Gap size : 106 (r=53)

Generated by program gapCounts : Mon Jun 27 12:45:02 2011

π(r,x) = actual gap count
L(r,x) = conjectured gap count
D(r,x) = L(r,x) - π(r,x)
S(r,x) = D(r,x)*ln(x)/x½

x π(r,x)L(r,x) D(r,x)S(r,x)
1.0000e+020-0-0.00-0.00
2.0000e+02000.000.00
3.0000e+02000.000.00
4.0000e+02000.000.00
5.0000e+02000.000.00
6.0000e+02000.000.00
7.0000e+02000.000.00
8.0000e+02000.000.00
9.0000e+02000.000.00
1.0000e+03000.000.00
1.1000e+03000.000.00
1.2000e+03000.000.00
1.3000e+03000.000.00
1.4000e+03000.000.00
1.5000e+03000.000.00
1.6000e+03000.000.00
1.7000e+03000.000.00
1.8000e+03000.000.00
1.9000e+03000.000.00
2.0000e+03000.000.00
2.1000e+03000.000.00
2.2000e+03000.000.00
2.3000e+03000.000.00
2.4000e+03000.000.00
2.5000e+03000.000.00
2.6000e+03000.000.00
2.7000e+03000.000.00
2.8000e+03000.000.00
2.9000e+03000.000.00
3.0000e+03000.000.00
3.1000e+03000.000.00
3.2000e+03000.000.00
3.3000e+03000.000.00
3.4000e+03000.000.00
3.5000e+03000.000.00
3.6000e+03000.000.00
3.7000e+03000.000.00
3.8000e+03000.000.00
3.9000e+03000.000.00
4.0000e+03000.000.00
4.1000e+03000.000.00
4.2000e+03000.000.00
4.3000e+03000.000.00
4.4000e+03000.000.00
4.5000e+03000.000.00
4.6000e+03000.000.00
4.7000e+03000.000.00
4.8000e+03000.000.00
4.9000e+03000.000.00
5.0000e+03000.000.00
5.2000e+030-0-0.00-0.00
5.4000e+030-0-0.00-0.00
5.6000e+030-0-0.00-0.00
5.8000e+030-0-0.00-0.00
6.0000e+030-0-0.00-0.00
6.2000e+030-0-0.00-0.00
6.4000e+030-0-0.00-0.00
6.6000e+030-0-0.00-0.00
6.8000e+030-0-0.00-0.00
7.0000e+030-0-0.00-0.00
7.2000e+030-0-0.00-0.00
7.4000e+030-0-0.00-0.00
7.6000e+03000.000.00
7.8000e+03000.000.00
8.0000e+03000.000.00
8.2000e+03000.000.00
8.4000e+03000.000.00
8.6000e+03000.000.00
8.8000e+03000.000.00
9.0000e+03000.000.00
9.2000e+03000.000.00
9.4000e+03000.000.00
9.6000e+03000.000.00
9.8000e+03000.000.00
1.0000e+04000.000.00
1.0500e+04000.000.00
1.1000e+04000.000.00
1.1500e+04000.000.00
1.2000e+04000.000.00
1.2500e+04000.000.00
1.3000e+04000.000.00
1.3500e+04000.000.00
1.4000e+04000.000.00
1.4500e+04000.000.00
1.5000e+04000.000.00
1.5500e+04000.000.00
1.6000e+04000.000.00
1.6500e+04000.000.00
1.7000e+04000.000.00
1.7500e+04000.000.00
1.8000e+04000.000.00
1.8500e+04000.000.00
1.9000e+04000.000.00
1.9500e+04000.000.00
2.0000e+04000.000.00
2.1000e+04000.000.00
2.2000e+04000.000.00
2.3000e+04000.000.00
2.4000e+04000.000.00
2.5000e+04000.000.00
2.6000e+04000.000.00
2.7000e+04000.000.00
2.8000e+04000.000.00
2.9000e+04000.000.00
3.0000e+04000.000.00
3.1000e+04000.000.00
3.2000e+04000.000.00
3.3000e+04000.000.00
3.4000e+04000.000.00
3.5000e+04000.000.00
3.6000e+04000.000.00
