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Old 2020-12-31, 09:16   #2
Batalov
 
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"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

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But why?
Thomas Nicely's tables from 1999 had shown billions of quads.
Why extend it to 10000?
Code:
                               Table 1.
  Counts of prime quadruplets and estimates of Brun's B_4 constant.
======================================================================
      x      pi_4(x) delta_4(x)        S_4(x)             F_4(x)
======================================================================
      10           1      10.29  0.510689310689311  0.964070321217938
     100           2      11.60  0.789976586880612  0.846649213196690
    1000           5      11.49  0.853473194253130  0.870265083531968
   10000          12      12.17  0.863733192400183  0.870817270689693
   10^05          38      14.88  0.867011003684134  0.870638051768363
   10^06         166      17.68  0.868379532753497  0.870478518913352
   10^07         899     -36.05  0.869267876960829  0.870589687487152
   10^08        4768     -33.36  0.869705293632323  0.870590803418512
   10^09       28388       8.84  0.869966856425087  0.870588778250229
   10^10      180529     545.93  0.870134891176928  0.870588272187457
   10^11     1209318     638.22  0.870247695545365  0.870588327409023
   10^12     8398278   -3699.97  0.870326020813441  0.870588394083423
   10^13    60070590    4848.36  0.870382016088034  0.870588379770569
   10^14   441296836   -6103.68  0.870423153466140  0.870588379781931
 2.0e+14   807947960    2717.36  0.870433368925933  0.870588379517423
 3.0e+14  1151928827  -12660.14  0.870438957019776  0.870588379757893
 4.0e+14  1482125418  -15032.60  0.870442759816539  0.870588379787802
 5.0e+14  1802539207  -23557.26  0.870445621161320  0.870588379871401
 6.0e+14  2115416076  -35177.17  0.870447903679533  0.870588379961704
 7.0e+14  2422194981  -49882.89  0.870449795732922  0.870588380059497
 8.0e+14  2723839871  -35301.69  0.870451407176393  0.870588379983029
 9.0e+14  3021126140  -38141.52  0.870452807976233  0.870588379996686
 1.0e+15  3314576487  -26197.22  0.870454044834374  0.870588379948604
 1.1e+15  3604646822  -19485.07  0.870455150797010  0.870588379922608
 1.2e+15  3891706125  -36034.00  0.870456149967533  0.870588379981021
 1.3e+15  4175985018  -18182.67  0.870457060200978  0.870588379923299
 1.4e+15  4457782901  -24552.75  0.870457895584737  0.870588379943262
 1.5e+15  4737286827  -38254.45  0.870458666969910  0.870588379980055
 1.6e+15  5014641832  -29496.94  0.870459383002448  0.870588379958289
======================================================================
Computing 10000 triplets or quads on the fly would be likely faster than fetching it from internet.
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