Gap size : 18 (r=9)

Generated by program gapCounts : Mon Jun 27 12:33:03 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+02000.070.03
2.0000e+02000.010.00
3.0000e+02000.060.02
4.0000e+02000.180.05
5.0000e+02000.350.10
6.0000e+0211-0.44-0.11
7.0000e+0211-0.19-0.05
8.0000e+02110.080.02
9.0000e+02110.370.08
1.0000e+03120.680.15
1.1000e+03220.000.00
1.2000e+03220.340.07
1.3000e+0333-0.31-0.06
1.4000e+0343-0.95-0.18
1.5000e+0343-0.58-0.11
1.6000e+0344-0.20-0.04
1.7000e+03440.180.03
1.8000e+0355-0.43-0.08
1.9000e+0355-0.03-0.01
2.0000e+0365-0.63-0.11
2.1000e+0366-0.22-0.04
2.2000e+0376-0.80-0.13
2.3000e+0377-0.38-0.06
2.4000e+03770.040.01
2.5000e+03770.460.07
2.6000e+0388-0.11-0.02
2.7000e+03880.330.05
2.8000e+03890.770.11
2.9000e+03990.210.03
3.0000e+039100.650.09
3.1000e+039101.090.16
3.2000e+039111.540.22
3.3000e+039111.990.28
3.4000e+039112.450.34
3.5000e+039122.900.40
3.6000e+039123.360.46
3.7000e+039133.820.52
3.8000e+039134.280.57
3.9000e+0310143.740.50
4.0000e+0311143.210.42
4.1000e+0311153.670.48
4.2000e+0312153.140.40
4.3000e+0312163.610.46
4.4000e+0313163.080.39
4.5000e+0315171.550.19
4.6000e+0315172.030.25
4.7000e+0316181.500.19
4.8000e+031818-0.02-0.00
4.9000e+0318180.460.06
5.0000e+0318190.940.11
5.2000e+0319200.900.11
5.4000e+0320210.860.10
5.6000e+0321220.830.10
5.8000e+0321231.810.21
6.0000e+0321242.780.31
6.2000e+0322252.760.31
6.4000e+0323262.750.30
6.6000e+0326270.730.08
6.8000e+0327280.720.08
7.0000e+0327291.710.18
7.2000e+0328301.710.18
7.4000e+0329311.700.18
7.6000e+033232-0.30-0.03
7.8000e+033333-0.30-0.03
8.0000e+033434-0.30-0.03
8.2000e+0334350.710.07
8.4000e+0335360.710.07
8.6000e+0335371.720.17
8.8000e+0336381.730.17
9.0000e+0336392.740.26
9.2000e+0337402.760.26
9.4000e+0338412.770.26
9.6000e+0338423.790.35
9.8000e+0339433.800.35
1.0000e+0440443.820.35
1.0500e+0441465.370.49
1.1000e+0443495.930.53
1.1500e+0444517.490.65
1.2000e+04445410.060.86
1.2500e+04445712.641.07
1.3000e+04495910.220.85
1.3500e+04506211.800.97
1.4000e+04536411.390.92
1.4500e+0458678.980.71
1.5000e+04587011.580.91
1.5500e+04617211.180.87
1.6000e+04647510.780.82
1.6500e+04667711.380.86
1.7000e+04698010.990.82
1.7500e+0474838.600.64
1.8000e+0477858.210.60
1.8500e+0480887.820.57
1.9000e+04809010.440.75
1.9500e+0484939.060.64
2.0000e+04849611.670.82
2.1000e+04931017.910.54
2.2000e+041021064.160.28
2.3000e+041101111.410.09
2.4000e+041151171.670.11
2.5000e+041211220.920.06
2.6000e+04128127-0.82-0.05
2.7000e+04135132-2.55-0.16
2.8000e+04139138-1.29-0.08
2.9000e+04146143-3.02-0.18
3.0000e+04151148-2.75-0.16
3.1000e+04159154-5.48-0.32
3.2000e+04163159-4.21-0.24
3.3000e+04166164-1.94-0.11
3.4000e+04174169-4.67-0.26
3.5000e+04183175-8.40-0.47
3.6000e+04187180-7.13-0.39
3.7000e+04192185-6.85-0.37
3.8000e+04198190-7.58-0.41
3.9000e+04204196-8.31-0.44
4.0000e+04209201-8.04-0.43
4.1000e+04213206-6.77-0.35
4.2000e+04216212-4.50-0.23
4.3000e+04220217-3.23-0.17
4.4000e+04225222-2.96-0.15
4.5000e+042272270.310.02
4.6000e+04234233-1.42-0.07
4.7000e+04240238-2.15-0.11
4.8000e+04248243-4.89-0.24
4.9000e+04256248-7.62-0.37
5.0000e+04261254-7.35-0.36
5.2000e+04272264-7.83-0.37
5.4000e+04288275-13.30-0.62
5.6000e+04302285-16.79-0.78
5.8000e+04312296-16.27-0.74
6.0000e+04322306-15.76-0.71
6.2000e+04329317-12.26-0.54
6.4000e+04346327-18.76-0.82
6.6000e+04361338-23.27-1.00
6.8000e+04367348-18.78-0.80
7.0000e+04378359-19.29-0.81
7.2000e+04385369-15.81-0.66
7.4000e+04391380-11.34-0.47
7.6000e+04399390-8.87-0.36
7.8000e+04413401-12.41-0.50
8.0000e+04423411-11.95-0.48
