Gap size : 62 (r=31)

Generated by program gapCounts : Mon Jun 27 12:44:02 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+020-0-0.00-0.00
3.0000e+020-0-0.00-0.00
4.0000e+020-0-0.00-0.00
5.0000e+020-0-0.00-0.00
6.0000e+020-0-0.00-0.00
7.0000e+020-0-0.00-0.00
8.0000e+020-0-0.00-0.00
9.0000e+020-0-0.00-0.00
1.0000e+030-0-0.00-0.00
1.1000e+030-0-0.00-0.00
1.2000e+030-0-0.00-0.00
1.3000e+030-0-0.00-0.00
1.4000e+030-0-0.00-0.00
1.5000e+030-0-0.00-0.00
1.6000e+030-0-0.00-0.00
1.7000e+030-0-0.00-0.00
1.8000e+030-0-0.00-0.00
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+030-0-0.00-0.00
3.0000e+030-0-0.00-0.00
3.1000e+030-0-0.00-0.00
3.2000e+030-0-0.00-0.00
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+03000.000.00
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+04000.010.00
1.4500e+04000.010.00
1.5000e+04000.010.00
1.5500e+04000.010.00
1.6000e+04000.010.00
1.6500e+04000.010.00
1.7000e+04000.010.00
1.7500e+04000.010.00
1.8000e+04000.010.00
1.8500e+04000.010.00
1.9000e+04000.010.00
1.9500e+04000.010.00
2.0000e+04000.020.00
2.1000e+04000.020.00
2.2000e+04000.020.00
2.3000e+04000.020.00
2.4000e+04000.020.00
2.5000e+04000.030.00
2.6000e+04000.030.00
2.7000e+04000.030.00
2.8000e+04000.040.00
2.9000e+04000.040.00
3.0000e+04000.040.00
3.1000e+04000.050.00
3.2000e+04000.050.00
3.3000e+04000.050.00
3.4000e+04000.060.00
3.5000e+0410-0.94-0.05
3.6000e+0410-0.93-0.05
3.7000e+0410-0.93-0.05
3.8000e+0410-0.93-0.05
3.9000e+0410-0.92-0.05
4.0000e+0410-0.92-0.05
4.1000e+0410-0.91-0.05
4.2000e+0410-0.91-0.05
4.3000e+0410-0.90-0.05
4.4000e+0410-0.90-0.05
4.5000e+0410-0.89-0.05
4.6000e+0410-0.89-0.04
4.7000e+0410-0.88-0.04
4.8000e+0410-0.88-0.04
4.9000e+0410-0.87-0.04
5.0000e+0410-0.86-0.04
5.2000e+0410-0.85-0.04
5.4000e+0410-0.84-0.04
5.6000e+0410-0.83-0.04
5.8000e+0410-0.82-0.04
6.0000e+0410-0.80-0.04
6.2000e+0410-0.79-0.03
6.4000e+0410-0.77-0.03
6.6000e+0410-0.76-0.03
6.8000e+0410-0.74-0.03
7.0000e+0410-0.73-0.03
7.2000e+0410-0.71-0.03
7.4000e+0410-0.70-0.03
7.6000e+0410-0.68-0.03
7.8000e+0410-0.66-0.03
8.0000e+0410-0.65-0.03
8.2000e+0410-0.63-0.02
8.4000e+0410-0.61-0.02
8.6000e+0410-0.59-0.02
8.8000e+0410-0.58-0.02
9.0000e+0410-0.56-0.02
9.2000e+0410-0.54-0.02
9.4000e+0410-0.52-0.02
9.6000e+0411-0.50-0.02
9.8000e+0411-0.48-0.02
1.0000e+0511-0.46-0.02
1.0500e+0511-0.41-0.01
1.1000e+0511-0.35-0.01
1.1500e+0511-0.30-0.01
1.2000e+0511-0.24-0.01
1.2500e+0511-0.18-0.01
1.3000e+0511-0.12-0.00
1.3500e+0511-0.06-0.00
1.4000e+05110.010.00
1.4500e+05110.070.00
1.5000e+05110.140.00
1.5500e+05110.210.01
1.6000e+05110.280.01
1.6500e+05110.350.01
1.7000e+05110.420.01
1.7500e+05110.490.01
1.8000e+05120.570.02
1.8500e+05120.650.02
1.9000e+05120.720.02
1.9500e+0522-0.20-0.01
2.0000e+0522-0.12-0.00
2.1000e+05220.050.00
2.2000e+05220.210.01
2.3000e+05220.390.01
2.4000e+05230.560.01
2.5000e+0533-0.26-0.01
2.6000e+0533-0.07-0.00
2.7000e+05330.120.00
