Gap size : 60 (r=30)

Generated by program gapCounts : Mon Jun 27 12:43:59 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+02000.000.00
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+030-0-0.00-0.00
2.0000e+030-0-0.00-0.00
2.1000e+030-0-0.00-0.00
2.2000e+030-0-0.00-0.00
2.3000e+030-0-0.00-0.00
2.4000e+030-0-0.00-0.00
2.5000e+030-0-0.00-0.00
2.6000e+030-0-0.00-0.00
2.7000e+030-0-0.00-0.00
2.8000e+030-0-0.00-0.00
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+03000.000.00
5.4000e+03000.000.00
5.6000e+03000.000.00
5.8000e+03000.000.00
6.0000e+03000.000.00
6.2000e+03000.000.00
6.4000e+03000.000.00
6.6000e+03000.000.00
6.8000e+03000.000.00
7.0000e+03000.000.00
7.2000e+03000.000.00
7.4000e+03000.000.00
7.6000e+03000.000.00
7.8000e+03000.000.00
8.0000e+03000.010.00
8.2000e+03000.010.00
8.4000e+03000.010.00
8.6000e+03000.010.00
8.8000e+03000.010.00
9.0000e+03000.010.00
9.2000e+03000.010.00
9.4000e+03000.010.00
9.6000e+03000.010.00
9.8000e+03000.010.00
1.0000e+04000.010.00
1.0500e+04000.010.00
1.1000e+04000.010.00
1.1500e+04000.020.00
1.2000e+04000.020.00
1.2500e+04000.020.00
1.3000e+04000.020.00
1.3500e+04000.030.00
1.4000e+04000.030.00
1.4500e+04000.030.00
1.5000e+04000.040.00
1.5500e+04000.040.00
1.6000e+04000.040.00
1.6500e+04000.050.00
1.7000e+04000.050.00
1.7500e+04000.050.00
1.8000e+04000.060.00
1.8500e+04000.060.00
1.9000e+04000.070.00
1.9500e+04000.070.01
2.0000e+04000.080.01
2.1000e+04000.090.01
2.2000e+04000.100.01
2.3000e+04000.110.01
2.4000e+04000.120.01
2.5000e+04000.130.01
2.6000e+04000.150.01
2.7000e+04000.160.01
2.8000e+04000.170.01
2.9000e+04000.190.01
3.0000e+04000.200.01
3.1000e+04000.220.01
3.2000e+04000.240.01
3.3000e+04000.250.01
3.4000e+04000.270.02
3.5000e+04000.290.02
3.6000e+04000.310.02
3.7000e+04000.330.02
3.8000e+04000.340.02
3.9000e+04000.360.02
4.0000e+04000.380.02
4.1000e+04000.410.02
4.2000e+04000.430.02
4.3000e+04000.450.02
4.4000e+0410-0.53-0.03
4.5000e+0410-0.51-0.03
4.6000e+0411-0.48-0.02
4.7000e+0411-0.46-0.02
4.8000e+0411-0.44-0.02
4.9000e+0411-0.41-0.02
5.0000e+0411-0.39-0.02
5.2000e+0411-0.34-0.02
5.4000e+0411-0.28-0.01
5.6000e+0411-0.23-0.01
5.8000e+0411-0.17-0.01
6.0000e+0411-0.12-0.01
6.2000e+0411-0.06-0.00
6.4000e+04110.000.00
6.6000e+04110.060.00
6.8000e+04110.130.01
7.0000e+04110.190.01
7.2000e+04110.260.01
7.4000e+04110.330.01
7.6000e+04110.400.02
7.8000e+04110.470.02
8.0000e+04120.540.02
8.2000e+04120.610.02
8.4000e+04120.680.03
8.6000e+04120.760.03
8.8000e+04120.840.03
9.0000e+04120.910.03
9.2000e+04120.990.04
9.4000e+04121.070.04
9.6000e+04121.150.04
9.8000e+04121.240.05
1.0000e+05121.320.05
1.0500e+05230.530.02
1.1000e+05230.750.03
1.1500e+0533-0.02-0.00
1.2000e+05330.210.01
1.2500e+0543-0.55-0.02
1.3000e+0544-0.30-0.01
1.3500e+0544-0.05-0.00
1.4000e+05440.210.01
1.4500e+0554-0.53-0.02
1.5000e+0565-1.26-0.04
1.5500e+0565-0.99-0.03
1.6000e+0575-1.71-0.05
1.6500e+0576-1.43-0.04
1.7000e+0576-1.14-0.03
1.7500e+0576-0.85-0.02
1.8000e+0576-0.55-0.02
1.8500e+0577-0.25-0.01
1.9000e+0587-0.94-0.03
1.9500e+0597-1.63-0.04
2.0000e+05108-2.31-0.06
