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.
======================================================================================== 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 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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 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