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Prime sum

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  • demichel patrick
    Hi Jon, primes up to 10^10 summed by 1000 like in your code upper limit sum previous (sum-previous)/sum*100 for p | sum
    Message 1 of 1 , Jan 29, 2003
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      Hi Jon,

      primes up to 10^10 summed by 1000 like in your code

      upper limit sum previous
      (sum-previous)/sum*100

      for p | sum ratio
      | | | |
      V V V V
      58207208000 1280558564874 3376017975046
      163.6363589804
      58510443000 994677522373 2632969867349
      164.7058778475
      75334322000 1280683466519 3390044420491
      164.7058784717
      92043573000 1564740732893 4141960719053
      164.7058795098
      95664384000 1626294519203 4304897213415
      164.7058796905
      33584307000 671686130734 1779968191661
      164.9999918438
      37948328000 758966548514 2011261302961
      164.9999933329
      69514971000 1390299410208 3684293381869
      164.9999960309
      72979632000 1459592630180 3867920415491
      164.9999962670
      97502472000 1950049431206 5167630931073
      164.9999968399
      83726993000 1674539850230 4437530552497
      164.9999969775
      93675412000 1873508231022 4964796756955
      164.9999970508
      53247298000 1224687844011 3248085085305
      165.2173858987
      6713651000 140986660965 375964371304
      166.6666255734
      7362854000 132531362540 353416918130
      166.6666299634
      18665088000 391966836853 1045244841044
      166.6666520658
      55009096000 990163720444 2640436538152
      166.6666616474
      59997934000 1259956604683 3359884219662
      166.6666619449
      69355486000 1248398740570 3329063256416
      166.6666625197
      86239623000 1552313204372 4139501833472
      166.6666637772
      92719660000 1668953871338 4450543610048
      166.6666638593
      96531916000 2027170223665 5405787211552
      166.6666641235
      47385015000 1042470318966 2795715797429
      168.1818126200
      89285710000 1964285609174 5267856803599
      168.1818152613
      59765969000 1135553403281 3048064342739
      168.4210477404
      89637185000 1703106505735 4571496358033
      168.4210495726
      85921590000 1632510199999 4382001013949
      168.4210496174
      61457938000 983326999794 2642691273425
      168.7499960825
      42742560000 854851191626 2308098160434
      169.9999933373
      46707390000 934147790228 2522198977626
      169.9999940063
      76106104000 1522122070882 4109729539854
      169.9999966148
      92795376000 1855907510988 5010950219960
      169.9999967828
      99900354000 1998007070796 5394619033990
      169.9999971392
      81934159000 1392880693753 3768971246276
      170.5882322283
      92078492000 1565334352839 4235610561244
      170.5882327033
      16140204000 338944272711 919991541161
      171.4285548484
      21439092000 450220921543 1222028160249
      171.4285591307
      42704548000 768681855144 2092522777153
      172.2222156214
      54262132000 976718368396 2658844396435
      172.2222170145
      62485316000 1124735679400 3061780412235
      172.2222179231
      96156488000 1730816776264 4711667837289
      172.2222191224
      81819137000 1472744454844 4009137641969
      172.2222194613
      69766098000 1534854146028 4185965791942
      172.7272687620
      34095575000 511433619311 1397918514227
      173.3333244909
      45834075000 870847414191 2383371822776
      173.6842050556
      63918980000 1214460610133 3323786878502
      173.6842060393
      41865284000 669844535740 1842072431028
      174.9999936915
      68814460000 1101031354210 3027836173628
      174.9999954180
      65541669000 1310833369646 3604791711365
      174.9999957919
      75327938000 1506558751900 4143036508255
      174.9999960526
      72818742000 1456374829660 4005030726529
      174.9999962210
      79800546000 1596010908364 4389029946045
      174.9999967446
      92597930000 1481566872952 4074308855144
      174.9999969307
      99044484000 1584711735816 4357957231048
      174.9999973215
      44572514000 757732729395 2094908087127
      176.4705820217
      99601273000 1693221631667 4681259759937
      176.4705855623
      52417349000 943512271930 2620867370834
      177.7777723519
      96443043000 1735974765100 4822152075078
      177.7777748860
      46917309000 891428861609 2486617296225
      178.9473622984
      64905115000 1233197177077 3439971015129
      178.9473637365
      71583408000 1360084743483 3793920543727
      178.9473642658
      88317763000 1678037489243 4680841357041
      178.9473648263
      74538881000 1416238729115 3950560616347
      178.9473649556
      99104281000 1882981328217 5252526814729
      178.9473658617
      49058530000 981170589778 2747277595566
      179.9999943117
      57433961000 1148679209350 3216301733658
      179.9999954276
      72994011000 1459880209998 4087664530858
      179.9999960862
      87192280000 1307884193731 3662075697254
      179.9999965446
      97816094000 1956321872192 5477701179048
      179.9999967751
      97291702000 2043125729623 5740210333255
      180.9523785065
      65984342000 1319686830412 3761107406565
      184.9999954452
      44331045000 664965665929 1906234873901
      186.6666613889
      95978030000 1535648474118 4414989314726
      187.4999968506
      62208051000 1057536858713 3048194426723
      188.2352895418
      99434747000 1690390690741 4872302530291
      188.2352912246
      98395815000 1672728846107 4821394861553
      188.2352912592
      30477528000 579073022623 1676263956439
      189.4736744679
      8208073000 164161449874 476068144242
      189.9999632115
      24461025000 489220490652 1418739365740
      189.9999883180
      10786741000 226521551479 657991108577
      190.4761618843
      19935331000 418641940283 1216055100953
      190.4761764029
      67642179000 1420485749021 4126172827215
      190.4761860553
      83087916000 1329406649032 3905131980353
      193.7499961503
      43499706000 739494993831 2174985226580
      194.1176403795
      61498973000 1045482529803 3074948575154
      194.1176430498
      17614062000 334667168887 986387391894
      194.7368261949
      48169332000 915217299133 2697482507998
      194.7368357824
      46915203000 891388847265 2627251285830
      194.7368361059
      68579315000 1371586289354 4046179493143
      194.9999955926
      68935444000 1102967096412 3308901240938
      199.9999956211
      31982487000 671632214825 2046879073762
      204.7618962553
      40333290000 806665791572 2460330599013
      204.9999919072
      61690070000 987041110292 3022813355677
      206.2499954822
      97574652000 1561194425068 4781157875677
      206.2499967273
      80334082000 1446013466460 4498708505768
      211.1111072002
      95140115000 1712522060630 5327846357392
      211.1111079896
      32978582000 626593047517 1978714829868
      215.7894645830
      33994296000 543908727116 1733709020667
      218.7499913560
      76076712000 1217227384156 3879912234751
      218.7499957078
      83985193000 1343763079592 4283244764669
      218.7499961652