2.1000e+05128-3.67-0.10
2.2000e+05129-3.01-0.08
2.3000e+051410-4.33-0.11
2.4000e+051610-5.64-0.14
2.5000e+051711-5.94-0.15
2.6000e+051812-6.22-0.15
2.7000e+052013-7.49-0.18
2.8000e+052013-6.74-0.16
2.9000e+052014-5.98-0.14
3.0000e+052115-6.21-0.14
3.1000e+052216-6.42-0.15
3.2000e+052316-6.63-0.15
3.3000e+052517-7.82-0.17
3.4000e+052518-7.00-0.15
3.5000e+052619-7.17-0.15
3.6000e+052620-6.33-0.14
3.7000e+052721-6.48-0.14
3.8000e+052721-5.62-0.12
3.9000e+052722-4.75-0.10
4.0000e+052823-4.87-0.10
4.1000e+053024-5.98-0.12
4.2000e+053125-6.07-0.12
4.3000e+053226-6.16-0.12
4.4000e+053227-5.25-0.10
4.5000e+053328-5.32-0.10
4.6000e+053329-4.38-0.08
4.7000e+053430-4.44-0.08
4.8000e+053631-5.48-0.10
4.9000e+053931-7.52-0.14
5.0000e+053932-6.55-0.12
5.2000e+054034-5.59-0.10
5.4000e+054236-5.60-0.10
5.6000e+054638-7.57-0.13
5.8000e+055140-10.52-0.18
6.0000e+055543-12.44-0.21
6.2000e+055745-12.33-0.21
6.4000e+056047-13.20-0.22
6.6000e+056049-11.04-0.18
6.8000e+056551-13.86-0.23
7.0000e+056753-13.65-0.22
7.2000e+056756-11.42-0.18
7.4000e+057058-12.16-0.19
7.6000e+057460-13.88-0.22
7.8000e+057662-13.58-0.21
8.0000e+057765-12.26-0.19
8.2000e+058067-12.92-0.19
8.4000e+058269-12.56-0.19
8.6000e+058572-13.18-0.19
8.8000e+058674-11.78-0.17
9.0000e+058877-11.35-0.16
9.2000e+058879-8.91-0.13
9.4000e+058982-7.45-0.11
9.6000e+059384-8.98-0.13
9.8000e+059587-8.48-0.12
1.0000e+069689-6.97-0.10
1.0500e+0610495-8.62-0.12
1.1000e+06106102-4.16-0.06
1.1500e+06116108-7.61-0.10
1.2000e+06119115-3.96-0.05
1.2500e+06129122-7.22-0.09
1.3000e+06131129-2.40-0.03
1.3500e+06136136-0.49-0.01
1.4000e+061391433.500.04
1.4500e+061421507.570.09
1.5000e+061531573.720.04
1.5500e+061611642.930.03
1.6000e+061701711.220.01
1.6500e+061741794.580.05
1.7000e+061831863.000.03
1.7500e+061871936.490.07
1.8000e+061942017.050.08
1.8500e+062012097.660.08
1.9000e+0620621610.330.11
1.9500e+0620822416.070.17
2.0000e+0621323218.860.19
2.1000e+0623124816.600.17
2.2000e+0624226421.560.21
2.3000e+0625428025.720.25
2.4000e+0627029626.080.25
2.5000e+0628131331.620.29
2.6000e+0630332926.340.24
2.7000e+0631834628.240.25
2.8000e+0633136332.300.29
2.9000e+0635438126.520.23
3.0000e+0637239825.900.22
3.1000e+0639741518.430.16
3.2000e+0641943314.100.12
3.3000e+0644045110.920.09
3.4000e+064624696.870.06
3.5000e+064784878.950.07
3.6000e+065025053.170.03
3.7000e+065235240.510.00
3.8000e+065395422.970.02
3.9000e+065585612.550.02
4.0000e+065795790.240.00
4.1000e+065925986.050.05
4.2000e+066116175.970.04
4.3000e+0662663610.000.07
4.4000e+066476558.130.06
4.5000e+0666367411.370.08
4.6000e+066866947.710.06
4.7000e+067047139.140.06
4.8000e+067237339.670.07
4.9000e+067437529.300.06
5.0000e+067637729.020.06
5.2000e+0679981212.720.09
5.4000e+0684085211.780.08
5.6000e+068888924.170.03
5.8000e+069329330.880.01
6.0000e+06981974-7.10-0.05
6.2000e+0610271015-11.77-0.07
6.4000e+0610711057-14.16-0.09
6.6000e+0611031099-4.26-0.03
6.8000e+0611481141-7.08-0.04
7.0000e+06118011833.360.02
7.2000e+061207122619.050.11
7.4000e+061246126923.000.13
7.6000e+061277131235.190.20
