A table of prime counts pi(x) to 5e15

A table of prime counts pi(x) to 5e15
Thomas R. Nicely

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

Last updated 2255 EDT 7 August 2005.
This is an extended table of the values of pi(x), the number of primes <= x.
The domain of this table consists of each decade from 10 through 1e12, then each 1e12 to 5e15.
See also on this site A table of prime counts pi(x) beyond 5e15.
The counts in this table were obtained by the author, employing a direct and explicit generation and enumeration of the primes.
These counts have been verified by the work of Tomás Oliveira e Silva, among others. Silva has accumulated the most extensive tables of pi(x) of which I am aware.
Additional tables of pi(x), with other domains and granularities, are available from Tomás Oliveira e Silva, Dr. Chris K. Caldwell's Prime Pages, and the work of Xavier Gourdon, Pascal Sebah, and Patrick Demichel.
Also given are the differences Li(x) - pi(x) and R(x) - pi(x). Positive values of these differences indicate a deficit of primes (compared to the number predicted by the corresponding theoretical estimate); negative values indicate a surplus of primes. Here Li(x) is the principal-value logarithmic integral,
Li(x) = integral(1/ln(t), t, 0, x) = Li(2) + integral(1/ln(t), t, 2, x) .
where
Li(2) = 1.0451637801174927848445888891946131365226155781512...
In this document, we will also employ (for clarity) the notations Li(0,x) = integral(1/ln(t), t, 0, x) and Li(2,x) = integral(1/ln(t), t, 2, x); thus
Li(x) = Li(0, x) = Li(2, x) + Li(2) .
Li(x) is now usually defined as Li(0, x), with a lower limit of zero, the Cauchy principal value being employed near the singularity at t=1; in some references, Li(2, x) is still used, with the lower limit of 2. Adoption of the lower limit zero eliminates the trivial exceptions (n=2,3,4,5,7) to the conditional inequality Li(n) > pi(n) (n an integer > 1). The fact that Li(0, x) <= 0 for 0 <= x < 1 and for 1 < x < 1.45136923488338105... is not considered to constitute an exception, the domain of the inequality being commonly taken as those integers n > 1.
SKEWES' PROBLEM: Gauss and Riemann conjectured that Li(n) > pi(n) for all sufficiently large integers n. Excluded trivial exceptions include all n < 2; n=2,3,4,5,7 if Li(2, n) is used; and scattered values of n as large as n=23 if a rounded or truncated value of Li(2, n) is used. While the inequality is true for all other integers for which pi(n) has been computed to date, it was proven by J. E. Littlewood (1914) that it is false for infinitely many values of n; more specifically, there exists a monotonically increasing infinite sequence of integers over which the sign of Li(n) - pi(n) is strictly alternating. Thus there must exist an integer N > 23 such that Li(n) > pi(n) for all integers n, 23 < n < N, but Li(N) <= pi(N). However, Littlewood's proof was not constructive, and the problem of determining an upper bound for N was first attacked by S. Skewes, who proved (1933) that the Riemann Hypothesis implies N < exp(exp(exp(79))) < 10^(10^(10^34)))---the infamous "Skewes' number." Skewes also proved a weaker (even larger) upper bound unconditionally (1955), namely N < exp(exp(exp(exp(7.7)))) < 10^(10^(10^1000))) (the final exponent can in fact be replaced by 959). In consequence, the problem of determining N, or at least confining it within ever narrower bounds, is sometimes referred to as "Skewes' problem." R. S. Lehman (1966) improved the upper bound to N < 1.65e1165, and H. J. J. te Riele (1986) improved it to N < 6.69e370. Most recently, Carter Bays and Richard H. Hudson (2000) proved that N < 1.39822e316.
It is not entirely clear which of these upper bounds were established for Li(0, N) and which ones were established for Li(2, N). More likely than not, each one is valid for both quantities; and in any case, an upper bound valid for Li(0, N) would also be valid for the smaller quantity Li(2, N).
