A table of prime counts pi(x) 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 2255 EDT 7 August 2005.


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     x                 pi(x)        Li - pi         R - pi
==========================================================
 1.0000e01                4         2.1656         0.5646
 2.0000e01                8         1.9053        -0.4728
 3.0000e01               10         3.0226         0.1691
 4.0000e01               12         3.8395         0.6325
 5.0000e01               15         3.4687        -0.0243
 6.0000e01               17         3.9654         0.2300
 7.0000e01               19         4.3618         0.4146
 8.0000e01               22         3.6786        -0.4576
 9.0000e01               24         3.9299        -0.3776
 1.0000e02               25         5.1261         0.6616
 2.0000e02               46         4.1922        -1.4100
 3.0000e02               62         6.3336        -0.0346
 4.0000e02               78         7.4179         0.4515
 5.0000e02               95         6.7939        -0.6720
 6.0000e02              109         8.6465         0.7474
 7.0000e02              125         8.0889        -0.1957
 8.0000e02              139         9.1967         0.5631
 9.0000e02              154         9.0236         0.0699
 1.0000e03              168         9.6097         0.3594
 2.0000e03              303        11.8092         0.3353
 3.0000e03              430        12.7592        -0.2741
 4.0000e03              550        15.3645         1.0857
 5.0000e03              669        15.2808        -0.0539
 6.0000e03              783        17.4141         1.1525
 7.0000e03              900        14.3308        -2.7629
 8.0000e03             1007        19.4164         1.5637
 9.0000e03             1117        19.9488         1.3955
 1.0000e04             1229        17.1372        -2.0688
 2.0000e04             2262        26.6140         2.4194
 3.0000e04             3245        31.8991         4.1257
 4.0000e04             4203        30.0113        -0.6586
 5.0000e04             5133        33.5468         0.3986
 6.0000e04             6057        25.8469        -9.4916
 7.0000e04             6935        50.2945        12.9786
 8.0000e04             7837        39.2132         0.0851
 9.0000e04             8713        44.2916         3.4842
 1.0000e05             9592        37.8090        -4.5683
 2.0000e05            17984        52.0521        -2.4680
 3.0000e05            25997        89.6922        26.3336
 4.0000e05            33860        62.6219        -7.9510
 5.0000e05            41538        68.2888        -8.4941
 6.0000e05            49098        74.8270        -7.4695
 7.0000e05            56543       101.6627        14.3704
 8.0000e05            63951        86.2974        -5.5873
 9.0000e05            71274        88.0546        -8.0972
 1.0000e06            78498       129.5492        29.3994
 2.0000e06           148933       121.8332        -9.4921
 3.0000e06           216816       154.5644         0.3228
 4.0000e06           283146       206.2546        33.1979
 5.0000e06           348513       125.1150       -64.2044
 6.0000e06           412849       227.5041        23.6997
 7.0000e06           476648       178.8123       -38.1506
 8.0000e06           539777       222.6901        -6.3947
 9.0000e06           602489       187.2538       -53.1147
 1.0000e07           664579       339.4050        88.4476
 2.0000e07          1270607       298.0363       -35.9674
 3.0000e07          1857859       354.0973       -41.3796
 4.0000e07          2433654       362.4394       -83.7209
 5.0000e07          3001134       423.4267       -66.6722
 6.0000e07          3562115       568.4771        39.1531
