Enumeration of the prime quadruplets to 1e16

Enumeration of the prime quadruplets to 1e16
Thomas R. Nicely

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

Last updated 1000 GMT 18 January 2010.
This is a table of values of pi_4(x), the count of prime quadruplets (q, q+2, q+6, q+8) such that q <= x. The first three such quadruplets are (5, 7, 11, 13), (11, 13, 17, 19), and (101, 103, 107, 109). Also provided are the values of the related functions delta_4(x), S_4(x), and F_4(x). The counts in this table were obtained by a direct and explicit generation and enumeration of the primes.
The domain of this table consists of each decade from 10 through 1e12, then each 1e12 to 1e16. See also Enumeration of the prime quadruplets from 1e16 to 2e16.
Complete counts and reciprocal sums of the prime constellations from Nicely's computations (1993-2009), including the prime quadruplets, 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.
Symbols are defined as follows; for further details, see the paper Enumeration to $1.6 \times 10^{15}$ of the prime quadruplets.
pi_4(x) = Number of prime quadruplets (q, q+2, q+6, q+8) such that the first element q <= x .
delta_4(x) = Li_4(x) - pi_4(x) . A positive value indicates a deficit of quadruplets (compared to the theoretical estimate); a negative value indicates a surplus of quadruplets.
Li_4(x) = integral(27/2*c_4/((ln(t))^4), t, 2, x) = Hardy-Littlewood integral approximation for pi_4(x) . Although this is the traditional formula, note that a slightly more accurate (for small x) approximation is produced by the asymptotically equivalent formula Li_4*(x) = integral(27/2*c_4/((ln(t+6))^4), t, 2, x) .
c_4 = Hardy-Littlewood quadruplets constant = 0.30749 48787 58327 09312 33544 86071 07685 3.... The kth Hardy-Littlewood constant (k > 1) is defined as c_k = prod((p^(k-1))*(p-k)/(p-1)^k, p; p prime, p > k) .
S_4(x) = Sum of the reciprocals of all of the elements of the prime quadruplets (q, q+2, q+6, q+8) such that q <= x . Note that if x >= 11, the terms 1/11 and 1/13 are included twice.
F_4(x) = First order extrapolation, from S_4(x), of the Brun's constant B_4 of the quadruplets (the limit of the sum of the reciprocals as x approaches +infinity): B_4 \approx F_4(x) = S_4(x) + 18c_4/(ln(x))^3 .
The values given for pi_4(x) are believed to be exact. The values for delta_4(x), S_4(x), and F_4(x) are believed to be correct to all digits shown, except for a possible (rounding) error of one ulp (one unit in the last decimal place or least significant digit).
Please inform me of any errors you find in these values.
========================================================================================
      x               pi_4(x)     delta_4(x)          S_4(x)                F_4(x)
========================================================================================
 1.000000e+01               1        10.2859  0.51068931068931068931  0.964070321217938
 2.000000e+01               2        10.1262  0.78997658688061164841  0.995850537119856
 3.000000e+01               2        10.5214  0.78997658688061164841  0.930650926150766
 4.000000e+01               2        10.7836  0.78997658688061164841  0.900238875296448
 5.000000e+01               2        10.9823  0.78997658688061164841  0.882426432864690
 6.000000e+01               2        11.1438  0.78997658688061164841  0.870617832532254
 7.000000e+01               2        11.2808  0.78997658688061164841  0.862154610092485
 8.000000e+01               2        11.4004  0.78997658688061164841  0.855755297061471
 9.000000e+01               2        11.5071  0.78997658688061164841  0.850724023718443
 1.000000e+02               2        11.6037  0.78997658688061164841  0.846649213196690
 2.000000e+02               4        10.2832  0.84862463816744839238  0.885837792658963
 3.000000e+02               4        10.7341  0.84862463816744839238  0.878452459213742
 4.000000e+02               4        11.0882  0.84862463816744839238  0.874358881947354
 5.000000e+02               4        11.3869  0.84862463816744839238  0.871685161149193
 6.000000e+02               4        11.6492  0.84862463816744839238  0.869769052839529
 7.000000e+02               4        11.8853  0.84862463816744839238  0.868311278942790
