Counts of twin-prime pairs and Brun's constant to 5e15

Counts of twin-prime pairs and Brun's constant to 5e15

Thomas R. Nicely

http://www.trnicely.net
Current e-mail address

Copyright © 2005 Thomas R. Nicely. All rights reserved. This document may be reproduced and distributed for educational and non-profit purposes.

Last updated 2302 EDT 7 August 2005.

This is a table of the values of pi_2(x), the count of twin-prime pairs <= x. The values in this table were obtained by the author's direct and explicit generation and enumeration of the twin primes. Also given are the values of the related functions delta_2(x), S_2(x), and F_2(x).

The domain of this table consists of each decade from 10 through 1e12, then each 1e12 to 5e15.

See also on this site Counts of twin-prime pairs and Brun's constant beyond 5e15. The most extensive counts of pi_2(x) of which I am aware have been compiled by Tomás Oliveira e Silva (but do not include the values of the related functions delta_2(x), S_2(x), and F_2(x)).

Symbols are defined as follows; for further details, see the papers A new error analysis for Brun's constant and Enumeration to 1.6e15 of the twin primes and Brun's constant.

pi_2(x) = Number of twin-prime pairs <= x. The convention is followed
          that a twin-prime pair is <= x if its smaller member is <= x.
          Thus, pi_2(30) = 5, since (29, 31) is counted, as well as
          (3, 5), (5, 7), (11, 13), and (17, 19).
delta_2(x) = L_2(x) - pi_2(x). Referred to as r_3(x) in some papers.
             Positive values indicate a deficit of twin primes (compared
             to theory); negative values indicate a surplus of twin primes.
L_2(x) = integral(2*c_2/(ln t)^2, t, 2, x), the Hardy-Littlewood integral
         approximation for pi_2(x). Here c_2 is the twin-primes constant,
         c_2 = 0.66016 18158 46869 57392 78121 10014 55577 84326 23...
S_2(x) = Sum of the reciprocals of all the twin-prime pairs <= x. Referred
         to as B(x) in some papers. Note that S_2(30) includes the term
         1/31; although counterintuitive, this is the convention dictated
         by prior usage in the literature, as with pi_2(30).
F_2(x) = First order extrapolation (referred to as B*(x) in some papers) of
         Brun's constant B_2 (often referred to as simply B) from S_2(x).
         B_2 ~ F_2(x) = S_2(x) + 4c_2/ln(x) .