 7.0000e07          4118064       520.9295       -44.0939
 8.0000e07          4669382       708.7454       110.7840
 9.0000e07          5216954       856.2234       227.5602
 1.0000e08          5761455       754.3754        96.8673
 2.0000e08         11078937      1037.8525       153.1722
 3.0000e08         16252325      1084.1472        30.4409
 4.0000e08         21336326      1052.0119      -141.4858
 5.0000e08         26355867       965.1489      -349.8050
 6.0000e08         31324703      1342.2521       -81.3140
 7.0000e08         36252931      1311.0438      -211.5094
 8.0000e08         41146179      1683.2333        69.2433
 9.0000e08         46009215      2433.6333       734.3285
 1.0000e09         50847534      1700.9570       -78.5723
 2.0000e09         98222287      3015.1378       601.7873
 3.0000e09        144449537      3191.7309       304.9513
 4.0000e09        189961812      2778.7703      -500.4800
 5.0000e09        234954223      4557.8739       937.0539
 6.0000e09        279545368      3498.9274      -427.7411
 7.0000e09        323804352      4067.5164      -138.1936
 8.0000e09        367783654      5241.6802       777.9819
 9.0000e09        411523195      5058.5772       353.9783
 1.0000e10        455052511      3103.5866     -1827.6932
 2.0000e10        882206716      8163.2048      1436.6258
 3.0000e10       1300005926     10205.6671      2134.0410
 4.0000e10       1711955433      8698.8221      -489.8988
 5.0000e10       2119654578     11961.2941      1799.0736
 6.0000e10       2524038155     10162.7505      -872.0577
 7.0000e10       2925699539     10280.3473     -1551.2344
 8.0000e10       3325059246     12346.4597      -222.3001
 9.0000e10       3722428991     15270.6039      2013.0737
 1.0000e11       4118054813     11587.6216     -2318.3686
 2.0000e11       8007105059     13344.6556     -5707.0635
 3.0000e11      11818439135     23766.7958       850.6010
 4.0000e11      15581005657     35813.5524      9683.0924
 5.0000e11      19308136142     35586.1714      6651.6536
 6.0000e11      23007501786     30191.6689     -1258.3116
 7.0000e11      26684074310     39428.2630      5679.8281
 8.0000e11      30341383527     34506.1467     -1370.0344
 9.0000e11      33981987586     45948.4896      8083.3095
 1.0000e12      37607912018     38262.8049     -1475.7741
 2.0000e12      73301896139     48195.4975     -6432.3993
 3.0000e12     108340298703     80927.2802     15095.6042
 4.0000e12     142966208126     61847.6795    -13313.8699
 5.0000e12     177291661649     72125.9698    -11181.7988
 6.0000e12     211381427039     99289.4065      8668.9067
 7.0000e12     245277688804    110789.8197     13483.7731
 8.0000e12     279010070811     79478.0329    -24019.8995
 9.0000e12     312600354108    127830.8386     18542.4553
 1.0000e13     346065536839    108971.0503     -5773.1740
 1.1000e13     379418886337    112657.5542     -7258.1337
 1.2000e13     412671294782     88008.6253    -36833.0266
 1.3000e13     445831610611    157230.3263     27677.3989
 1.4000e13     478907544860    151774.5337     17700.1158
 1.5000e13     511905471132    125904.1735    -12522.4150
 1.6000e13     544830816681    193903.6546     51277.1576
 1.7000e13     577688618018    144607.2552     -2081.2814
 1.8000e13     610482945548    146117.6119     -4507.3708
 1.9000e13     643217611048    138409.5740    -16036.8298
 2.0000e13     675895909271    170356.4223     12194.4469
 2.1000e13     708520996055     84243.3484    -77536.3752
 2.2000e13     741095263696    190877.2552     25570.5392
 2.3000e13     773621469799    181878.4100     13129.1952
 2.4000e13     806101694965    205855.8980     33743.0993
 2.5000e13     838538039510    199809.3947     24406.9314
 2.6000e13     870932387429    148708.9651    -29913.7369
