.837113212457405
1.014300e+16 632194675684 -327885.0289 0.83395686196083786964 0.837113212462222
1.014400e+16 632251761805 -320172.3525 0.83395687884439517023 0.837113212459941
1.014500e+16 632308862509 -327500.8129 0.83395689573060071102 0.837113212462108
1.014600e+16 632365944927 -317001.3603 0.83395691260973467586 0.837113212459004
1.014700e+16 632423049074 -328688.9445 0.83395692949362967214 0.837113212462459
1.014800e+16 632480136928 -324541.5154 0.83395694637104410430 0.837113212461233
1.014900e+16 632537211787 -307857.0231 0.83395696324295401307 0.837113212456301
1.015000e+16 632594301652 -306636.4176 0.83395698011763704913 0.837113212455940
1.015100e+16 632651387018 -301374.6488 0.83395699698932783174 0.837113212454385
1.015200e+16 632708470265 -294451.6666 0.83395701385873043584 0.837113212452339
1.015300e+16 632765573554 -308028.4213 0.83395703073239371389 0.837113212456351
1.015400e+16 632822677341 -322560.8627 0.83395704760454232323 0.837113212460645
1.015500e+16 632879764514 -320936.9409 0.83395706447012089279 0.837113212460165
1.015600e+16 632936855814 -323897.6059 0.83395708133525805407 0.837113212461039
1.015700e+16 632993942457 -322658.8079 0.83395709819735907248 0.837113212460673
1.015800e+16 633051037758 -330535.4968 0.83395711506035726320 0.837113212463000
1.015900e+16 633108127012 -332822.6227 0.83395713191990955204 0.837113212463675
1.016000e+16 633165220744 -340045.1358 0.83395714877912469767 0.837113212465808
1.016100e+16 633222305132 -338380.9861 0.83395716563392167819 0.837113212465317
1.016200e+16 633279385051 -332705.1237 0.83395718248574059056 0.837113212463641
1.016300e+16 633336466076 -328592.4987 0.83395719933622775244 0.837113212462427
1.016400e+16 633393545061 -322897.0613 0.83395721618445470684 0.837113212460746
1.016500e+16 633450633652 -327264.7617 0.83395723303385932835 0.837113212462035
1.016600e+16 633507712539 -322385.5499 0.83395724987874253486 0.837113212460595
1.016700e+16 633564799207 -325744.3761 0.83395726672426499241 0.837113212461586
1.016800e+16 633621877120 -320805.1905 0.83395728356554741332 0.837113212460129
1.016900e+16 633678962031 -323320.9432 0.83395730040723826287 0.837113212460871
1.017000e+16 633736056793 -336144.5845 0.83395731725017899605 0.837113212464654
1.017100e+16 633793142119 -339989.0645 0.83395733408868039329 0.837113212465788
1.017200e+16 633850238194 -355039.3336 0.83395735092869668123 0.837113212470227
1.017300e+16 633907321768 -358045.3417 0.83395736776337074026 0.837113212471114
1.017400e+16 633964399142 -355308.0393 0.83395738459456177559 0.837113212470306
1.017500e+16 634021485700 -362211.3766 0.83395740142680660772 0.837113212472342
1.017600e+16 634078565522 -362835.3038 0.83395741825541119650 0.837113212472526
1.017700e+16 634135641278 -359849.7711 0.83395743508116350916 0.837113212471646
1.017800e+16 634192725126 -365412.7289 0.83395745190764784097 0.837113212473286
1.017900e+16 634249795124 -357582.1273 0.83395746872839698925 0.837113212470978
1.018000e+16 634306888890 -373975.9168 0.83395748555449839053 0.837113212475809
1.018100e+16 634363962722 -370892.0477 0.83395750237307281722 0.837113212474901
1.018200e+16 634421034240 -365950.4701 0.83395751918931342579 0.837113212473444
1.018300e+16 634478105869 -361576.1345 0.83395753600393537134 0.837113212472156
1.018400e+16 634535192182 -372341.9912 0.83395755282123193974 0.837113212475327
1.018500e+16 634592273714 -378782.9905 0.83395756963546892864 0.837113212477225
1.018600e+16 634649348846 -379280.0828 0.83395758644617011722 0.837113212477371
1.018700e+16 634706424638 -380893.2184 0.83395760325541534426 0.837113212477846
1.018800e+16 634763494393 -376925.3478 0.83395762006123271479 0.837113212476678
1.018900e+16 634820573538 -382803.4213 0.83395763686816549730 0.837113212478409
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========================================================================================