===============================================================================
   x             pi_2(x)    delta_2(x)         S_2(x)               F_2(x)
===============================================================================
1.000e01               2        2.8362  0.8761904761904761905  2.0230090113326
2.000e01               4        2.6932  1.1554777523817771496  2.0369474640442
3.000e01               5        2.9780  1.2222185755185958370  1.9986061141027
4.000e01               5        4.0262  1.2222185755185958370  1.9380585199338
5.000e01               6        3.9391  1.2698646333745232335  1.9448727454749
6.000e01               7        3.7623  1.3032072285398469345  1.9481571645448
7.000e01               7        4.5206  1.3032072285398469345  1.9247560624074
8.000e01               8        4.2294  1.3309903657190867570  1.9335990405484
9.000e01               8        4.8986  1.3309903657190867570  1.9178256891770
1.000e02               8        5.5355  1.3309903657190867570  1.9043996332901
2.000e02              15        3.8602  1.4285773116927212820  1.9269708734034
3.000e02              19        4.2075  1.4601826850603106058  1.9231469153971
4.000e02              21        6.0620  1.4723401812161230710  1.9130750370473
5.000e02              24        6.6031  1.4860607920209119267  1.9109704921286
6.000e02              27        6.9214  1.4967343490285787439  1.9095335207741
7.000e02              30        7.0701  1.5061161857996046986  1.9092019561361
8.000e02              30       10.0838  1.5061161857996046986  1.9011499395863
9.000e02              35        7.9864  1.5180324635595909885  1.9062262328517
1.000e03              35       10.7955  1.5180324635595909885  1.9003053086070
2.000e03              61        9.6674  1.5548814828536703983  1.9022938167763
3.000e03              82       10.2875  1.5722345783232268733  1.9020529686326
4.000e03             103        9.1368  1.5842648307199776139  1.9026433524279
5.000e03             126        4.8087  1.5947356010063237235  1.9047728637572
6.000e03             143        5.6165  1.6009469373654262271  1.9044865415636
7.000e03             162        3.7508  1.6067369675936610061  1.9049916605060
8.000e03             175        7.3386  1.6102049556797575550  1.9040281929006
9.000e03             190        8.4697  1.6137276528118344401  1.9037499598414
1.000e04             205        9.2109  1.6168935574322006462  1.9035981912177
2.000e04             342       15.7597  1.6359323266459082661  1.9025704427014
3.000e04             467       19.7339  1.6462112719850103020  1.9023621488310
4.000e04             591       16.4389  1.6534144750921512344  1.9026112559475
5.000e04             705       17.5078  1.6584642393664188941  1.9025216677143
6.000e04             811       22.3655  1.6623276067607388692  1.9023406316833
7.000e04             905       35.8959  1.6652148478321607792  1.9019115102466
8.000e04            1007       38.6960  1.6679482710743175988  1.9018453723277
9.000e04            1116       32.1936  1.6705237563345362811  1.9020058715029
1.000e05            1224       24.7087  1.6727995848277415480  1.9021632918562
2.000e05            2160       21.9743  1.6858421613775262996  1.9021809740385
3.000e05            2994       43.7886  1.6926268061080038142  1.9020102544211
4.000e05            3804       44.5253  1.6973132695272491079  1.9020269885730
5.000e05            4565       63.0467  1.7007169286152501873  1.9019495257810
6.000e05            5331       52.9770  1.7035089800383006861  1.9019839741060
7.000e05            6061       60.0997  1.7057635740199276667  1.9019653361275
8.000e05            6766       76.6763  1.7076455334976987710  1.9019198097952
9.000e05            7472       79.0616  1.7093073738344116030  1.9019126520581
1.000e06            8169       79.0297  1.7107769308042211063  1.9019133533279
2.000e06           14871      -72.8835  1.7201317659453991052  1.9021366978266
3.000e06           20932      -43.4468  1.7250589801947331416  1.9021158068377
4.000e06           26860     -153.2264  1.7284730348384985286  1.9021792017998
5.000e06           32463     -128.5861  1.7309768070886263592  1.9021700702917
6.000e06           37916      -99.1354  1.7329641388408161114  1.9021575505513
7.000e06           43259      -76.1626  1.7346125242594923926  1.9021511816225
8.000e06           48618     -165.9674  1.7360432289447380939  1.9021744161816
9.000e06           53867     -228.2483  1.7372796048853705860  1.9021888000401