Lower bounds for N (applicable to both Li(0, N) and Li(2, N)) have been less well investigated. Apparently Gauss himself verified that N > 3000000. J. B. Rosser and L. Schoenfeld extended this to N > 1e8 ("Approximate formulas for some functions of prime numbers," Illinois J. Math. 6 (1962), 64-94). Richard P. Brent verified that N > 1e11 ("Irregularities in the distribution of primes and twin primes, " Math. Comp. 29:129 (1975), 43-56, MR 51 #5522; also Corrigendum, ibid. 30:133 (1976), 198, MR 53 #302, and Addendum, "Tables concerning irregularities in the distribution of primes and twin primes to 1e11," (August, 1975), reviewed ibid. 30:379 (1976)). Andrew Odlyzko improved the lower bound to N > 1.59e13 (1993, unpublished). Most recently, Tadej Kotnik (2004, in preparation) has verified computationally that N > 1e14. Kotnik also contributed some of the information herein presented.
The function R(x) is Riemann's prime number formula,
R(x) = sum(µ(n)*Li(x^(1/n)/n, n, 1, +infinity) ,
where µ(n) is Möbius' function,
µ(n) = 1 , if n=1;
µ(n) = 0 , if n contains a repeated prime factor;
µ(n) = (-1)^k , if n is the product of k distinct primes.
See pp. 41-59 of "Prime numbers and computer methods for factorization," by Hans Riesel (2nd ed., Birkhäuser, Boston, 1994) for additional details and explanation; also "The new book of prime number records," Paulo Ribenboim (3rd ed., Springer-Verlag New York, 1996), pp. 213-248.
==========================================================
     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
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 1.8740e15   54898642592972   1535210.3452    220538.0037
 1.8750e15   54927078251699   1530219.4305    215218.0721
 1.8760e15   54955513592269   1412145.9529     96815.6705
 1.8770e15   54983948268868   1527046.8536    211387.7399
 1.8780e15   55012382551226   1605434.8072    289446.9549
 1.8790e15   55040816509870   1577025.2225    260708.7240
 1.8800e15   55069249987500   1599360.2426    282715.1904
 1.8810e15   55097683088802   1567995.7455    251022.2321
 1.8820e15   55126115725925   1571024.3446    253722.4622
 1.8830e15   55154547984903   1522653.3890    205023.2298
 1.8840e15   55182979711662   1577197.9638    259239.6201
 1.8850e15   55211411015374   1625726.8910    307440.4548
 1.8860e15   55239841993182   1571337.7295    252723.2929
 1.8870e15   55268272481098   1578258.7756    259316.4305
 1.8880e15   55296702549620   1576232.0636    256961.9018
 1.8890e15   55325132282765   1481480.3659    161882.4793
 1.8900e15   55353561484141   1490635.1939    170709.6741
 1.8910e15   55381990237498   1520185.7979    199932.7367
 1.8920e15   55410418574163   1539044.1681    218463.6569
 1.8930e15   55438846593491   1448094.0343    127186.1647
 1.8940e15   55467274147133   1395922.8670     74687.7305
 1.8950e15   55495701122751   1495106.8774    173544.5653
 1.8960e15   55524127737592   1528637.0181    206747.6216
 1.8970e15   55552553945477   1542929.9832    220713.5935
 1.8980e15   55580979699191   1585438.2089    262894.9172
 1.8990e15   55609404987164   1667968.8741    345098.7714
 1.9000e15   55637829945151   1655003.9004    331807.0778
 1.9010e15   55666254453598   1666333.9529    342810.5012
 1.9020e15   55694678500721   1713979.4403    390129.4503
 1.9030e15   55723102095969   1788727.5155    464551.0781
 1.9040e15   55751525300283   1829873.0761    505370.2818
 1.9050e15   55779948250511   1700803.7644    375974.7040
 1.9060e15   55808370560171   1788236.9685    463081.7324
 1.9070e15   55836792571258   1750412.8218    424931.5006
 1.9080e15   55865214145380   1725958.2044    400150.8884
 1.9090e15   55893635502276   1495368.7426    169235.5222
 1.9100e15   55922056249640   1451184.8100    124725.7754
 1.9110e15   55950476537753   1443359.5275    116574.7689
 1.9120e15   55978896509022   1329719.7638      2609.3714
 1.9130e15   56007316029869   1244077.1360    -83358.8003
 1.9140e15   56035735190089   1096870.0096   -230891.3806
 1.9150e15   56064153728263   1149750.4994   -178336.2549
 1.9160e15   56092571885745   1161597.4693   -166814.5591
 1.9170e15   56120989619737   1175441.5333   -153295.6795
 1.9180e15   56149406946914   1174840.0556   -154222.2520
 1.9190e15   56177823985835   1041466.1510   -287921.1617
 1.9200e15   56206240540415    971636.6853   -358075.5430
 1.9210e15   56234656629638    946599.2757   -383437.7787
 1.9220e15   56263072146492   1073597.2914   -256764.4998