3.7000e+04000.000.00
3.8000e+04000.000.00
3.9000e+04000.000.00
4.0000e+04000.000.00
4.1000e+04000.000.00
4.2000e+04000.000.00
4.3000e+04000.000.00
4.4000e+04000.000.00
4.5000e+04000.000.00
4.6000e+04000.000.00
4.7000e+04000.000.00
4.8000e+04000.000.00
4.9000e+04000.000.00
5.0000e+04000.000.00
5.2000e+04000.000.00
5.4000e+04000.000.00
5.6000e+04000.000.00
5.8000e+04000.000.00
6.0000e+04000.000.00
6.2000e+04000.000.00
6.4000e+04000.000.00
6.6000e+04000.000.00
6.8000e+04000.000.00
7.0000e+04000.000.00
7.2000e+04000.000.00
7.4000e+04000.000.00
7.6000e+04000.000.00
7.8000e+04000.000.00
8.0000e+04000.000.00
8.2000e+04000.000.00
8.4000e+04000.000.00
8.6000e+04000.000.00
8.8000e+04000.000.00
9.0000e+04000.000.00
9.2000e+04000.000.00
9.4000e+04000.000.00
9.6000e+04000.000.00
9.8000e+04000.000.00
1.0000e+05000.000.00
1.0500e+05000.000.00
1.1000e+05000.000.00
1.1500e+05000.000.00
1.2000e+05000.000.00
1.2500e+05000.000.00
1.3000e+05000.000.00
1.3500e+05000.000.00
1.4000e+05000.000.00
1.4500e+05000.000.00
1.5000e+05000.000.00
1.5500e+05000.000.00
1.6000e+05000.000.00
1.6500e+05000.000.00
1.7000e+05000.010.00
1.7500e+05000.010.00
1.8000e+05000.010.00
1.8500e+05000.010.00
1.9000e+05000.010.00
1.9500e+05000.010.00
2.0000e+05000.010.00
2.1000e+05000.010.00
2.2000e+05000.010.00
2.3000e+05000.010.00
2.4000e+05000.010.00
2.5000e+05000.010.00
2.6000e+05000.010.00
2.7000e+05000.020.00
2.8000e+05000.020.00
2.9000e+05000.020.00
3.0000e+05000.020.00
3.1000e+05000.020.00
3.2000e+05000.020.00
3.3000e+05000.030.00
3.4000e+05000.030.00
3.5000e+05000.030.00
3.6000e+05000.030.00
3.7000e+05000.030.00
3.8000e+05000.040.00
3.9000e+05000.040.00
4.0000e+05000.040.00
4.1000e+05000.040.00
4.2000e+05000.040.00
4.3000e+05000.050.00
4.4000e+05000.050.00
4.5000e+05000.050.00
4.6000e+05000.050.00
4.7000e+05000.060.00
4.8000e+05000.060.00
4.9000e+05000.060.00
5.0000e+05000.060.00
5.2000e+05000.070.00
5.4000e+05000.080.00
5.6000e+05000.080.00
5.8000e+05000.090.00
6.0000e+05000.090.00
6.2000e+05000.100.00
6.4000e+05000.110.00
6.6000e+05000.110.00
6.8000e+05000.120.00
7.0000e+05000.130.00
7.2000e+05000.140.00
7.4000e+05000.140.00
7.6000e+05000.150.00
7.8000e+05000.160.00
8.0000e+05000.170.00
8.2000e+05000.180.00
8.4000e+05000.190.00
8.6000e+05000.190.00
8.8000e+05000.200.00
9.0000e+05000.210.00
9.2000e+05000.220.00
9.4000e+05000.230.00
9.6000e+05000.240.00
9.8000e+05000.250.00
1.0000e+06000.260.00
1.0500e+06000.290.00
1.1000e+0610-0.68-0.01
1.1500e+0610-0.66-0.01
1.2000e+0610-0.63-0.01
1.2500e+0610-0.60-0.01
1.3000e+0610-0.57-0.01
1.3500e+0610-0.53-0.01
1.4000e+0611-0.50-0.01