8.2000e+04432422-10.50-0.41
8.4000e+04439432-7.05-0.28
8.6000e+04449442-6.61-0.26
8.8000e+04458453-5.17-0.20
9.0000e+04466463-2.74-0.10
9.2000e+04476474-2.32-0.09
9.4000e+04485484-0.90-0.03
9.6000e+044924952.520.09
9.8000e+045025052.930.11
1.0000e+055145151.330.05
1.0500e+055395412.320.08
1.1000e+05569567-1.72-0.06
1.1500e+05594593-0.79-0.03
1.2000e+056166193.100.10
1.2500e+05646645-1.03-0.03
1.3000e+056686712.800.09
1.3500e+056926974.610.15
1.4000e+057207222.390.08
1.4500e+057487480.140.00
1.5000e+05785774-11.14-0.34
1.5500e+05807800-7.45-0.23
1.6000e+05838825-12.78-0.38
1.6500e+05861851-10.14-0.30
1.7000e+05889876-12.52-0.37
1.7500e+05912902-9.93-0.29
1.8000e+05939928-11.37-0.32
1.8500e+05968953-14.83-0.42
1.9000e+05990979-11.31-0.32
1.9500e+0510121004-7.82-0.22
2.0000e+0510351030-5.35-0.15
2.1000e+0510831081-2.48-0.07
2.2000e+0511321131-0.70-0.02
2.3000e+05117411828.000.21
2.4000e+051221123311.610.29
2.5000e+051265128318.150.45
2.6000e+051316133417.600.43
2.7000e+051358138425.980.63
2.8000e+051411143423.280.55
2.9000e+051463148521.520.50
3.0000e+051508153526.680.61
3.1000e+051562158522.770.52
3.2000e+051602163532.800.73
3.3000e+051654168530.760.68
3.4000e+051710173524.660.54
3.5000e+051759178425.500.55
3.6000e+051812183422.270.47
3.7000e+051859188424.990.53
3.8000e+051907193426.650.56
3.9000e+051953198330.250.62
4.0000e+052011203321.800.44
4.1000e+052060208222.290.45
4.2000e+052111213220.730.41
4.3000e+052170218111.120.22
4.4000e+052220223010.450.20
4.5000e+05227422805.740.11
4.6000e+052317232911.980.23
4.7000e+05237723781.160.02
4.8000e+0524292427-1.70-0.03
4.9000e+05247424762.400.04
5.0000e+052512252513.450.25
5.2000e+052613262310.410.19
5.4000e+052710272111.200.20
5.6000e+0528232819-4.18-0.07
5.8000e+0529212916-4.73-0.08
6.0000e+0530193014-5.43-0.09
6.2000e+05310731113.720.06
6.4000e+053189320818.710.31
6.6000e+05329833056.560.11
6.8000e+053390340111.270.18
7.0000e+053487349810.840.17
7.2000e+053578359416.270.26
7.4000e+053656369134.580.54
7.6000e+053758378728.760.45
7.8000e+053849388333.810.52
8.0000e+053948397930.740.47
8.2000e+054051407523.560.35
8.4000e+054153417017.250.26
8.6000e+054246426619.840.29
8.8000e+0543644361-2.69-0.04
9.0000e+05445344573.670.05
9.2000e+05454345528.930.13
9.4000e+05464046477.080.10
9.6000e+0547434742-0.87-0.01
9.8000e+054818483719.080.27
1.0000e+064909493222.930.32
1.0500e+065145516923.640.32
1.1000e+06539654058.760.12
1.1500e+065619564021.340.28
1.2000e+065839587536.380.46
1.2500e+066069611040.910.51
1.3000e+066305634438.960.48
1.3500e+066555657822.530.27
1.4000e+066799681111.640.14
1.4500e+06704170432.310.03
1.5000e+067250727625.560.30
1.5500e+067476750731.390.36
1.6000e+067697773941.830.47
1.6500e+067930797039.880.44
1.7000e+068157820143.550.48
1.7500e+068372843158.850.64
1.8000e+068624866136.800.40
1.8500e+068854889036.400.39
1.9000e+069088912031.670.33
1.9500e+069324934924.610.26
2.0000e+069559957718.220.19
2.1000e+0610031100342.530.03
2.2000e+06104781048910.640.10
2.3000e+06109181094324.610.24
2.4000e+06113731139522.500.21
2.5000e+06118361184711.330.11
2.6000e+0612292122986.170.06
2.7000e+06127351274813.040.12
2.8000e+06131641319732.970.29
2.9000e+0613636136459.010.08
3.0000e+0614088140924.180.04
3.1000e+061454014539-1.49-0.01
3.2000e+06149631498421.030.18
3.3000e+06154151542913.770.11
3.4000e+061588215873-9.26-0.08
3.5000e+061633016316-14.03-0.11
3.6000e+061676216758-3.52-0.03
3.7000e+0617197172003.290.03
3.8000e+061765117641-9.57-0.07
3.9000e+06180631808218.900.15
4.0000e+06184711852250.720.39