 8.000000e+02               4        12.1016  0.84862463816744839238  0.867154911802740
 9.000000e+02               5        11.3023  0.85347319425313039516  0.871057486661900
 1.000000e+03               5        11.4902  0.85347319425313039516  0.870265083531968
 2.000000e+03               7        10.9677  0.85830014856295221497  0.870904337774445
 3.000000e+03               8        11.0818  0.86021861820386389916  0.871003212669616
 4.000000e+03              10        10.0204  0.86260190012786715074  0.872302766031642
 5.000000e+03              10        10.8508  0.86260190012786715074  0.871560103082273
 6.000000e+03              11        10.6060  0.86330923898742867245  0.871715934275308
 7.000000e+03              11        11.3052  0.86330923898742867245  0.871284429624808
 8.000000e+03              11        11.9605  0.86330923898742867245  0.870934200107401
 9.000000e+03              11        12.5802  0.86330923898742867245  0.870642099508084
 1.000000e+04              12        12.1702  0.86373319240018343749  0.870817270689693
 2.000000e+04              19        10.0856  0.86543869869358331799  0.871137006593710
 3.000000e+04              22        11.0488  0.86596668397742072590  0.871018723695818
 4.000000e+04              24        12.5192  0.86620756159806221122  0.870859205909501
 5.000000e+04              25        14.6727  0.86629891708557767456  0.870668654175279
 6.000000e+04              27        15.5994  0.86644910843780001277  0.870605186029452
 7.000000e+04              30        15.3530  0.86662968424609036084  0.870615852425834
 8.000000e+04              33        14.9685  0.86678702796906112160  0.870633421664927
 9.000000e+04              36        14.4703  0.86692977367980420769  0.870658251310591
 1.000000e+05              38        14.8762  0.86701100368413418480  0.870638051768363
 2.000000e+05              52        21.6400  0.86740403498179808375  0.870447599700749
 3.000000e+05              70        21.0872  0.86768899658409668347  0.870448343208639
 4.000000e+05              87        19.7418  0.86787972810538295799  0.870458542348862
 5.000000e+05             103        18.2132  0.86802351105101137206  0.870472992827201
 6.000000e+05             117        17.8214  0.86812515604747137518  0.870475311600818
 7.000000e+05             133        14.7607  0.86822366496408022150  0.870493989413471
 8.000000e+05             141        19.1598  0.86826662648062421767  0.870470695119222
 9.000000e+05             156        16.1096  0.86833754968946299463  0.870485299894500
 1.000000e+06             166        17.6772  0.86837953275349680687  0.870478518913352
 2.000000e+06             295        -9.0770  0.86875115958464441262  0.870563453719610
 3.000000e+06             397       -22.7249  0.86891935252277718154  0.870587818073754
 4.000000e+06             467       -12.1047  0.86900044121055585862  0.870575964861992
 5.000000e+06             546       -15.6834  0.86907139254206552425  0.870579524096043
 6.000000e+06             606        -4.1053  0.86911513490071583438  0.870571028240301
 7.000000e+06             695       -24.5372  0.86917004780686241981  0.870583640552685
 8.000000e+06             772       -35.4207  0.86921132018043422700  0.870589585161601
 9.000000e+06             836       -35.3582  0.86924143341928998178  0.870589507727509
 1.000000e+07             899       -36.0537  0.86926787696082905324  0.870589687487152
 2.000000e+07            1468       -44.7793  0.86942727158737936677  0.870592231357484
 3.000000e+07            1952       -34.7441  0.86950643077473118266  0.870591006938357
 4.000000e+07            2404       -30.3628  0.86955845087572910926  0.870590426522459
 5.000000e+07            2847       -42.6425  0.86959800487800295493  0.870591499323441
 6.000000e+07            3258       -42.0797  0.86962783621130663545  0.870591297288180
 7.000000e+07            3647       -34.6385  0.86965184685808291993  0.870590852496671
 8.000000e+07            4034       -37.5920  0.86967253048758811253  0.870591016496520
 9.000000e+07            4402       -31.9864  0.86968990025115242585  0.870590780038970
 1.000000e+08            4768       -33.3596  0.86970529363232326145  0.870590803418512
 2.000000e+08            8097       -40.5221  0.86979790703974411924  0.870590531328663