1.000e07           58980     -226.1835  1.7383570439172709388  1.9021882632233
2.000e07          107407     -161.2847  1.7451033549540519277  1.9021796217032
3.000e07          152892     -102.1228  1.7487989223082130119  1.9021759368134
4.000e07          196753     -186.8625  1.7513240142704469276  1.9021803001259
5.000e07          239101       -6.3050  1.7532144782180676310  1.9021718757006
6.000e07          280558      109.0897  1.7547261793627140019  1.9021671969291
7.000e07          321466        2.8283  1.7559872341007733523  1.9021700516121
8.000e07          361450      177.7970  1.7570551546107614613  1.9021652997603
9.000e07          401090      147.1979  1.7579890729084367205  1.9021660368093
1.000e08          440312       55.7942  1.7588156210679749679  1.9021679379607
2.000e08          813371      407.7123  1.7640099575366161787  1.9021637210745
3.000e08         1166480      688.5798  1.7668768311452305992  1.9021607914288
4.000e08         1507733      702.2516  1.7688418037440473543  1.9021608617718
5.000e08         1840170      923.2030  1.7703261748876588838  1.9021600051653
6.000e08         2166301      822.9858  1.7715156797011759670  1.9021603339605
7.000e08         2486868      926.1591  1.7725042164060158568  1.9021600472350
8.000e08         2802751     1229.0302  1.7733480245849554463  1.9021593178346
9.000e08         3115262     1060.1631  1.7740842395031871405  1.9021596779262
1.000e09         3424506      802.1557  1.7747359576385368007  1.9021602393210
2.000e09         6388041      983.8568  1.7788594045466685474  1.9021595697624
3.000e09         9210144      461.4644  1.7811506048419952322  1.9021597704228
4.000e09        11944438     1031.8028  1.7827248616069346793  1.9021594971099
5.000e09        14618166      291.2249  1.7839185702670445660  1.9021598406936
6.000e09        17244409     -769.8450  1.7848764907205487931  1.9021602702179
7.000e09        19830161     -119.3035  1.7856738237172544953  1.9021600720493
8.000e09        22384176     -248.3593  1.7863559952794308268  1.9021601065870
9.000e09        24911210    -1324.1393  1.7869513462126333295  1.9021603672963
1.000e10        27412679    -1262.4677  1.7874785027192415475  1.9021603562335
2.000e10        51509099    -4666.8568  1.7908302841345388669  1.9021607564878
3.000e10        74555618    -3348.1628  1.7927013191110304745  1.9021606359654
4.000e10        96956707     1868.6768  1.7939908991225617806  1.9021603054530
5.000e10       118903682     1629.5831  1.7949706930759641280  1.9021603136355
6.000e10       140494397     1554.6255  1.7957581700531061973  1.9021603264620
7.000e10       161795029     2030.7880  1.7964149820222782810  1.9021603179253
8.000e10       182855913     -984.7408  1.7969775082884140993  1.9021604001576
9.000e10       203710414    -6872.3564  1.7974688086494609236  1.9021605328060
1.000e11       224376048    -7183.3188  1.7979043109551191615  1.9021605414226
2.000e11       424084653    -8611.8922  1.8006814416927376524  1.9021605578071
3.000e11       615885700   -11077.6106  1.8022384256102747742  1.9021605672075
4.000e11       802817718   -23093.6365  1.8033145225947969238  1.9021606357850
5.000e11       986222314   -13877.9157  1.8041332877368367779  1.9021605956722
6.000e11      1166916933   -18008.4652  1.8047923140849210016  1.9021606116015
7.000e11      1345394380   -23486.6805  1.8053426418478639658  1.9021606277580
8.000e11      1521998439   -22360.2638  1.8058143376506919815  1.9021606255806
9.000e11      1696987738   -14624.6557  1.8062265887136356841  1.9021606083085
1.000e12      1870585220   -25353.1815  1.8065924191758825917  1.9021606304377
2.000e12      3552770943    46121.5048  1.8089310496647459843  1.9021605219566
3.000e12      5173760785    34043.1324  1.8102468189318128999  1.9021605313764
4.000e12      6756832076   -19173.3958  1.8111580952374658287  1.9021605611781
5.000e12      8312493003   -17742.0725  1.8118525634078677438  1.9021605596273
6.000e12      9846842484     4228.5059  1.8124121584203050714  1.9021605510219
7.000e12     11363874338   -28648.1077  1.8128799246698847592  1.9021605616545
8.000e12     12866256870   -50032.5587  1.8132811953468179639  1.9021605673653
9.000e12     14356002120   -58481.4512  1.8136321563413008737  1.9021605696628
1.000e13     15834664872   -66566.9380  1.8139437606846070596  1.9021605710802
1.100e13     17303503748  -115241.0649  1.8142237655485216835  1.9021605804906
1.200e13     18763393645   -94516.4534  1.8144778302898030049  1.9021605769058
1.300e13     20215240639   -98088.8613  1.8147102581844494734  1.9021605776141