1.4500e+0611-0.47-0.01
1.5000e+0611-0.43-0.01
1.5500e+0611-0.40-0.00
1.6000e+0611-0.36-0.00
1.6500e+0611-0.32-0.00
1.7000e+0611-0.28-0.00
1.7500e+0611-0.25-0.00
1.8000e+0611-0.21-0.00
1.8500e+0611-0.16-0.00
1.9000e+0611-0.12-0.00
1.9500e+0611-0.08-0.00
2.0000e+0611-0.04-0.00
2.1000e+06110.050.00
2.2000e+0621-0.86-0.01
2.3000e+0621-0.76-0.01
2.4000e+0621-0.67-0.01
2.5000e+0621-0.57-0.01
2.6000e+0622-0.46-0.00
2.7000e+0622-0.36-0.00
2.8000e+0622-0.25-0.00
2.9000e+0632-1.14-0.01
3.0000e+0632-1.03-0.01
3.1000e+0632-0.91-0.01
3.2000e+0632-0.79-0.01
3.3000e+0632-0.67-0.01
3.4000e+0632-0.55-0.00
3.5000e+0633-0.42-0.00
3.6000e+0633-0.30-0.00
3.7000e+0633-0.17-0.00
3.8000e+0633-0.03-0.00
3.9000e+0643-0.90-0.01
4.0000e+0643-0.76-0.01
4.1000e+0643-0.63-0.00
4.2000e+0654-1.49-0.01
4.3000e+0664-2.34-0.02
4.4000e+0664-2.20-0.02
4.5000e+0664-2.05-0.01
4.6000e+0664-1.91-0.01
4.7000e+0664-1.76-0.01
4.8000e+0664-1.60-0.01
4.9000e+0665-1.45-0.01
5.0000e+0665-1.30-0.01
5.2000e+0665-0.98-0.01
5.4000e+0665-0.66-0.00
5.6000e+0666-0.33-0.00
5.8000e+06660.010.00
6.0000e+06660.360.00
6.2000e+06670.710.00
6.4000e+06671.060.01
6.6000e+06671.430.01
6.8000e+06681.790.01
7.0000e+0698-0.83-0.00
7.2000e+0699-0.45-0.00
7.4000e+0699-0.06-0.00
7.6000e+06109-0.67-0.00
7.8000e+061010-0.27-0.00
8.0000e+0610100.130.00
8.2000e+0610110.540.00
8.4000e+0610110.950.01
8.6000e+0611110.370.00
8.8000e+0611120.790.00
9.0000e+0612120.220.00
9.2000e+0612130.660.00
9.4000e+0612131.100.01
9.6000e+0612141.540.01
9.8000e+0612141.990.01
1.0000e+0712142.440.01
1.0500e+0712163.590.02
1.1000e+0715171.770.01
1.1500e+0716181.980.01
1.2000e+0717192.210.01
1.2500e+0720200.470.00
1.3000e+072222-0.25-0.00
1.3500e+072423-0.94-0.00
1.4000e+072524-0.61-0.00
1.4500e+0725260.740.00
1.5000e+0727270.110.00
1.5500e+0728290.510.00
1.6000e+0728301.930.01
1.6500e+0730311.370.01
1.7000e+0731331.820.01
1.7500e+0733341.300.01
1.8000e+0735360.800.00
1.8500e+0737370.310.00
1.9000e+0737391.850.01
1.9500e+0739401.400.01
2.0000e+0739422.970.01
2.1000e+0740455.160.02
2.2000e+0743485.420.02
2.3000e+0745526.740.02
2.4000e+0747558.130.03
2.5000e+0749599.580.03
2.6000e+07526210.090.03
2.7000e+07546611.650.04
2.8000e+07586911.270.04
2.9000e+07597313.950.04
3.0000e+07627714.670.05
3.1000e+07658015.450.05
3.2000e+07668418.280.06
3.3000e+07688820.160.06
3.4000e+07729220.080.06
3.5000e+07779619.050.06
3.6000e+078210018.070.05
3.7000e+079110413.130.04
3.8000e+079410814.240.04
3.9000e+079611216.390.05
4.0000e+079911717.580.05
4.1000e+0710512115.810.04
4.2000e+0710712518.080.05
4.3000e+0711112918.390.05
4.4000e+0711513418.740.05