7.8000e+061315135640.620.23
8.0000e+061362139937.280.21
8.2000e+061407144336.160.20
8.4000e+061450148737.260.20
8.6000e+061497153234.580.19
8.8000e+061534157642.110.23
9.0000e+061589162131.840.17
9.2000e+061640166625.770.14
9.4000e+061700171110.890.06
9.6000e+061740175616.210.08
9.8000e+06179218029.710.05
1.0000e+071834184713.400.07
1.0500e+07195819624.390.02
1.1000e+07207120787.440.04
1.1500e+0722042196-8.49-0.04
1.2000e+0723312314-17.46-0.08
1.2500e+0724432433-10.49-0.05
1.3000e+0725882552-35.64-0.16
1.3500e+0727002673-26.93-0.12
1.4000e+0728302795-35.40-0.16
1.4500e+0729642917-47.08-0.20
1.5000e+0730723040-32.00-0.14
1.5500e+0732023164-38.19-0.16
1.6000e+0733223288-33.66-0.14
1.6500e+0734423414-28.45-0.12
1.7000e+0735703539-30.56-0.12
1.7500e+0736733666-7.04-0.03
1.8000e+0738163793-22.89-0.09
1.8500e+0739593921-38.12-0.15
1.9000e+0740804049-30.77-0.12
1.9500e+0742104178-31.85-0.12
2.0000e+0743474308-39.36-0.15
2.1000e+0745714568-2.77-0.01
2.2000e+0748454831-14.11-0.05
2.3000e+07509450961.520.01
2.4000e+07535753625.030.02
2.5000e+0756345630-3.66-0.01
2.6000e+07589659004.370.01
2.7000e+0761806172-7.94-0.03
2.8000e+07644564450.330.00
2.9000e+0767326720-11.87-0.04
3.0000e+0770136996-16.59-0.05
3.1000e+0772957274-20.90-0.06
3.2000e+0775777553-23.84-0.07
3.3000e+0778437834-9.45-0.03
3.4000e+0781358115-19.77-0.06
3.5000e+0784428398-43.85-0.13
3.6000e+0787148682-31.73-0.09
3.7000e+0789848968-16.44-0.05
3.8000e+07924892545.990.02
3.9000e+079518954223.520.07
4.0000e+07982298308.130.02
4.1000e+07101001012019.780.05
4.2000e+07103951041015.460.04
4.3000e+07106901070212.120.03
4.4000e+071100710995-12.25-0.03
4.5000e+071131511288-26.67-0.07
4.6000e+071158511583-2.18-0.01
4.7000e+071189111878-12.78-0.03
4.8000e+071222112175-46.50-0.12
4.9000e+071250212472-30.36-0.08
5.0000e+071279612770-26.38-0.07
5.2000e+071341313368-44.97-0.11
5.4000e+071401013970-40.40-0.10
5.6000e+071461714574-42.79-0.10
5.8000e+071520315182-21.27-0.05
6.0000e+071584215792-49.94-0.12
6.2000e+071646016405-54.91-0.13
6.4000e+071708117021-60.25-0.14
6.6000e+071768317639-44.08-0.10
6.8000e+07182451826014.540.03
7.0000e+07188541888328.530.06
7.2000e+07194951950812.810.03
7.4000e+07200922013543.310.09
7.6000e+07207292076535.970.07
7.8000e+07213542139742.730.09
8.0000e+07220002203130.530.06
8.2000e+07226252266641.320.08
8.4000e+07232212330483.040.17
8.6000e+07239082394435.640.07
8.8000e+07245452458540.070.08
9.0000e+0725227252281.290.00
9.2000e+072590925873-35.74-0.07
9.4000e+072656126520-41.06-0.08
9.6000e+072717827168-9.72-0.02
9.8000e+072782327818-4.75-0.01
1.0000e+08284392847030.810.06
1.0500e+08300673010538.460.07
1.1000e+08317393175011.340.02
1.1500e+083342933404-25.00-0.04
1.2000e+083511135066-44.98-0.08
1.2500e+08367043673632.020.05
1.3000e+08383763841437.660.06
1.3500e+08400584009940.620.07
1.4000e+084167441791116.590.18
1.4500e+08433994348990.310.14
1.5000e+08451234519571.510.11
1.5500e+08468604690645.980.07
1.6000e+08485684862355.470.08
1.6500e+08503025034744.790.07
1.7000e+08520215207654.740.08
1.7500e+08537595381051.150.07