1.400e13     21659728567  -128708.7023  1.8149243607901637846  1.9021605821346
1.500e13     23097407328  -157370.0069  1.8151227452389744071  1.9021605861733
1.600e13     24528698600  -107888.2514  1.8153074963071113237  1.9021605797878
1.700e13     25954158265  -103611.5872  1.8154803357302471936  1.9021605793075
1.800e13     27374126549  -105641.6255  1.8156426649590351791  1.9021605796002
1.900e13     28788943566  -119175.8845  1.8157956578049759126  1.9021605810203
2.000e13     30198862775   -99750.4284  1.8159402986628532188  1.9021605790108
2.100e13     31604193351   -89876.3843  1.8160774330678041674  1.9021605780582
2.200e13     33005189279  -103519.5992  1.8162077833100728790  1.9021605793334
2.300e13     34401997792   -70784.5625  1.8163319658664542670  1.9021605764486
2.400e13     35794933091  -108549.7136  1.8164505325984079621  1.9021605796541
2.500e13     37184054452   -96016.8158  1.8165639470414563750  1.9021605786430
2.600e13     38569581143   -87489.8241  1.8166726306228284665  1.9021605779631
2.700e13     39951669974   -88123.9361  1.8167769523752031195  1.9021605779905
2.800e13     41330446795   -83896.1147  1.8168772388225470969  1.9021605776864
2.900e13     42706091461  -125266.2627  1.8169737858280891426  1.9021605805820
3.000e13     44078684643  -172868.7109  1.8170668524994479201  1.9021605838288
3.100e13     45448289600  -178317.6830  1.8171566712386503861  1.9021605841992
3.200e13     46815045236  -176425.5679  1.8172434571131252699  1.9021605840597
3.300e13     48179073481  -191852.6310  1.8173274043553449059  1.9021605850025
3.400e13     49540407917  -167092.5593  1.8174086844599347601  1.9021605835076
3.500e13     50899201599  -169730.2165  1.8174874609865199212  1.9021605836692
3.600e13     52255496369  -161258.3585  1.8175638773379596659  1.9021605831932
3.700e13     53609405389  -179169.9651  1.8176380690926544075  1.9021605841956
3.800e13     54960945981  -169406.3866  1.8177101558091833985  1.9021605836811
3.900e13     56310221397  -167777.7526  1.8177802522325498838  1.9021605835974
4.000e13     57657248284  -127115.1193  1.8178484599999115711  1.9021605815369
4.100e13     59002149701  -110006.6717  1.8179148784868126374  1.9021605807041
4.200e13     60344965825   -99250.9929  1.8179795958598637971  1.9021605801975
4.300e13     61685782714  -126391.9947  1.8180426962257541950  1.9021605814784
4.400e13     63024570959  -110164.5846  1.8181042526046886017  1.9021605807450
4.500e13     64361429081   -99704.5505  1.8181643388056639926  1.9021605802752
4.600e13     65696351526   -42373.4852  1.8182230192355870055  1.9021605777630
4.700e13     67029450278    -5216.8630  1.8182803591668504859  1.9021605761649
4.800e13     68360832678   -52641.6236  1.8183364195777399889  1.9021605781643
4.900e13     69690406447   -51309.8302  1.8183912494377281587  1.9021605781192
5.000e13     71018282471   -72805.1430  1.8184449029335380664  1.9021605789865
5.100e13     72344462123   -80846.0081  1.8184974267329403026  1.9021605793128
5.200e13     73668934769   -28691.5883  1.8185488642868422615  1.9021605772917
5.300e13     74991834588   -15869.5804  1.8185992620898380836  1.9021605768024
5.400e13     76313144936     7544.8410  1.8186486583959443757  1.9021605759247
5.500e13     77632940380    -1026.3751  1.8186970927094042907  1.9021605762475
5.600e13     78951216673    -6566.4103  1.8187445995262149164  1.9021605764455
5.700e13     80267986070     8287.8456  1.8187912121200664734  1.9021605759137
5.800e13     81583340502   -19865.6294  1.8188369648028447584  1.9021605768912
5.900e13     82897215505      935.1656  1.8188818847716214872  1.9021605761825
6.000e13     84209699420     8870.3702  1.8189260029945684215  1.9021605759283
6.100e13     85520823314    -1532.3163  1.8189693469817926383  1.9021605762718
6.200e13     86830525087    56542.3985  1.8190119399066255748  1.9021605743828
6.300e13     88138959397    52316.3253  1.8190538107491656063  1.9021605745131
6.400e13     89446130188     4930.8623  1.8190949823866703149  1.9021605760051
6.500e13     90751952247    21928.4336  1.8191354738504317774  1.9021605754732
6.600e13     92056502802    47690.5062  1.8191753082801716865  1.9021605746892
6.700e13     93359851755    33238.3698  1.8192145075261050720  1.9021605751199
6.800e13     94662013136   -15189.1483  1.8192530908385185589  1.9021605765578
6.900e13     95962951236   -42238.8800  1.8192910751449138779  1.9021605773429
7.000e13     97262712867   -75675.2822  1.8193284790412377684  1.9021605783032