4.5000e+0712013818.130.05
4.6000e+0712414318.550.05
4.7000e+0713114716.020.04
4.8000e+0713915212.510.03
4.9000e+0714515611.050.03
5.0000e+071521618.620.02
5.2000e+071641705.860.01
5.4000e+071761793.230.01
5.6000e+071831895.730.01
5.8000e+071911987.360.02
6.0000e+072012087.110.02
6.2000e+072142183.980.01
6.4000e+072262281.970.00
6.6000e+07239238-0.93-0.00
6.8000e+07251248-2.72-0.01
7.0000e+072582590.590.00
7.2000e+07272269-2.99-0.01
7.4000e+072772802.540.01
7.6000e+072842906.160.01
7.8000e+072933017.880.02
8.0000e+073043127.700.02
8.2000e+0731032312.610.03
8.4000e+073283345.620.01
8.6000e+073373457.710.02
8.8000e+073483567.890.02
9.0000e+073593678.160.02
9.2000e+0736537913.520.03
9.4000e+0737139018.950.04
9.6000e+0738640115.480.03
9.8000e+0739141322.080.04
1.0000e+0840442520.760.04
1.0500e+0844045414.300.03
1.1000e+0847348411.310.02
1.1500e+0849851516.770.03
1.2000e+0853254613.670.02
1.2500e+0855157725.990.04
1.3000e+0859060918.710.03
1.3500e+0862464116.820.03
1.4000e+086716732.310.00
1.4500e+086987068.170.01
1.5000e+0872473915.390.02
1.5500e+0875877314.960.02
1.6000e+0878880718.860.03
1.6500e+0882084121.090.03
1.7000e+0886187614.640.02
1.7500e+0889391117.500.03
1.8000e+089379468.670.01
1.8500e+089779814.140.01
1.9000e+0810181017-1.11-0.00
1.9500e+0810541053-1.07-0.00
2.0000e+0810901089-0.76-0.00
2.1000e+08115811634.680.01
2.2000e+081218123719.160.02
2.3000e+081285131327.640.04
2.4000e+081373138916.080.02
2.5000e+081433146633.450.04
2.6000e+081492154552.710.06
2.7000e+081563162460.830.07
2.8000e+081631170472.790.08
2.9000e+081708178576.570.09
3.0000e+081794186672.120.08
3.1000e+081876194872.440.08
3.2000e+081960203271.500.08
3.3000e+082046211569.280.07
3.4000e+082117220082.760.09
3.5000e+082201228583.930.09
3.6000e+082274237196.760.10
3.7000e+082367245790.240.09
3.8000e+082458254486.350.09
3.9000e+082548263284.080.08
4.0000e+082645272075.420.07
4.1000e+082741280968.350.07
4.2000e+082832289966.850.06
4.3000e+082912298976.930.07
4.4000e+083004308075.550.07
4.5000e+083095317175.730.07
4.6000e+083190326272.430.07
4.7000e+083289335565.650.06
4.8000e+083383344764.390.06
4.9000e+083494354146.630.04
5.0000e+083586363448.370.04
5.2000e+083812382311.280.01
5.4000e+083981401433.070.03
5.6000e+084169420737.660.03
5.8000e+084351440150.010.04
6.0000e+084550459747.060.04
6.2000e+084763479531.750.03
6.4000e+084948499446.040.04
6.6000e+08518551959.880.01
6.8000e+085366539731.230.02
7.0000e+085567560134.050.03
7.2000e+085762580644.310.03
7.4000e+085966601346.960.04
7.6000e+086155622165.970.05
7.8000e+086338643092.310.07
8.0000e+086545664195.950.07