 3.000000e+08           10973        57.7615  0.86984469000401724839  0.870588938799399
 4.000000e+08           13713        91.2700  0.86987631749299986737  0.870588605980516
 5.000000e+08           16331       108.5381  0.86989969451376988659  0.870588441681838
 6.000000e+08           18839       131.8167  0.86991796256617200326  0.870588239303962
 7.000000e+08           21275       144.5210  0.86993299081504378794  0.870588162881789
 8.000000e+08           23660       140.2061  0.86994572656645063927  0.870588179086770
 9.000000e+08           26082        41.3535  0.86995713750309794580  0.870588642467898
 1.000000e+09           28388         8.8390  0.86996685642508722448  0.870588778250229
 2.000000e+09           49262        58.5006  0.87002514268475659175  0.870588611896844
 3.000000e+09           68341       -60.1497  0.87005609161903126524  0.870588731909245
 4.000000e+09           85912       180.6245  0.87007631769297149368  0.870588435740552
 5.000000e+09          102950       157.1272  0.87009153390081200390  0.870588453901904
 6.000000e+09          119474        44.2854  0.87010359599274363877  0.870588541649325
 7.000000e+09          135206       242.0673  0.87011330043036036008  0.870588420296803
 8.000000e+09          150507       472.7621  0.87012147809097871253  0.870588299913627
 9.000000e+09          165764       409.5839  0.87012866653505132186  0.870588328612067
 1.000000e+10          180529       545.9324  0.87013489117692849269  0.870588272187457
 2.000000e+10          319107       234.7134  0.87017357442665777759  0.870588357830011
 3.000000e+10          445369       479.1215  0.87019410213547726849  0.870588321011766
 4.000000e+10          565240       164.1969  0.87020790956094688591  0.870588355150816
 5.000000e+10          679610       494.0065  0.87021812647061302041  0.870588327324660
 6.000000e+10          790510       600.8505  0.87022621747464535866  0.870588319125475
 7.000000e+10          898998       161.8631  0.87023291100908785908  0.870588348208985
 8.000000e+10         1004516       238.9699  0.87023854866328073871  0.870588344419846
 9.000000e+10         1107901       360.6512  0.87024342012893015679  0.870588338456998
 1.000000e+11         1209318       638.2234  0.87024769554536542390  0.870588327409023
 2.000000e+11         2161156     -1248.1586  0.87027424475201135760  0.870588374628232
 3.000000e+11         3037193     -1220.8308  0.87028848298680229330  0.870588374666210
 4.000000e+11         3870114     -2111.1838  0.87029807841303991038  0.870588385745922
 5.000000e+11         4671000     -1900.5081  0.87030523156323761765  0.870588384091468
 6.000000e+11         5449176     -2598.6611  0.87031090927030425737  0.870588389435862
 7.000000e+11         6207640     -2562.7448  0.87031558730969668814  0.870588389182302
 8.000000e+11         6949946     -2155.4212  0.87031955316731335619  0.870588387155889
 9.000000e+11         7680011     -2973.0004  0.87032299338343396351  0.870588391074637
 1.000000e+12         8398278     -3699.9678  0.87032602081344096759  0.870588394083423
 2.000000e+12        15133490      1440.6209  0.87034480075276844714  0.870588379220184
 3.000000e+12        21393554     -1222.1010  0.87035497393944024876  0.870588384305203
 4.000000e+12        27357696      2197.7238  0.87036184329476933330  0.870588380061640
 5.000000e+12        33122014       898.3817  0.87036699142494094394  0.870588381340192
 6.000000e+12        38728915       312.0027  0.87037108207994458731  0.870588381843058
 7.000000e+12        44210040      -752.0671  0.87037446280276011544  0.870588382638302
 8.000000e+12        49581777      2313.1199  0.87037733251638009439  0.870588380957126
 9.000000e+12        54864496      4438.7009  0.87037982176320194686  0.870588379957074
 1.000000e+13        60070590      4848.3594  0.87038201608803389106  0.870588379770569
 1.100000e+13        65205425      7277.0525  0.87038397392095709017  0.870588378871596
 1.200000e+13        70276639     11396.8524  0.87038573906238776639  0.870588377417667
 1.300000e+13        75297182     10249.6688  0.87038734665375502820  0.870588377831101
 1.400000e+13        80262909     12975.2948  0.87038881875137318392  0.870588377031747
 1.500000e+13        85186849     10767.8464  0.87039017767208909650  0.870588377623505