7.100e13     98561247191   -46183.0437  1.8193653175521935659  1.9021605774679
7.200e13     99858661426   -43048.2157  1.8194016094869030216  1.9021605773790
7.300e13    101154948767   -42055.7566  1.8194373697399530963  1.9021605773514
7.400e13    102450102768   -19849.3940  1.8194726126026810615  1.9021605767464
7.500e13    103744155743     7688.2880  1.8195073528355690007  1.9021605760086
7.600e13    105037164482     -260.3807  1.8195416052529883072  1.9021605762173
7.700e13    106329126139   -25317.4522  1.8195753825408768857  1.9021605768739
7.800e13    107620027433   -39092.6515  1.8196086966146374832  1.9021605772303
7.900e13    108909897081   -55599.5967  1.8196415600088871848  1.9021605776519
8.000e13    110198743491   -68932.8913  1.8196739842687760037  1.9021605779839
8.100e13    111486603994  -102485.0290  1.8197059812403302773  1.9021605788177
8.200e13    112773406156   -70244.0639  1.8197375596298841597  1.9021605780279
8.300e13    114059261253   -70254.9954  1.8197687322865766784  1.9021605780346
8.400e13    115344130549   -50884.8257  1.8197995079888911775  1.9021605775697
8.500e13    116628072044   -57558.2482  1.8198298975109963710  1.9021605777252
8.600e13    117911107421   -99692.9299  1.8198599104020469688  1.9021605787149
8.700e13    119193138971   -67613.3512  1.8198895531020126259  1.9021605779745
8.800e13    120474283458   -66405.1721  1.8199188367461228319  1.9021605779498
8.900e13    121754511996   -55782.0923  1.8199477687910817194  1.9021605777093
9.000e13    123033833767   -33794.1795  1.8199763573028322787  1.9021605772178
9.100e13    124312314519   -55316.6367  1.8200046113244009972  1.9021605776913
9.200e13    125589926505   -81979.9856  1.8200325375656784709  1.9021605782751
9.300e13    126866655921   -89599.6432  1.8200601428101361277  1.9021605784384
9.400e13    128142524559   -89820.8681  1.8200874343950419568  1.9021605784439
9.500e13    129417551440   -91744.0592  1.8201144193587564082  1.9021605784850
9.600e13    130691759922  -109025.3857  1.8201411046086882527  1.9021605788435
9.700e13    131965134049  -116218.7315  1.8201674960343277866  1.9021605789937
9.800e13    133237670312  -100529.9385  1.8201935995852289413  1.9021605786718
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1.295e15   1501183722670  -829123.6497  1.8262739979937692841  1.9021605823862
1.296e15   1502274091967  -813117.9598  1.8262756813119632718  1.9021605823615
1.297e15   1503364412119  -796322.1576  1.8262773632559805410  1.9021605823356
1.298e15   1504454680754  -776323.7483  1.8262790438242923046  1.9021605823048
1.299e15   1505544920947  -776157.3022  1.8262807230545407845  1.9021605823045
1.300e15   1506635099560  -762644.4544  1.8262824008978027694  1.9021605822837
1.301e15   1507725256422  -775573.9052  1.8262840774174802874  1.9021605823036
1.302e15   1508815345584  -768956.4192  1.8262857525449717594  1.9021605822934
1.303e15   1509905400846  -776551.8260  1.8262874263343381203  1.9021605823051
1.304e15   1510995436885  -812997.0191  1.8262890988101172116  1.9021605823610
1.305e15   1512085390065  -814615.9566  1.8262907698767989253  1.9021605823635
1.306e15   1513175293167  -814149.6606  1.8262924395867305147  1.9021605823627
1.307e15   1514265181238  -846605.2168  1.8262941079956516980  1.9021605824124
1.308e15   1515355017714  -875378.7752  1.8262957750496188547  1.9021605824564
1.309e15   1516444765729  -863564.5491  1.8262974406943501022  1.9021605824384
1.310e15   1517534455688  -841527.8153  1.8262991049784453714  1.9021605824047
1.311e15   1518624104338  -825975.9139  1.8263007679295405644  1.9021605823810
1.312e15   1519713709958  -815148.2485  1.8263024295470445262  1.9021605823645
1.313e15   1520803255029  -791486.2853  1.8263040898062853071  1.9021605823284
1.314e15   1521892739734  -755133.5535  1.8263057487096058709  1.9021605822730
1.315e15   1522982250418  -792395.6453  1.8263074063904692297  1.9021605823298
1.316e15   1524071686319  -802471.2151  1.8263090626975141714  1.9021605823451
1.317e15   1525161058569  -796452.9799  1.8263107176497582366  1.9021605823359
1.318e15   1526250364665  -771798.7192  1.8263123712454185869  1.9021605822985
1.319e15   1527339674953  -798815.2743  1.8263140235933027734  1.9021605823395
1.320e15   1528428912639  -800669.5487  1.8263156745788847677  1.9021605823423
1.321e15   1529518113535  -813134.5076  1.8263173242584774978  1.9021605823612
1.322e15   1530607230082  -788612.1782  1.8263189725620697793  1.9021605823241
1.323e15   1531696332667  -797450.6489  1.8263206195981975585  1.9021605823374