 2.7000e13     903286330549    181201.5326      -576.0420
 2.8000e13     935601570432    184574.8917      -295.8708
 2.9000e13     967879555617    181932.1009     -5973.5162
 3.0000e13    1000121668853    157352.6492    -33532.5500
 3.1000e13    1032329128089    165616.0979    -28196.2148
 3.2000e13    1064503165321    162662.9859    -34026.5486
 3.3000e13    1096644814079    226232.6590     26713.4205
 3.4000e13    1128755244845    227568.7290     25265.1113
 3.5000e13    1160835361525    241218.4329     36173.7301
 3.6000e13    1192886020432    331592.2735    123847.8949
 3.7000e13    1224908399841    188325.5273    -22078.8704
 3.8000e13    1256902966055    164588.3757    -48438.0181
 3.9000e13    1288870563991    190407.7223    -25204.1696
 4.0000e13    1320811971702    221645.5455      3483.2265
 4.1000e13    1352727915540    227980.4036      7301.3918
 4.2000e13    1384619087497    178399.0723    -44764.1529
 4.3000e13    1416485977705    211254.9384    -14361.2001
 4.4000e13    1448329305292    205728.4656    -22310.3965
 4.5000e13    1480149581844    220467.5918     -9964.8508
 4.6000e13    1511947346053    260852.1600     28054.2918
 4.7000e13    1543723130448    314006.3077     78870.2350
 4.8000e13    1575477577153    234633.0364     -2814.9035
 4.9000e13    1607210998134    186224.8812    -53509.4260
 5.0000e13    1638923764567    253032.6281     11036.6592
 5.1000e13    1670616577394    170737.3355    -73496.3438
 5.2000e13    1702289545955    248948.4567      2500.3015
 5.3000e13    1733943394789    165444.6029    -83195.4759
 5.4000e13    1765578211937    218832.3911    -31977.7086
 5.5000e13    1797194471859    306518.8760     53560.0387
 5.6000e13    1828792681047    279922.2349     24835.3525
 5.7000e13    1860372997715    325545.6544     68350.8550
 5.8000e13    1891935863219    334266.7326     74983.6052
 5.9000e13    1923481549450    354604.1569     93251.7745
 6.0000e13    1955010428258    323907.9257     60504.8676
 6.1000e13    1986522749171    291212.9524     25777.3249
 6.2000e13    2018018738052    319116.5086     51665.9645
 6.3000e13    2049498854984    226392.6228    -43055.6198
 6.4000e13    2080963092223    290506.2548     19077.1139
 6.5000e13    2112411916194    306054.7934     32661.1537
 6.6000e13    2143845585991    266678.1938     -8663.9309
 6.7000e13    2175264258758    260062.8515    -17212.1150
 6.8000e13    2206668169844    288148.1248      8955.6027
 6.9000e13    2238057667938    232331.2440    -48763.8907
 7.0000e13    2269432871304    197552.1958    -85430.9397
 7.1000e13    2300793964184    216192.0299    -68664.8133
 7.2000e13    2332141323100    122054.9153   -164661.6505
 7.3000e13    2363474848702    218788.1579    -69774.4422
 7.4000e13    2394794929574    316329.2938     25934.0613
 7.5000e13    2426101844625    328754.2801     36539.5401
 7.6000e13    2457395721409    316183.7201     22162.3301
 7.7000e13    2488676723897    297224.9896      1409.5486
 7.8000e13    2519944991438    310214.0589     12616.9155
 7.9000e13    2551200765947    286219.7439    -13146.9950
 8.0000e13    2582444113487    327644.0662     26519.6043
 8.1000e13    2613675379008    253656.3466    -49214.1928
 8.2000e13    2644894475517    311187.6115      6582.4204
 8.3000e13    2676101820037    239127.8508    -67200.7792
 8.4000e13    2707297202782    399299.6220     91258.5594
 8.5000e13    2738481140597    423159.4638    113416.7744
 8.6000e13    2769653677359    411531.5467    100097.8421
 8.7000e13    2800814916205    402507.9599     89393.6629
 8.8000e13    2831964992460    398643.0039     83858.3541
 8.9000e13    2863104043147    397559.8344     81114.8937
 9.0000e13    2894232250783    348265.7794     30170.4365