1.8000e+08554865555063.830.09
1.8500e+085730557295-10.36-0.01
1.9000e+08590195904425.410.04
1.9500e+08607716079928.000.04
2.0000e+086257662558-17.71-0.02
2.1000e+086616266090-71.59-0.09
2.2000e+086965969640-19.18-0.02
2.3000e+087309773206108.650.14
2.4000e+08767567678731.110.04
2.5000e+088027680383107.500.13
2.6000e+088385683994138.140.17
2.7000e+088751787618101.440.12
2.8000e+089107491256181.840.21
2.9000e+089468194906224.820.26
3.0000e+089833698568231.890.26
3.1000e+08101838102242403.620.45
3.2000e+08105626105927300.580.33
3.3000e+08109309109622313.400.34
3.4000e+08113080113329248.700.26
3.5000e+08116819117045226.140.24
3.6000e+08120451120771320.400.33
3.7000e+08124201124507306.180.31
3.8000e+08127884128252368.190.37
3.9000e+08131586132006420.170.42
4.0000e+08135436135769332.850.33
4.1000e+08139232139540308.000.30
4.2000e+08142984143319335.380.32
4.3000e+08146793147107313.780.30
4.4000e+08150664150902237.990.23
4.5000e+08154520154705184.820.17
4.6000e+08158313158515202.070.19
4.7000e+08162208162333124.560.11
4.8000e+08165990166157167.120.15
4.9000e+08169764169989224.600.20
5.0000e+08173611173827215.820.19
5.2000e+08181293181523229.930.20
5.4000e+08188971189244273.320.24
5.6000e+08196728196990261.930.22
5.8000e+08204364204759394.810.33
6.0000e+08212267212550283.060.23
6.2000e+08220021220363341.850.28
6.4000e+08227955228196241.390.19
6.6000e+08235803236050246.970.20
6.8000e+08243646243923276.900.22
7.0000e+08251517251815297.540.23
7.2000e+08259498259724226.310.17
7.4000e+08267369267652282.620.21
7.6000e+08275260275596335.960.25
7.8000e+08283258283557298.820.22
8.0000e+08291130291534403.720.29
8.2000e+08299096299526430.210.31
8.4000e+08306998307534535.870.38
8.6000e+08315054315556502.290.35
8.8000e+08323134323593459.080.32
9.0000e+08331211331644432.880.30
9.2000e+08339319339708389.340.26
9.4000e+08347601347786185.120.12
9.6000e+08355737355877139.900.09
9.8000e+08363817363980163.390.11
1.0000e+09371839372096257.280.17
1.0500e+09392144392438294.480.19
1.1000e+09412499412852353.450.22
1.1500e+09433203433335131.520.08
1.2000e+0945379045388191.330.06
1.2500e+09474496474490-6.14-0.00
1.3000e+094951504951577.320.00
1.3500e+09516077515881-195.86-0.11
1.4000e+09536882536659-223.04-0.13
1.4500e+09557722557489-233.38-0.13
1.5000e+09578504578368-135.92-0.07
1.5500e+095992885992957.460.00
1.6000e+09620096620269173.030.09
1.6500e+09641104641287183.130.10
1.7000e+09661976662348372.240.19
1.7500e+09683065683451385.940.20
1.8000e+09704112704594481.860.24
1.8500e+09725499725776276.740.14
1.9000e+09746525746995470.390.23
1.9500e+09767931768252320.680.16
2.0000e+0978945478954489.540.04
2.1000e+0983218783223042.970.02
2.2000e+09874710875047337.220.15
2.3000e+09917503917989485.520.22
2.4000e+09960758961048289.740.13
2.5000e+0910039151004219304.280.13
2.6000e+0910475171047498-18.97-0.01
2.7000e+0910912131090879-333.72-0.14
2.8000e+0911347341134359-375.28-0.15
2.9000e+0911784641177932-531.67-0.22
3.0000e+0912222111221596-614.58-0.24
3.1000e+0912660181265348-670.47-0.26
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