1.324e15   1532785415298  -833619.0699  1.8263222653597248644  1.9021605823921
1.325e15   1533874391927  -811030.6523  1.8263239097186411872  1.9021605823580
1.326e15   1534963371273  -838365.6686  1.8263255528410855791  1.9021605823992
1.327e15   1536052292497  -854746.4523  1.8263271946372022498  1.9021605824239
1.328e15   1537141167667  -872202.3975  1.8263288351271837132  1.9021605824502
1.329e15   1538229969474  -863385.9592  1.8263304742718903154  1.9021605824370
1.330e15   1539318729075  -859415.6531  1.8263321121201978157  1.9021605824310
1.331e15   1540407461137  -874920.0550  1.8263337486960970529  1.9021605824543
1.332e15   1541496122637  -866837.8012  1.8263353839368965577  1.9021605824422
1.333e15   1542584715797  -837352.5881  1.8263370178479001714  1.9021605823979
1.334e15   1543673262226  -808035.1722  1.8263386504635387828  1.9021605823539
1.335e15   1544761829694  -846617.3697  1.8263402818873269112  1.9021605824118
1.336e15   1545850299845  -834705.0567  1.8263419119437893026  1.9021605823939
1.337e15   1546938770793  -870374.1687  1.8263435407818004846  1.9021605824473
1.338e15   1548027150255  -861303.7009  1.8263451682651938887  1.9021605824337
1.339e15   1549115539496  -908720.7075  1.8263467945472790462  1.9021605825046
1.340e15   1550203868829  -942900.3022  1.8263484195258475666  1.9021605825556
1.341e15   1551292129703  -955253.6576  1.8263500431900467977  1.9021605825741
1.342e15   1552380365852  -989477.0051  1.8263516656070452460  1.9021605826251
1.343e15   1553468496890  -965146.6351  1.8263532866589426738  1.9021605825888
1.344e15   1554556626240  -985647.8966  1.8263549065017410548  1.9021605826193
1.345e15   1555644664017  -961058.1968  1.8263565250035272561  1.9021605825828
1.346e15   1556732656721  -937840.0017  1.8263581422354300548  1.9021605825482
1.347e15   1557820654425  -966028.8353  1.8263597582736938815  1.9021605825901
1.348e15   1558908610983  -999441.2796  1.8263613730516048035  1.9021605826397
1.349e15   1559996537336 -1048980.9748  1.8263629865872597105  1.9021605827132
1.350e15   1561084329425 -1010551.6189  1.8263645987282379888  1.9021605826562
1.351e15   1562172089272  -986137.9675  1.8263662096277746750  1.9021605826201
1.352e15   1563259816308  -975133.8337  1.8263678192868057809  1.9021605826038
1.353e15   1564347537173 -1004142.0883  1.8263694277465730570  1.9021605826467
1.354e15   1565435166155  -987413.6591  1.8263710348821879125  1.9021605826220
1.355e15   1566522795418 -1017075.5314  1.8263726408316910104  1.9021605826658
1.356e15   1567610312845  -980973.7473  1.8263742454314392529  1.9021605826125
1.357e15   1568697780621  -941256.4059  1.8263758487750816372  1.9021605825539
1.358e15   1569785237648  -936788.6631  1.8263774509217917984  1.9021605825474
1.359e15   1570872670919  -954526.7315  1.8263790518541790780  1.9021605825735
1.360e15   1571960022424  -936423.8800  1.8263806514886928796  1.9021605825468
1.361e15   1573047378404  -968684.4342  1.8263822499540078358  1.9021605825943
1.362e15   1574134609646  -922058.7759  1.8263838470620394487  1.9021605825258
1.363e15   1575221862944  -943304.3428  1.8263854430302669752  1.9021605825570
1.364e15   1576309047700  -941786.6291  1.8263870377274512773  1.9021605825547
1.365e15   1577396201270  -954825.1843  1.8263886312102160047  1.9021605825738
1.366e15   1578483254329  -913058.6141  1.8263902233788178590  1.9021605825127
1.367e15   1579570332611  -942184.5798  1.8263918144191878439  1.9021605825553
1.368e15   1580657329712  -935762.7980  1.8263934041773671859  1.9021605825459
1.369e15   1581744272902  -921027.0408  1.8263949926950626909  1.9021605825244
1.370e15   1582831160695  -896455.1356  1.8263965799719552819  1.9021605824885
1.371e15   1583918038841  -907760.9649  1.8263981660765773806  1.9021605825050
1.372e15   1585004866284  -913852.4662  1.8263997509507937656  1.9021605825139
1.373e15   1586091625948  -897617.6320  1.8264013345715083181  1.9021605824902
1.374e15   1587178337853  -879040.5093  1.8264029169696886496  1.9021605824631
1.375e15   1588265050796  -906882.2001  1.8264044982181418197  1.9021605825037
1.376e15   1589351647937  -864266.8606  1.8264060781486196040  1.9021605824417
1.377e15   1590438249683  -871565.7016  1.8264076569379960830  1.9021605824523
1.378e15   1591524786833  -859541.9881  1.8264092344874686027  1.9021605824348
1.379e15   1592611314345  -883118.0393  1.8264108108785521837  1.9021605824690
1.380e15   1593697795937  -905976.2283  1.8264123860603571112  1.9021605825022