2.8000e+05330.310.01
2.9000e+05340.510.01
3.0000e+0544-0.29-0.01
3.1000e+0554-1.09-0.02
3.2000e+0564-1.88-0.04
3.3000e+0564-1.67-0.04
3.4000e+0565-1.46-0.03
3.5000e+0565-1.24-0.03
3.6000e+0565-1.02-0.02
3.7000e+0565-0.80-0.02
3.8000e+0565-0.58-0.01
3.9000e+0566-0.35-0.01
4.0000e+0566-0.12-0.00
4.1000e+05660.120.00
4.2000e+05660.350.01
4.3000e+05670.590.01
4.4000e+05670.840.02
4.5000e+05671.080.02
4.6000e+05671.330.03
4.7000e+05681.580.03
4.8000e+0588-0.17-0.00
4.9000e+05880.090.00
5.0000e+05880.340.01
5.2000e+05890.860.02
5.4000e+05990.390.01
5.6000e+059100.930.02
5.8000e+059101.480.03
6.0000e+059112.040.03
6.2000e+059122.600.04
6.4000e+0510122.170.04
6.6000e+0510132.750.05
6.8000e+0510133.340.05
7.0000e+0512141.930.03
7.2000e+0512152.530.04
7.4000e+0513152.140.03
7.6000e+0513162.750.04
7.8000e+0514162.370.04
8.0000e+0514173.000.05
8.2000e+0514183.630.05
8.4000e+0514184.270.06
8.6000e+0514194.920.07
8.8000e+0515204.570.07
9.0000e+0516204.230.06
9.2000e+0516214.890.07
9.4000e+0516225.560.08
9.6000e+0516226.230.09
9.8000e+0516236.910.10
1.0000e+0616247.600.10
1.0500e+0617258.330.11
1.1000e+0618279.100.12
1.1500e+0619299.890.13
1.2000e+0623317.710.10
1.2500e+0626336.560.08
1.3000e+0629345.440.07
1.3500e+0632364.340.05
1.4000e+0633385.270.06
1.4500e+0633407.220.09
1.5000e+0636426.200.07
1.5500e+0640444.190.05
1.6000e+0641465.210.06
1.6500e+0643485.250.06
1.7000e+0647503.310.04
1.7500e+0648524.390.05
1.8000e+0652542.500.03
1.8500e+0654572.610.03
1.9000e+0656592.750.03
1.9500e+0658612.910.03
2.0000e+0658635.080.05
2.1000e+0663674.480.05
2.2000e+0670721.950.02
2.3000e+0673763.470.03
2.4000e+0679812.060.02
2.5000e+0683862.710.03
2.6000e+0685905.410.05
2.7000e+0690955.170.05
2.8000e+06981001.980.02
2.9000e+061021052.840.02
3.0000e+061041105.750.05
3.1000e+061101154.700.04
3.2000e+061181201.710.01
3.3000e+061201254.750.04
3.4000e+061251304.840.04
3.5000e+061291355.970.05
3.6000e+061331407.150.06
3.7000e+061391456.360.05
3.8000e+06151151-0.39-0.00
3.9000e+06157156-1.10-0.01
4.0000e+061601611.220.01
4.1000e+061661670.580.00
4.2000e+06172172-0.02-0.00
4.3000e+06180177-2.59-0.02
4.4000e+06186183-3.13-0.02
4.5000e+06192188-3.63-0.03
4.6000e+06198194-4.10-0.03
4.7000e+06205199-5.54-0.04
4.8000e+06211205-5.95-0.04
4.9000e+06218211-7.33-0.05
5.0000e+06226216-9.68-0.07
5.2000e+06244228-16.29-0.11
5.4000e+06256239-16.79-0.11
5.6000e+06263251-12.18-0.08
5.8000e+06274263-11.47-0.07
6.0000e+06285274-10.66-0.07
6.2000e+06296286-9.76-0.06
6.4000e+06308298-9.75-0.06
6.6000e+06322310-11.66-0.07
6.8000e+06333323-10.48-0.06
7.0000e+06347335-12.21-0.07
7.2000e+06357347-9.87-0.06
7.4000e+06373360-13.43-0.08
7.6000e+06384372-11.92-0.07
7.8000e+06395385-10.34-0.06
8.0000e+06408397-10.68-0.06
8.2000e+06423410-12.94-0.07
8.4000e+06436423-13.14-0.07
8.6000e+06445436-9.26-0.05
8.8000e+06459449-10.32-0.06
9.0000e+06472462-10.31-0.06
9.2000e+06487475-12.23-0.06
9.4000e+06496488-8.10-0.04