      observe that the values of the gaps ratios are not
      random.

      They are frequently very close to an int or int +
      fraction of type "small_int/small_int"

      like 194.1176403795 is close to 194 + 2/17

      Can somebody explain the special properties of the
      ratios ?

      Patrick.
      --- In primenumbers@yahoogroups.com, "Jon Perry"
      <perry@g...> wrote:
      > Here's an interesting puzzle:
      >
      > Calculate the sums of primes per 10000:
      >
      > pv=vector(200);forprime
      >
      (p=2,200000,pv[p\1000+1]=pv[p\1000+1]+p);write("primesums.txt",pv)
      >
      > [76127, 200923, 316773, 419684, 534629, 626598,
      760737, 803095, 935224,
      > 1062606, 1112190, 1185849, 1362757, 1417399,
      1481378, 1673536, 1617104,
      > 1820728, 1735092, 2028762, 2007600, 2234774,
      2247894, 2443290, 2300968,
      > 2500168, 2677675, 2587424, 2793506, 2711374,
      2897129, 2894592, 3444212,
      > 3350240, 3243076, 3265954, 3615395, 3525086,
      3467340, 3791778, 3564578,
      > 4192173, 4334840, 3699107, 4272036, 3913680,
      4184638, 4513925, 4317595,
      > 4850070, 4493077, 4996599, 4673755, 4922218,
      4905138, 5163289, 5596465,
      > 5232567, 5263136, 5589186, 5323758, 5351613,
      5500248, 5906767, 5159888,
      > 6418650, 5587768, 6683189, 5481728, 5628071,
      6909012, 6794231, 6526174,
      > 6101115, 6853152, 6870959, 6349635, 7362233,
      6594258, 7237021, 7085320,
      > 7496244, 7339651, 7012664, 7350193, 7265479,
      7609930, 8138385, 6728984,
      > 8412256, 8051783, 7776987, 8973613, 8040892,
      8221701, 9071881, 8107090,
      > 7995812, 8572841, 8656623, 8140801, 9439325,
      8913581, 8281818, 9510131,
      > 8651996, 9799616, 8170924, 9874421, 9635906,
      9175039, 9367824, 9111219,
      > 9984232, 9388364, 10743877, 9438083, 10577200,
      9362307, 10397991, 10606394,
      > 10447596, 10777774, 10869172, 10334157, 10541370,
      10496533, 10966708,
      > 11438525, 10746825, 11090169, 10915313, 11529129,
      10945942, 10758622,
      > 12058149, 13105034, 11001232, 11771671, 11720614,
      12225263, 12311799,
      > 11685308, 11052105, 11416579, 12368429, 12305266,
      12241163, 12327243,
      > 13602171, 12792125, 13634880, 13421056, 11820111,
      12976850, 13216101,
      > 11893780, 13857020, 12204185, 13558111, 13642461,
      13567090, 13166433,
      > 13572043, 12664039, 13239640, 13488103, 13898589,
      12299705, 14746721,
      > 14832605, 13891347, 15351763, 13708387, 14482389,
      13166101, 16766033,
      > 12958271, 15887981, 16875172, 12811787, 14339577,
      16606785, 14496781,
      > 15312975, 16882121, 14730463, 16309521, 15082912,
      16678224, 14289809,
      > 15511417, 17132971, 16255398, 14394400, 16617589,
      14933722, 17181865,
      > 17072284, 15363673]
      >
      > The sequence is reasonably well behaved.
      >
      > 1) Find the curve.
      > 2) Find a larger variation than 16875172->12811787
      (21 & 20 from the end),
      > percentage wise,
      > i.e. (16875172-12811787)/16875172%
      >
      > This takes a while before it becomes 'stable', so
      for this one, the first 10
      > sums don't count.
      >
      > Jon Perry
      > perry@g...
      > http://www.users.globalnet.co.uk/~perry/maths/
      > http://www.users.globalnet.co.uk/~perry/DIVMenu/
      > BrainBench MVP for HTML and JavaScript
      > http://www.brainbench.com


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