1.381e15   1594784189104  -885575.9823  1.8264139599730325867  1.9021605824726
1.382e15   1595870554448  -882483.7822  1.8264155327061404037  1.9021605824682
1.383e15   1596956896982  -901677.1625  1.8264171042686548574  1.9021605824959
1.384e15   1598043208324  -934738.7114  1.8264186746501287223  1.9021605825437
1.385e15   1599129440735  -933894.0704  1.8264202437833558903  1.9021605825425
1.386e15   1600215648141  -953033.9344  1.8264218117479180022  1.9021605825701
1.387e15   1601301785724  -947305.0515  1.8264233784808851468  1.9021605825619
1.388e15   1602387893431  -956619.2227  1.8264249440416166844  1.9021605825753
1.389e15   1603473881184  -890863.3022  1.8264265083020446088  1.9021605824806
1.390e15   1604559873070  -874089.1969  1.8264280714426519875  1.9021605824564
1.391e15   1605645840818  -877990.8664  1.8264296334243794769  1.9021605824620
1.392e15   1606731738034  -856139.3230  1.8264311941822122399  1.9021605824306
1.393e15   1607817557002  -800783.6315  1.8264327537068307728  1.9021605823511
1.394e15   1608903418963  -833129.9090  1.8264343121740142732  1.9021605823975
1.395e15   1609989203703  -832929.3248  1.8264358694128730886  1.9021605823973
1.396e15   1611074931923  -820848.1004  1.8264374254548155503  1.9021605823799
1.397e15   1612160634479  -827707.5095  1.8264389803457706451  1.9021605823898
1.398e15   1613246254870  -796971.8773  1.8264405340065011192  1.9021605823458
1.399e15   1614331835706  -771216.5812  1.8264420864997262855  1.9021605823090
1.400e15   1615417411648  -785068.0501  1.8264436378766369280  1.9021605823288
1.401e15   1616502987637  -843432.7644  1.8264451881458706831  1.9021605824121
1.402e15   1617588470278  -852881.2562  1.8264467371757564837  1.9021605824256
1.403e15   1618673873665  -827473.1086  1.8264482849881418195  1.9021605823893
1.404e15   1619759279590  -848965.9562  1.8264498317013158573  1.9021605824200
1.405e15   1620844603823  -833095.4846  1.8264513771969025751  1.9021605823974
1.406e15   1621929903645  -837108.4303  1.8264529215581572164  1.9021605824031
1.407e15   1623015173155  -855069.5810  1.8264544647783024742  1.9021605824286
1.408e15   1624100432831  -907422.7749  1.8264560068880309626  1.9021605825030
1.409e15   1625185591788  -903248.9009  1.8264575477598818628  1.9021605824971
1.410e15   1626270701486  -893973.8985  1.8264590874686491642  1.9021605824839
1.411e15   1627355797158  -914796.7577  1.8264606260659061842  1.9021605825135
1.412e15   1628440875607  -962486.5187  1.8264621635487111059  1.9021605825810
1.413e15   1629525843849  -944025.2721  1.8264636997869867082  1.9021605825549
1.414e15   1630610767700  -925195.1584  1.8264652348756387488  1.9021605825282
1.415e15   1631695670447  -929249.3683  1.8264667688491937371  1.9021605825340
1.416e15   1632780562396  -966460.1423  1.8264683017237834250  1.9021605825865
1.417e15   1633865376258  -969504.7707  1.8264698334059718950  1.9021605825908
1.418e15   1634950176211 -1002527.5934  1.8264713639879857076  1.9021605826374
1.419e15   1636034898421 -1001661.0000  1.8264728933813697337  1.9021605826362
1.420e15   1637119612078 -1036061.4295  1.8264744216852774919  1.9021605826847
1.421e15   1638204276101 -1064614.3703  1.8264759488434142105  1.9021605827249
1.422e15   1639288854568 -1051364.3600  1.8264774748068511910  1.9021605827062
1.423e15   1640373384223 -1033021.9852  1.8264789996289274777  1.9021605826804
1.424e15   1641457909209 -1053696.8818  1.8264805233732615335  1.9021605827095
1.425e15   1642542363773 -1047602.7345  1.8264820459490537806  1.9021605827009
1.426e15   1643626809204 -1075995.2769  1.8264835674439282335  1.9021605827407
1.427e15   1644711175706 -1069045.2910  1.8264850877615553298  1.9021605827310
1.428e15   1645795441785 -1005225.6078  1.8264866068734725292  1.9021605826416
1.429e15   1646879719228  -996290.1067  1.8264881249378556699  1.9021605826291
1.430e15   1647963982538 -1016708.7153  1.8264896419205249193  1.9021605826576
1.431e15   1649048181286 -1016019.4097  1.8264911577524638063  1.9021605826567
1.432e15   1650132292318  -971035.2142  1.8264926724029376995  1.9021605825938
1.433e15   1651216402216  -968305.2010  1.8264941859944882051  1.9021605825900
1.434e15   1652300451467  -948283.4905  1.8264956984455543548  1.9021605825621
1.435e15   1653384479883  -950749.2508  1.8264972098132338252  1.9021605825655
1.436e15   1654468471650  -959855.6979  1.8264987200769911443  1.9021605825782
1.437e15   1655552438988  -987790.0954  1.8265002292553922640  1.9021605826171
1.438e15   1656636314103  -966725.7546  1.8265017372556261047  1.9021605825878