 1.600000e+13        90066180     10063.5642  0.87039143735155746628  0.870588377807987
 1.700000e+13        94908314      6576.2203  0.87039261161736383736  0.870588378662067
 1.800000e+13        99706681      9604.0205  0.87039370870904388422  0.870588377954098
 1.900000e+13       104475159      7669.4723  0.87039474001564453933  0.870588378372780
 2.000000e+13       109213708      2939.9393  0.87039571227008331805  0.870588379346602
 2.100000e+13       113916305      3335.8368  0.87039663006257139528  0.870588379276147
 2.200000e+13       118590700      2809.2627  0.87039749990234176040  0.870588379381752
 2.300000e+13       123237805      1983.0752  0.87039832621522000555  0.870588379535802
 2.400000e+13       127857201      2666.8873  0.87039911263931239315  0.870588379429208
 2.500000e+13       132451167      3847.0731  0.87039986279763071287  0.870588379241878
 2.600000e+13       137016789      9593.6094  0.87040057907968089011  0.870588378342679
 2.700000e+13       141567321      7712.3805  0.87040126604397678344  0.870588378626140
 2.800000e+13       146093569      8372.4319  0.87040192448954803056  0.870588378530404
 2.900000e+13       150598984      9022.5513  0.87040255690162665872  0.870588378439014
 3.000000e+13       155086540      7521.4743  0.87040316545284183150  0.870588378645824
 3.100000e+13       159557551      3327.9508  0.87040375187468101409  0.870588379196286
 3.200000e+13       164007487      1690.8641  0.87040431699825054616  0.870588379402948
 3.300000e+13       168441140     -1511.4475  0.87040486272563396724  0.870588379795534
 3.400000e+13       172856180     -3322.5389  0.87040538994253252268  0.870588380015566
 3.500000e+13       177253295     -3843.7771  0.87040589979340977772  0.870588380076167
 3.600000e+13       181634741     -4780.7445  0.87040639351188932844  0.870588380179337
 3.700000e+13       185999299     -4397.0585  0.87040687185471992342  0.870588380138636
 3.800000e+13       190350901     -6137.5486  0.87040733605676416319  0.870588380324435
 3.900000e+13       194684918     -4913.7430  0.87040778637343920083  0.870588380197917
 4.000000e+13       199006240     -5181.6232  0.87040822400132247918  0.870588380224340
 4.100000e+13       203311891     -3554.6119  0.87040864927460369219  0.870588380063073
 4.200000e+13       207605728     -3500.7662  0.87040906315917093880  0.870588380056061
 4.300000e+13       211885250     -2150.1484  0.87040946595993705607  0.870588379930209
 4.400000e+13       216156208     -4903.3559  0.87040985871286467680  0.870588380185047
 4.500000e+13       220412455     -5280.1891  0.87041024131546585379  0.870588380219372
 4.600000e+13       224651617      -589.4428  0.87041061400551830660  0.870588379806539
 4.700000e+13       228883691      -525.8074  0.87041097806997729807  0.870588379800333
 4.800000e+13       233102899       977.1330  0.87041133338534486568  0.870588379672614
 4.900000e+13       237313392        43.8162  0.87041168065749757065  0.870588379750725
 5.000000e+13       241512180       -72.4618  0.87041201996742285091  0.870588379761043
 5.100000e+13       245697652      2491.2216  0.87041235150234680868  0.870588379558154
 5.200000e+13       249872701      5083.1203  0.87041267579056956857  0.870588379357926
 5.300000e+13       254037464      7797.4677  0.87041299311908820324  0.870588379153545
 5.400000e+13       258198873      3924.0749  0.87041330426152420850  0.870588379442001
 5.500000e+13       262345548      5055.8817  0.87041360861523044537  0.870588379359898
 5.600000e+13       266478834     10052.4669  0.87041390651840571056  0.870588378999384
 5.700000e+13       270609323      8518.5198  0.87041419895105460039  0.870588379108035
 5.800000e+13       274729676      7982.2781  0.87041448559131067273  0.870588379144207
 5.900000e+13       278838729      9789.9336  0.87041476655874741844  0.870588379019446
 6.000000e+13       282940804      9795.0100  0.87041504233619934326  0.870588379019498
 6.100000e+13       287036384      7683.7140  0.87041531312434332441  0.870588379158145
 6.200000e+13       291121998      7090.2624  0.87041557886219069828  0.870588379197007
 6.300000e+13       295198132      7686.1879  0.87041583974020183329  0.870588379158036
 6.400000e+13       299261260     13149.6240  0.87041609569080502227  0.870588378813451
