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Aproximation for pn

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  • Sebastian Martin
    E=2.7182818284590... EulerGamma=0.5772156649... The FLOOR function returns the largest number that is less than or equal to the specified number.
    Message 1 of 1 , Nov 27, 2008
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      E=2.7182818284590...
      EulerGamma=0.5772156649...

      The FLOOR function returns the largest number that is less than or equal to the specified number.

      G[n_]:=Floor[n Log[n]+(E-EulerGamma) n]


      Do[Print[G[n],"
      ",Prime[n]],{n,100000000,10000000000,100000000}]


      2056174690 2038074743
      4250978817 4222234741
      6498107758 6461335109
      8779216507 8736028057
      11085592409 11037271757
      13412103826 13359555403
      15755359939 15699342107
      18112950759 18054236957
      20483074336 20422213579
      22864332000 22801763489
      25255606398 25191867719
      27655984268 27591444869
      30064705144 29999858327
      32481125931 32416190071
      34904695662 34840062373
      37334937007 37270791697
      39771432427 39708229123
      42213813597 42151671491
      44661753184 44601021791
      47114958362 47055833459
      49573165624 49515912443
      52036136593 51980824361
      54503654583 54450530317
      56975521770 56924869123
      59451556830 59403556879
      61931592958 61886415293
      64415476188 64373242723
      66903063969 66864033133
      69394223938 69358391041
      71888832867 71856445751
      74386775747 74358036521
      76887944992 76862786989
      79392239747 79370946857
      81899565269 81882324553
      84409832391 84396675733
      86922957045 86914060703
      89438859834 89434278433
      91957465655 91957378453
      94478703359 94483159541
      97002505446 97011687217
      99528807794 99542707807
      102057549408 102076308361
      104588672199 104612516171
      107122120782 107151309641
      109657842287 109692247799
      112195786198 112235432899
      114735904193 114780843743
      117278150008 117328571431
      119822479307 119878605053
      122368849564 122430513841
      124917219955 124984528451
      127467551255 127540832401
      130019805751 130098810557
      132573947152 132659061989
      135129940510 135221143753
      137687752150 137785178317
      140247349599 140350965523
      142808701524 142918698271
      145371777673 145488029839
      147936548818 148059109201
      150502986707 150632097701
      153071064013 153207003401
      155640754293 155783260051
      158212031941 158361271499
      160784872153 160940840461
      163359250886 163522167691
      165935144830 166105103819
      168512531366 168689358917
      171091388543 171275105437
      173671695046 173862636221
      176253430170 176451547457
      178836573790 179041892879
      181421106345 181633670833
      184007008805 184226918219
      186594262657 186821628281
      189182849883 189417675203
      191772752936 192015086821
      194363954726 194613827843
      196956438603 197213910917
      199550188337 199815106433
      202145188103 202417940723


      Sincerely


      Sebastian Martin Ruiz





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