1.439e15   1657720182255  -981890.0340  1.8265032441978511249  1.9021605826089
1.440e15   1658804015373 -1005179.3397  1.8265047500445541902  1.9021605826413
1.441e15   1659887714423  -937527.1250  1.8265062546597497995  1.9021605825473
1.442e15   1660971433210  -932705.8903  1.8265077582585461121  1.9021605825406
1.443e15   1662055138607  -957556.1833  1.8265092607964143847  1.9021605825751
1.444e15   1663138774643  -956074.5983  1.8265107621972845018  1.9021605825730
1.445e15   1664222372946  -959856.7767  1.8265122625065292957  1.9021605825783
1.446e15   1665305903841  -939195.4067  1.8265137616845844685  1.9021605825497
1.447e15   1666389444780  -971510.2229  1.8265152598401089447  1.9021605825944
1.448e15   1667472923443  -984449.0068  1.8265167568745895344  1.9021605826122
1.449e15   1668556345831  -983980.5860  1.8265182527978715963  1.9021605826116
1.450e15   1669639673260  -931388.8348  1.8265197475580989406  1.9021605825390
1.451e15   1670722996354  -917265.6736  1.8265212412818271442  1.9021605825195
1.452e15   1671806257420  -883886.0690  1.8265227338910078934  1.9021605824736
1.453e15   1672889500298  -875058.0335  1.8265242254475079419  1.9021605824614
1.454e15   1673972695583  -861344.6259  1.8265257159123570411  1.9021605824425
1.455e15   1675055861868  -861306.9506  1.8265272053126025103  1.9021605824424
1.456e15   1676139016338  -892098.1579  1.8265286936733268889  1.9021605824848
1.457e15   1677222061365  -856058.4438  1.8265301808618881433  1.9021605824353
1.458e15   1678305129205  -885412.0497  1.8265316670613884411  1.9021605824756
1.459e15   1679388126954  -887223.2627  1.8265331521457795004  1.9021605824780
1.460e15   1680471083345  -890193.4152  1.8265346361559728884  1.9021605824821
1.461e15   1681553980467  -876379.8848  1.8265361190688962362  1.9021605824632
1.462e15   1682636882233  -909664.0945  1.8265376009735190399  1.9021605825087
1.463e15   1683719691347  -892718.5122  1.8265390817381930670  1.9021605824856
1.464e15   1684802473466  -891168.6509  1.8265405614541777449  1.9021605824835
1.465e15   1685885204864  -881257.0686  1.8265420400905031094  1.9021605824699
1.466e15   1686967871133  -848544.3679  1.8265435176289721689  1.9021605824253
1.467e15   1688050526150  -846876.1963  1.8265449941445545187  1.9021605824230
1.468e15   1689133122995  -829301.2458  1.8265464695747406810  1.9021605823991
1.469e15   1690215698948  -833068.2531  1.8265479439717450203  1.9021605824042
1.470e15   1691298259961  -864097.9991  1.8265494173450695195  1.9021605824464
1.471e15   1692380729110  -845435.3093  1.8265508895915237448  1.9021605824210
1.472e15   1693463188669  -859323.0533  1.8265523608244165934  1.9021605824399
1.473e15   1694545552038  -819130.1449  1.8265538309275186148  1.9021605823853
1.474e15   1695627925450  -831058.5419  1.8265553000465671234  1.9021605824015
1.475e15   1696710268775  -854947.2462  1.8265567681284586683  1.9021605824339
1.476e15   1697792558509  -867261.3036  1.8265582351427112036  1.9021605824506
1.477e15   1698874783370  -856687.8034  1.8265597010755198337  1.9021605824363
1.478e15   1699956967710  -847547.8790  1.8265611659613146766  1.9021605824239
1.479e15   1701039110156  -838437.7072  1.8265626297996449391  1.9021605824116
1.480e15   1702121244807  -863425.5082  1.8265640926380336294  1.9021605824453
1.481e15   1703203323033  -873850.5458  1.8265655544121229867  1.9021605824594
1.482e15   1704285338585  -863433.1273  1.8265670151149228762  1.9021605824454
1.483e15   1705367322857  -863536.6028  1.8265684747902218065  1.9021605824455
1.484e15   1706449298224  -896505.3659  1.8265699334695789495  1.9021605824900
1.485e15   1707531182023  -879645.8531  1.8265713910429678697  1.9021605824673
1.486e15   1708613002455  -841128.5440  1.8265728475498320299  1.9021605824154
1.487e15   1709694846145  -867547.9610  1.8265743031081641356  1.9021605824509
1.488e15   1710776615009  -860789.6694  1.8265757575873559944  1.9021605824418
1.489e15   1711858338828  -850604.2770  1.8265772110288863850  1.9021605824281
1.490e15   1712939999480  -818839.4345  1.8265786634098093375  1.9021605823855
1.491e15   1714021610350  -778849.8348  1.8265801147495089114  1.9021605823318
1.492e15   1715103226459  -785626.2136  1.8265815651231621167  1.9021605823409
1.493e15

Counts of twin-prime pairs and Brun's constant to 5e15 Thomas R. Nicely

http://www.trnicely.net Current e-mail address

Counts of twin-prime pairs and Brun's constant to 5e15

Thomas R. Nicely

http://www.trnicely.net
Current e-mail address