9.6000e+06513501-11.90-0.06
9.8000e+06524514-9.64-0.05
1.0000e+07543528-15.31-0.08
1.0500e+07568561-6.76-0.03
1.1000e+07613595-17.86-0.09
1.1500e+07654629-24.62-0.12
1.2000e+07682664-18.07-0.09
1.2500e+07726699-27.21-0.13
1.3000e+07754734-20.06-0.09
1.3500e+07782769-12.63-0.06
1.4000e+07824805-18.92-0.08
1.4500e+07853841-11.96-0.05
1.5000e+078748773.250.01
1.5500e+079129141.710.01
1.6000e+079469504.400.02
1.6500e+079859872.320.01
1.7000e+0710371024-12.54-0.05
1.7500e+0710851062-23.18-0.09
1.8000e+0711291099-29.62-0.12
1.8500e+0711621137-24.86-0.10
1.9000e+0711991175-23.90-0.09
1.9500e+0712391213-25.75-0.10
2.0000e+0712821252-30.41-0.11
2.1000e+0713691329-40.19-0.15
2.2000e+0714561407-49.29-0.18
2.3000e+0715301485-44.73-0.16
2.4000e+0716111564-46.53-0.16
2.5000e+0717011644-56.74-0.19
2.6000e+0717771725-52.37-0.18
2.7000e+0718611806-55.44-0.18
2.8000e+0719461887-58.99-0.19
2.9000e+0720231969-54.01-0.17
3.0000e+0720942051-42.55-0.13
3.1000e+0721822134-47.60-0.15
3.2000e+0722652218-47.19-0.14
3.3000e+0723382302-36.34-0.11
3.4000e+0724192386-33.05-0.10
3.5000e+0725122471-41.35-0.12
3.6000e+0725852556-29.23-0.08
3.7000e+0726702641-28.72-0.08
3.8000e+0727502727-22.82-0.06
3.9000e+0728302813-16.56-0.05
4.0000e+0729132900-12.92-0.04
4.1000e+0730162987-28.93-0.08
4.2000e+0731133074-38.60-0.10
4.3000e+0731873162-24.93-0.07
4.4000e+0732783250-27.93-0.07
4.5000e+0733533338-14.61-0.04
4.6000e+0734583427-30.97-0.08
4.7000e+0735433516-27.03-0.07
4.8000e+0736283605-22.79-0.06
4.9000e+0737343695-39.26-0.10
5.0000e+0738143785-29.44-0.07
5.2000e+0739793965-13.96-0.03
5.4000e+0741604147-13.40-0.03
5.6000e+0743314329-1.81-0.00
5.8000e+0745174513-4.21-0.01
6.0000e+0747064697-8.66-0.02
6.2000e+0749004883-17.18-0.04
6.4000e+0750825069-12.80-0.03
6.6000e+0752685256-11.55-0.03
6.8000e+0754585445-13.47-0.03
7.0000e+075614563319.430.04
7.2000e+075786582337.120.08
7.4000e+075970601443.570.09
7.6000e+076174620530.770.06
7.8000e+076367639729.690.06
8.0000e+076562658927.310.06
8.2000e+076752678330.620.06
8.4000e+076923697753.590.11
8.6000e+077151717120.220.04
8.8000e+077353736613.480.03
9.0000e+077544756218.360.04
9.2000e+07775377595.850.01
9.4000e+077938795617.920.03
9.6000e+078123815430.580.06
9.8000e+078316835235.790.07
1.0000e+088496855154.560.10
1.0500e+089023905026.830.05
1.1000e+089521955231.310.06
1.1500e+08100021005855.830.10
1.2000e+08105491056617.280.03
1.2500e+08110461107731.500.05
1.3000e+08115441159147.390.08
1.3500e+08120571210850.830.08
1.4000e+08125871262739.730.06
1.4500e+08130951314852.990.08
1.5000e+0813665136726.520.01
1.5500e+08141821419715.240.02
1.6000e+08146861472539.080.06
1.6500e+08152011525553.970.08
1.7000e+08157101578776.830.11
1.7500e+08162691632151.610.07
1.8000e+08168311685625.250.04
1.8500e+08173411739452.690.07
1.9000e+08178631793369.880.10
1.9500e+08184031847470.770.10
2.0000e+08189601901656.320.08
2.1000e+08200312010675.190.10