 9.1000e13    2925349680455    314182.6280     -5553.3961
 9.2000e13    2956456424040    329028.1725      7661.0246
 9.3000e13    2987552707985    289133.2633    -33855.6098
 9.4000e13    3018638618871    227970.6227    -96630.7314
 9.5000e13    3049714111381    308275.6448    -17929.0967
 9.6000e13    3080779512073    318358.3962     -9440.7854
 9.7000e13    3111834899511    292054.0177    -37330.7993
 9.8000e13    3142880294628    318437.7151    -12524.0712
 9.9000e13    3173915901399    301226.5156    -31303.7095
 1.0000e14    3204941750802    314889.9540    -19200.3110
 1.0100e14    3235957953875    351661.8462     16019.8119
 1.0200e14    3266964657483    365839.2947     28653.6361
 1.0300e14    3297961919299    398865.0633     60143.8035
 1.0400e14    3328949899119    388073.4522     47824.4951
 1.0500e14    3359928666221    359389.7924     17620.9258
 1.0600e14    3390898336950    289801.6775    -53479.4246
 1.0700e14    3421858875180    306951.0377    -37834.7364
 1.0800e14    3452810475850    305650.1610    -40632.8297
 1.0900e14    3483753161542    351353.7561      3580.8985
 1.1000e14    3514687156436    306252.1485    -43003.3294
 1.1100e14    3545612389797    325830.6961    -24900.2563
 1.1200e14    3576529121002    233887.5049   -118311.8747
 1.1300e14    3607437145217    316899.5218    -36761.3338
 1.1400e14    3638336835589    281872.0785    -73243.3962
 1.1500e14    3669228069876    329748.9529    -26814.3760
 1.1600e14    3700111147796    238102.0153   -119902.4928
 1.1700e14    3730985963099    189096.5209   -170342.5795
 1.1800e14    3761852488112    284982.1060    -75885.0859
 1.1900e14    3792711017819    304047.5448    -58241.3220
 1.2000e14    3823561506566    363949.3195       245.1117
 1.2100e14    3854404065940    423865.0526     58751.7571
 1.2200e14    3885238840993    408300.8504     41784.6414
 1.2300e14    3916065744631    472732.6022    104819.5765
 1.2400e14    3946885022584    438665.2782     69361.4567
 1.2500e14    3977696644164    402903.2673     32214.5967
 1.2600e14    4008500671789    368053.7936     -4013.8523
 1.2700e14    4039297092727    410809.4480     37368.6293
 1.2800e14    4070086022472    478597.8716    103789.6127
 1.2900e14    4100867625083    469267.6228     93097.5878
 1.3000e14    4131641836725    507571.2616    130045.0474
 1.3100e14    4162408891817    419040.6805     40163.8182
 1.3200e14    4193168652698    400343.7119     20121.6678
 1.3300e14    4223921229182    399751.0390     18189.2163
 1.3400e14    4254666679385    416330.4378     33434.1773
 1.3500e14    4285405133096    376596.3742     -7629.0441
 1.3600e14    4316136553949    372357.9816    -13191.3745
 1.3700e14    4346860978409    421752.4408     34884.3083
 1.3800e14    4377578583249    401786.7860     13604.9807
 1.3900e14    4408289361212    372694.1558    -16796.2752
 1.4000e14    4438993433550    265412.5116   -125381.5536
 1.4100e14    4469690620802    310823.8408    -81268.9215
 1.4200e14    4500381173274    309290.8651    -84095.7110
 1.4300e14    4531065071494    330218.2696    -64457.2896
 1.4400e14    4561742386568    351712.4712    -44247.2919
 1.4500e14    4592413163940    376836.9422    -20402.2966
 1.4600e14    4623077366181    490838.1039     92324.0678
 1.4700e14    4653735190109    544039.8058    144255.6018
 1.4800e14    4684386662395    556251.4049    155201.6141
 1.4900e14    4715031792533    563811.4576    161500.6138
 1.5000e14    4745670621117    571324.0389    167756.6293
 1.5100e14    4776303255014    516498.7004    111679.1665
 1.5200e14    4806929598685    538842.0797    132774.8177
 1.5300e14    4837549795480    538375.1721    131064.5344
 1.5400e14    4868163917331    485952.2775     77402.5726
 1.5500e14    4898772014629    373395.6308    -36388.8754