8.2000e+086753685399.860.07
8.4000e+086967706699.010.07
8.6000e+087188728092.380.06
8.8000e+087409749686.930.06
9.0000e+087638771374.640.05
9.2000e+087860793070.490.05
9.4000e+088064814985.470.06
9.6000e+088272837097.530.07
9.8000e+0884788591112.670.07
1.0000e+098719881393.870.06
1.0500e+0992679373105.840.07
1.1000e+0998369939103.000.06
1.1500e+09104711051140.090.02
1.2000e+09110511108937.860.02
1.2500e+091168911672-16.88-0.01
1.3000e+091227112261-10.36-0.01
1.3500e+0912851128543.240.00
1.4000e+09134361345316.750.01
1.4500e+09140381405618.010.01
1.5000e+0914660146643.870.00
1.5500e+091531015276-33.83-0.02
1.6000e+091594015893-47.20-0.03
1.6500e+091660116514-87.38-0.05
1.7000e+091722117139-82.49-0.04
1.7500e+091783617767-68.63-0.03
1.8000e+091847618400-75.91-0.04
1.8500e+091907019037-33.44-0.02
1.9000e+091970619677-29.30-0.01
1.9500e+092036420320-43.58-0.02
2.0000e+092099620968-28.38-0.01
2.1000e+092234622272-73.83-0.03
2.2000e+092371723590-127.26-0.06
2.3000e+092515024920-230.22-0.10
2.4000e+092648726262-225.22-0.10
2.5000e+092788327615-267.72-0.12
2.6000e+092931328980-333.17-0.14
2.7000e+093062630355-270.96-0.11
2.8000e+093202631741-285.46-0.12
2.9000e+093337033136-234.01-0.09
3.0000e+093474634541-204.95-0.08
3.1000e+093619935955-243.58-0.10
3.2000e+093767837379-299.17-0.12
3.3000e+093907138811-260.00-0.10
3.4000e+094055040252-298.31-0.11
3.5000e+094195741701-256.35-0.10
3.6000e+094345043158-292.33-0.11
3.7000e+094491744623-294.47-0.11
3.8000e+094640746095-311.98-0.11
3.9000e+094794447575-369.03-0.13
4.0000e+094941749062-354.82-0.12
4.1000e+095096950556-412.51-0.14
4.2000e+095250452058-446.27-0.15
4.3000e+095401653566-450.26-0.15
4.4000e+095555155080-470.63-0.16
4.5000e+095710656601-504.51-0.17
4.6000e+095864458129-515.05-0.17
4.7000e+096011959663-456.38-0.15
4.8000e+096164961202-446.62-0.14
4.9000e+096321362748-464.90-0.15
5.0000e+096471464300-414.33-0.13
5.2000e+096780667420-386.09-0.12
5.4000e+097093670562-373.73-0.11
5.6000e+097411573726-389.05-0.12
5.8000e+097727276910-361.77-0.11
6.0000e+098053380114-418.57-0.12
6.2000e+098372083338-382.09-0.11
6.4000e+098688886580-307.93-0.09
6.6000e+099018489840-343.64-0.10
6.8000e+099345093118-331.76-0.09
7.0000e+099676796413-353.77-0.10
7.2000e+0910006499725-339.16-0.09
7.4000e+09103415103053-362.36-0.10
7.6000e+09106766106396-369.79-0.10
7.8000e+09110150109755-394.86-0.10
8.0000e+09113508113129-378.94-0.10
8.2000e+09116884116518-366.40-0.09
8.4000e+09120393119920-472.58-0.12
8.6000e+09123784123337-446.80-0.11
8.8000e+09127170126768-402.38-0.10
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