2.2000e+082109621202106.180.14
2.3000e+08222042230499.970.13
2.4000e+082324823411163.300.20
2.5000e+082437724524146.920.18
2.6000e+082553725642104.600.13
2.7000e+082663226764132.130.16
2.8000e+08277982789193.310.11
2.9000e+082889329023129.970.15
3.0000e+083000530159153.940.17
3.1000e+083116031299139.060.15
3.2000e+083233232443111.190.12
3.3000e+083345933591132.190.14
3.4000e+083456234743180.930.19
3.5000e+083573835898160.300.17
3.6000e+083692537057132.190.14
3.7000e+08381213821998.480.10
3.8000e+083926939385116.080.12
3.9000e+08404654055488.880.09
4.0000e+084156741726158.820.16
4.1000e+084277342901127.780.13
4.2000e+084391344079165.710.16
4.3000e+084508045260179.520.17
4.4000e+084625246443191.130.18
4.5000e+084745447629175.480.16
4.6000e+084860648819212.500.20
4.7000e+084979550010215.130.20
4.8000e+085103051204174.310.16
4.9000e+085224552401155.980.14
5.0000e+085342053600180.080.16
5.2000e+085579456005211.370.19
5.4000e+085823058420189.790.16
5.6000e+086058260843260.970.22
5.8000e+086302163275253.560.21
6.0000e+086543265714282.250.23
6.2000e+086790268162259.740.21
6.4000e+087029070617326.760.26
6.6000e+087271073079369.040.29
6.8000e+087517275548376.350.29
7.0000e+087765378024371.460.29
7.2000e+088018180507326.160.25
7.4000e+088267382996323.250.24
7.6000e+088522185492270.530.20
7.8000e+088777087993222.830.16
8.0000e+089028090500219.970.16
8.2000e+089277693013236.810.17
8.4000e+089526595531266.180.19
8.6000e+089777798055277.940.19
8.8000e+08100346100584237.950.17
9.0000e+08102837103118281.080.19
9.2000e+08105369105657288.210.20
9.4000e+08107910108201291.210.20
9.6000e+08110421110750328.980.22
9.8000e+08112980113303323.400.21
1.0000e+09115558115861303.360.20
1.0500e+09121842122276433.520.28
1.1000e+09128116128716600.020.38
1.1500e+09134592135182589.550.36
1.2000e+09141176141671494.900.30
1.2500e+09147654148183528.970.31
1.3000e+09154174154717542.770.32
1.3500e+09160768161271503.370.29
1.4000e+09167310167846535.910.30
1.4500e+09173999174440440.620.24
1.5000e+09180629181052422.740.23
1.5500e+09187219187682462.610.25
1.6000e+09193883194329445.590.24
1.6500e+09200597200992395.090.21
1.7000e+09207394207672277.550.14
1.7500e+09214167214366199.450.10
1.8000e+09220855221076221.310.11
1.8500e+09227534227801266.650.13
1.9000e+09234380234539159.040.08
1.9500e+09240933241291358.080.17
2.0000e+09247659248056397.380.19
2.1000e+09260935261625690.270.32
2.2000e+09274634275243608.990.28
2.3000e+09288411288907496.070.22
2.4000e+09302170302615445.260.20
2.5000e+09315991316366374.520.16
2.6000e+09329805330156350.960.15
2.7000e+09343865343985119.880.05
2.8000e+09357968357851-117.33-0.05
2.9000e+09371865371752-113.14-0.05
3.0000e+09385804385687-116.91-0.05
3.1000e+09399904399655-248.90-0.10
3.2000e+09413849413655-194.31-0.08
3.3000e+09427749427685-64.23-0.02
3.4000e+09441786441744-41.69-0.02
3.5000e+09456057455832-224.68-0.08
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