 6.500000e+13       303319414     15595.5715  0.87041634736501162442  0.870588378661827
 6.600000e+13       307372401     15359.1483  0.87041659488165142565  0.870588378676836
 6.700000e+13       311415150     17648.8233  0.87041683806007932322  0.870588378539506
 6.800000e+13       315454016     16242.6354  0.87041707740585352337  0.870588378623476
 6.900000e+13       319485809     14459.3995  0.87041731284341813423  0.870588378727299
 7.000000e+13       323510017     12935.9000  0.87041754445682913342  0.870588378814804
 7.100000e+13       327525071     13362.0730  0.87041777226561260840  0.870588378790626
 7.200000e+13       331535393     11433.1771  0.87041799662320316424  0.870588378898335
 7.300000e+13       335538773      9472.9551  0.87041821750338705824  0.870588379006592
 7.400000e+13       339532243     10559.7864  0.87041843483896661712  0.870588378947550
 7.500000e+13       343523277      7326.8302  0.87041864912694043676  0.870588379121784
 7.600000e+13       347505956      5797.1614  0.87041886013354042435  0.870588379203095
 7.700000e+13       351481625      4726.8991  0.87041906801550380330  0.870588379259573
 7.800000e+13       355452541      1957.3272  0.87041927296895594406  0.870588379402270
 7.900000e+13       359412768      3520.0102  0.87041947476696639477  0.870588379322576
 8.000000e+13       363366270      5543.9012  0.87041967368850025912  0.870588379220987
 8.100000e+13       367317843      3323.4455  0.87041987004262404147  0.870588379331151
 8.200000e+13       371261352      3081.6780  0.87042006359202885735  0.870588379343237
 8.300000e+13       375201389       312.3167  0.87042025462681402004  0.870588379477568
 8.400000e+13       379134141     -1088.1496  0.87042044302491382287  0.870588379544919
 8.500000e+13       383058932      -362.3772  0.87042062881657873124  0.870588379510865
 8.600000e+13       386980653     -2322.0880  0.87042081229150054400  0.870588379602791
 8.700000e+13       390896126     -3711.9933  0.87042099335605911480  0.870588379667020
 8.800000e+13       394809015     -8120.7216  0.87042117223323322996  0.870588379868623
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 9.932000e+15     25226144083     12630.3121  0.87047762970876591242  0.870588379955331
 9.933000e+15     25228397836     13886.7345  0.87047763061639359014  0.870588379954825
 9.934000e+15     25230653103     13604.5038  0.87047763152453958243  0.870588379954939
 9.935000e+15     25232909529     12138.6230  0.87047763243306081292  0.870588379955529
 9.936000e+15     25235164742     11861.0949  0.87047763334100222672  0.870588379955641
 9.937000e+15     25237421537      9976.9223  0.87047763424948913035  0.870588379956399
 9.938000e+15     25239675662     10738.1080  0.87047763515680989843  0.870588379956093
 9.939000e+15     25241931981      9280.6548  0.87047763606492239309  0.870588379956680
 9.940000e+15     25244188071      8027.5656  0.87047763697285131717  0.870588379957184
 9.941000e+15     25246445183      5727.8431  0.87047763788110022191  0.870588379958109
 9.942000e+15     25248699666      6032.4901  0.87047763878819996769  0.870588379957987
 9.943000e+15     25250953966      6495.5096  0.87047763969513482771  0.870588379957800
 9.944000e+15     25253209389      5810.9043  0.87047764060243025080  0.870588379958076
 9.945000e+15     25255463717      6196.6769  0.87047764150919397315  0.870588379957921
 9.946000e+15     25257720377      4225.8304  0.87047764241680443700  0.870588379958713
 9.947000e+15     25259975519      3748.3675  0.87047764332371321683  0.870588379958905
 9.948000e+15     25262230191      3716.2910  0.87047764423034181256  0.870588379958918
 9.949000e+15     25264482542      5980.6038  0.87047764513594606541  0.870588379958008
 9.950000e+15     25266738372      4741.3087  0.87047764604285800735  0.870588379958506
 9.951000e+15     25268991715      5964.4084  0.87047764694867902639  0.870588379958014
 9.952000e+15     25271247554      4666.9058  0.87047764785541231473  0.870588379958536
 9.953000e+15     25273503273      3464.8037  0.87047764876200621378  0.870588379959019
 9.954000e+15     25275757231      3999.1049  0.87047764966780135531  0.870588379958804
 9.955000e+15     25278013793      1904.8122  0.87047765057455186472  0.870588379959646