 1.9230e15   56291487273139   1170699.8537   -159986.5849
 1.9240e15   56319902254023    993693.8364   -337317.1604
 1.9250e15   56348316577858   1054095.8665   -277239.5993
 1.9260e15   56376730466393   1130387.3244   -201272.5213
 1.9270e15   56405143998698   1143728.3441   -188255.7925
 1.9280e15   56433557166175   1102946.8139   -229361.5245
 1.9290e15   56461969944574   1032522.3767   -300110.0747
 1.9300e15   56490382119439   1147140.4304   -185816.0452
 1.9310e15   56518793930900   1206900.1281   -126380.2829
 1.9320e15   56547205435809   1155178.3787   -178425.8790
 1.9330e15   56575616505904   1120465.8474   -213462.1685
 1.9340e15   56604026920498   1323677.9555    -10573.7299
 1.9350e15   56632437120033   1324600.8817     -9974.3848
 1.9360e15   56660847049504   1178467.5615   -156431.1976
 1.9370e15   56689256433923   1160493.6885   -174728.4750
 1.9380e15   56717665372281   1171915.7141   -163629.7656
 1.9390e15   56746073882236   1195302.8480   -140565.8595
 1.9400e15   56774482064433   1130237.0591   -205954.7882
 1.9410e15   56802889768895   1126922.0751   -209592.8239
 1.9420e15   56831297030882   1150324.3835   -186513.4792
 1.9430e15   56859703985476   1065588.2316   -271572.5069
 1.9440e15   56888110396959   1108657.6273   -228825.8992
 1.9450e15   56916516334621   1210468.3388   -127337.8878
 1.9460e15   56944921912905   1256802.8958    -81325.9434
 1.9470e15   56973327115199   1264498.5890    -73952.7749
 1.9480e15   57001731995003   1180280.4714   -158493.3299
 1.9490e15   57030136357339   1199351.3578   -139744.7932
 1.9500e15   57058540304761   1219381.8258   -120036.5875
 1.9510e15   57086943897603   1180262.2160   -159478.3722
 1.9520e15   57115347021684   1196397.6322   -143665.0438
 1.9530e15   57143749719974   1225041.9418   -115342.7346
 1.9540e15   57172152031428   1227463.7764   -113242.8132
 1.9550e15   57200553944782   1215150.5321   -125877.8837
 1.9560e15   57228955328890   1319471.3697    -21878.7852
 1.9570e15   57257356311751   1412650.2151     70978.4080
 1.9580e15   57285757044412   1343862.7599      1869.3874
 1.9590e15   57314157356381   1283823.4614    -58491.3895
 1.9600e15   57342557139211   1341201.5434     -1434.6993
 1.9610e15   57370956539805   1369315.9961     26358.4484
 1.9620e15   57399355570172   1356379.5769     13100.8108
 1.9630e15   57427754224470   1308455.8104    -35144.0876
 1.9640e15   57456152419911   1308553.9890    -35366.9544
 1.9650e15   57484550138952   1374438.1733     30196.2709
 1.9660e15   57512947667900   1220022.1920   -124540.5831
 1.9670e15   57541344633234   1219047.6429   -125835.9185
 1.9680e15   57569741041949   1364739.8929     19535.6314
 1.9690e15   57598137105578   1445786.0785    100261.2029
 1.9700e15   57626532809296   1477231.1058    131385.7023
 1.9710e15   57654928238900   1373497.6514     27331.8061
 1.9720e15   57683323107239   1421956.1625     75469.9612
 1.9730e15   57711717542508   1494630.8571    147824.3857
 1.9740e15   57740111557896   1578551.7246    231425.0689
 1.9750e15   57768505245427   1581913.5260    234466.7718
 1.9760e15   57796898543643   1566392.7944    218626.0273
 1.9770e15   57825291458461   1526290.8352    178204.1409
 1.9780e15   57853683987253   1464453.7265    116047.1905
 1.9790e15   57882076151568   1359550.3196     10824.0274
 1.9800e15   57910467747972   1415232.2390     66186.2760
 1.9810e15   57938859182428   1225753.8832   -123611.6652
 1.9820e15   57967249968131   1278137.4247    -71547.6239
 1.9830e15   57995640361165   1316515.8105    -33488.6530
 1.9840e15   58024030297704   1404931.7624     54607.9691
 1.9850e15   58052419985547   1335802.7774    -14840.2607
 1.9860e15   58080809130651   1403388.1279     52425.9301
 1.9870e15   58109197998361   1342558.8623     -8722.4102
 1.9880e15   58137586240051   1502156.8052    150556.5429
 1.9890e15   58165974229898   1508220.5576    156301.3903
 1.9900e15   58194361851997   1476870.4975    124632.5099
 1.9910e15   5822274905916
A table of prime counts pi(x) to 5e15 Thomas R. Nicely

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

A table of prime counts pi(x) to 5e15
Thomas R. Nicely

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