 1.5600e14    4929373904757    424973.7282     13958.6444
 1.5700e14    4959969856070    413432.3582      1190.8789
 1.5800e14    4990559777556    470344.3465     56880.6133
 1.5900e14    5021143924065    380891.0257    -33790.8599
 1.6000e14    5051722055327    424854.4365      8958.4602
 1.6100e14    5082294389623    422956.2700      5850.2261
 1.6200e14    5112860910319    430333.5589     12021.4322
 1.6300e14    5143421606927    495487.1262     75972.8639
 1.6400e14    5173976653126    482269.7979     61557.3100
 1.6500e14    5204526059204    417453.3868     -4453.4530
 1.6600e14    5235069759055    403740.4566    -19356.8975
 1.6700e14    5265607888075    341876.8696    -82407.1965
 1.6800e14    5296140436573    277249.1281   -148217.8826
 1.6900e14    5326667328592    321071.5125   -105574.7096
 1.7000e14    5357188774246    298057.0252   -129764.7090
 1.7100e14    5387704641728    374417.1432    -54576.4371
 1.7200e14    5418215171667    343512.3875    -86649.4057
 1.7300e14    5448720375535    227452.7132   -203873.6920
 1.7400e14    5479220023907    288844.7261   -143642.7222
 1.7500e14    5509714376816    300443.7304   -133201.2232
 1.7600e14    5540203513601    215312.6138   -219486.3386
 1.7700e14    5570687141599    358136.5721    -77812.9029
 1.7800e14    5601165748499    272875.6809   -164220.8705
 1.7900e14    5631638989187    335926.3161   -102313.8952
 1.8000e14    5662107115450    326423.4296   -112957.0544
 1.8100e14    5692570027609    374613.6822    -65903.7160
 1.8200e14    5723027793732    442648.4403       997.4579
 1.8300e14    5753480619691    354532.6370    -88248.6274
 1.8400e14    5783928266147    379145.5045    -64762.7675
 1.8500e14    5814370916870    361926.1793    -83105.8532
 1.8600e14    5844808531911    371707.1839    -74445.3886
 1.8700e14    5875241143480    404841.7894    -42428.1293
 1.8800e14    5905668811897    429258.2615    -19125.8357
 1.8900e14    5936091509809    500247.9925     50752.8586
 1.9000e14    5966509342461    540199.5235     89596.4694
 1.9100e14    5996922371373    514926.4591     63218.5763
 1.9200e14    6027330527893    520119.2777     67309.6327
 1.9300e14    6057733891436    503111.0394     49202.6742
 1.9400e14    6088132486606    465759.9952     10755.9280
 1.9500e14    6118526253137    494513.1001     38416.3250
 1.9600e14    6148915233741    572562.4310    115375.9188
 1.9700e14    6179299673258    480699.5142     22426.2123
 1.9800e14    6209679392236    423739.5627    -35617.6042
 1.9900e14    6240054324930    492526.6274     32088.4973
 2.0000e14    6270424651315    531924.6626     70408.4491
 2.0100e14    6300790459485    478422.5096     15831.0703
 2.0200e14    6331151572773    533017.7998     69353.9705
 2.0300e14    6361508161919    549052.7784     84319.3736
 2.0400e14    6391860221546    555742.0530     89941.8657
 2.0500e14    6422207871571    456765.2659    -10098.9316
 2.0600e14    6452550837021    550454.6951     82529.2388
 2.0700e14    6482889421657    556174.7830     87190.7990
 2.0800e14    6513223550502    571797.5971    101757.7963
 2.0900e14    6543553215770    627777.2218    156684.2950
 2.1000e14    6573878505038    658981.0852    186837.7036
 2.1100e14    6604199447389    658550.2211    185359.0365
 2.1200e14    6634516003563    687751.4683    213515.1132
 2.1300e14    6664828342019    599918.6088    124639.6966
 2.1400e14    6695136335828    543562.4453     67243.5707
 2.1500e14    6725440028975    496071.8214     18715.5606
 2.1600e14    6755739250020    650055.5841    171664.4948
 2.1700e14    6786034466254    559189.4903     79766.1123
 2.1800e14    6816325358776    563142.0596     82688.9146
 2.1900e14    6846612049065    561005.3735     79524.9654
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