 9.956000e+15     25280267052      3088.9284  0.87047765147988418078  0.870588379959170
 9.957000e+15     25282521352      3207.4563  0.87047765238554381666  0.870588379959122
 9.958000e+15     25284773906      5047.3987  0.87047765329041112536  0.870588379958383
 9.959000e+15     25287026379      6943.7584  0.87047765419515500668  0.870588379957622
 9.960000e+15     25289278406      9261.5383  0.87047765509962894367  0.870588379956691
 9.961000e+15     25291531256     10731.7411  0.87047765600434254342  0.870588379956100
 9.962000e+15     25293785411     10872.3696  0.87047765690948934116  0.870588379956044
 9.963000e+15     25296039280     11274.4266  0.87047765781443046080  0.870588379955882
 9.964000e+15     25298294299     10501.9149  0.87047765871974246174  0.870588379956193
 9.965000e+15     25300547355     11667.8374  0.87047765962417561039  0.870588379955725
 9.966000e+15     25302802502     10718.1969  0.87047766052935728589  0.870588379956106
 9.967000e+15     25305057233     10159.9960  0.87047766143428118239  0.870588379956330
 9.968000e+15     25307309644     11897.2377  0.87047766233818326366  0.870588379955633
 9.969000e+15     25309564703     10961.9247  0.87047766324305720525  0.870588379956008
 9.970000e+15     25311817635     12129.0598  0.87047766414698698381  0.870588379955540
 9.971000e+15     25314069206     14632.6459  0.87047766505028010161  0.870588379954535
 9.972000e+15     25316322441     15447.6856  0.87047766595415011958  0.870588379954208
 9.973000e+15     25318578668     13246.1819  0.87047766685912959325  0.870588379955091
 9.974000e+15     25320833287     12628.1375  0.87047766776337343370  0.870588379955339
 9.975000e+15     25323087944     11947.5551  0.87047766866754185258  0.870588379955612
 9.976000e+15     25325342502     11341.4377  0.87047766957157994881  0.870588379955855
 9.977000e+15     25327598162      9608.7880  0.87047767047596927700  0.870588379956550
 9.978000e+15     25329853009      8664.6087  0.87047767137994201962  0.870588379956928
 9.979000e+15     25332106884      8667.9027  0.87047767228343454172  0.870588379956927
 9.980000e+15     25334360017      9388.6728  0.87047767318653912005  0.870588379956638
 9.981000e+15     25336615091      8143.9217  0.87047767409033110778  0.870588379957137
 9.982000e+15     25338869245      7794.6523  0.87047767499366386108  0.870588379957277
 9.983000e+15     25341120944      9875.8673  0.87047767589592238972  0.870588379956443
 9.984000e+15     25343375774      8801.5696  0.87047767679934502506  0.870588379956873
 9.985000e+15     25345628368      9938.7618  0.87047767770178143534  0.870588379956418
 9.986000e+15     25347884462      7551.4468  0.87047767860552950171  0.870588379957374
 9.987000e+15     25350136499      9196.6275  0.87047767950756204177  0.870588379956715
 9.988000e+15     25352390440      8913.3065  0.87047768041026683181  0.870588379956829
 9.989000e+15     25354644833      8153.4866  0.87047768131306222713  0.870588379957133
 9.990000e+15     25356895691     10904.1708  0.87047768221435179151  0.870588379956031
 9.991000e+15     25359147460     12719.3616  0.87047768311591590241  0.870588379955305
 9.992000e+15     25361402080     11659.0619  0.87047768401853111676  0.870588379955729
 9.993000e+15     25363656605     10669.2746  0.87047768492101800331  0.870588379956125
 9.994000e+15     25365909172     11613.0023  0.87047768582263087405  0.870588379955748
 9.995000e+15     25368164280      9991.2479  0.87047768672517046972  0.870588379956397
 9.996000e+15     25370416537     11196.0142  0.87047768762647887384  0.870588379955915
 9.997000e+15     25372669575     11595.3038  0.87047768852800962422  0.870588379955755
 9.998000e+15     25374925066      9517.1197  0.87047768943043161888  0.870588379956586
 9.999000e+15     25377179498      8473.4646  0.87047769033233968739  0.870588379957004
 1.000000e+16     25379433651      7684.3412  0.87047769123404595410  0.870588379957320
========================================================================================
Enumeration of the prime quadruplets to 1e16 Thomas R. Nicely

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

Enumeration of the prime quadruplets to 1e16
Thomas R. Nicely

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