4.1000e+06189151896145.910.35
4.2000e+06193421939957.500.43
4.3000e+06197401983797.480.72
4.4000e+062016720275107.870.79
4.5000e+06206172071294.700.68
4.6000e+06210712114876.970.55
4.7000e+062148321584100.690.71
4.8000e+06219252201993.870.66
4.9000e+06223992245454.530.38
5.0000e+06228422288845.680.32
5.2000e+06237022375452.480.36
5.4000e+06245542461965.350.44
5.6000e+06253982548284.350.55
5.8000e+06262672634476.570.50
6.0000e+062708927203114.050.73
6.2000e+062793728061123.870.78
6.4000e+062880828917109.070.68
6.6000e+062965829772113.700.69
6.8000e+063046430625160.820.97
7.0000e+063133931476137.460.82
7.2000e+063215132327175.681.03
7.4000e+063300733176168.510.98
7.6000e+063384334023179.991.03
7.8000e+063469634869173.160.98
8.0000e+063557735714137.050.77
8.2000e+063637336558184.701.03
8.4000e+063720937400191.121.05
8.6000e+063803738241204.371.11
8.8000e+063891039081171.460.92
9.0000e+063970639920214.421.14
9.2000e+064057240758186.270.98
9.4000e+064137541595220.041.15
9.6000e+064221042431220.761.15
9.8000e+064305843265207.451.07
1.0000e+074385144099248.121.26
1.0500e+074597246179207.021.03
1.1000e+074800248253251.031.23
1.1500e+075008850321233.421.12
1.2000e+075214152384243.451.15
1.2500e+075418154442261.351.21
1.3000e+075624156495254.331.16
1.3500e+075829558544248.591.11
1.4000e+076039060587197.300.87
1.4500e+076244162627185.650.80
1.5000e+076443164662230.770.98
1.5500e+076651366693179.820.76
1.6000e+076855968720160.940.67
1.6500e+077060670743137.240.56
1.7000e+077259872763164.860.67
1.7500e+077464874779130.910.52
1.8000e+077665776791134.480.53
1.8500e+07787117880189.690.35
1.9000e+07807458080761.620.24
1.9500e+07827688280941.370.16
2.0000e+07847828480927.010.10
2.1000e+07887838879916.330.06
2.2000e+07927189277860.160.22
2.3000e+079678096746-33.93-0.12
2.4000e+071006941007049.530.03
2.5000e+07104668104651-16.99-0.06
2.6000e+0710856310858925.920.09
2.7000e+0711243411251883.650.28
2.8000e+0711637011643867.560.22
2.9000e+0712025512034993.970.30
3.0000e+0712417112425281.190.26
3.1000e+0712807012814877.500.24
3.2000e+0713195113203584.180.26
3.3000e+07135773135915142.480.43
3.4000e+07139671139789117.620.35
3.5000e+07143534143655120.840.35
3.6000e+07147410147514104.330.30
3.7000e+0715134315136724.290.07
3.8000e+0715516215521451.920.15
3.9000e+0715896215905492.370.26
4.0000e+0716282816288960.830.17
4.1000e+0716666616671751.450.14
4.2000e+07170407170540133.380.36
4.3000e+0717432917435828.750.08
4.4000e+0717813617817033.720.09
4.5000e+0718193318197643.390.11
4.6000e+0718572018577857.910.15
4.7000e+0718955918957415.390.04
4.8000e+0719332219336643.940.11
4.9000e+0719709119715361.660.16
5.0000e+0720088620093548.670.12
5.2000e+0720841520848569.930.17
5.4000e+07216112216017-94.54-0.23
5.6000e+07223607223533-74.04-0.18
5.8000e+07231139231032-106.94-0.25
6.0000e+07238576238515-60.63-0.14
6.2000e+0724591124598372.440.17
6.4000e+0725335225343784.790.19
6.6000e+0726078826087687.910.19
6.8000e+0726821226830189.240.20
7.0000e+07275567275713146.220.32
7.2000e+0728303528311277.260.16
7.4000e+07290305290499193.730.41
7.6000e+07297541297873331.990.69
7.8000e+07304776305235459.380.95
8.0000e+07311815312586771.231.57
8.2000e+07319147319926778.831.57
8.4000e+07326471327254783.491.56
8.6000e+07333770334572802.471.58
8.8000e+07341139341880741.031.45
9.0000e+07348421349177756.441.46
9.2000e+07355721356465743.931.42
9.4000e+07362976363743766.721.45
9.6000e+07370255371011756.041.42
9.8000e+07377570378270700.091.30
1.0000e+08384738385520782.081.44
1.0500e+08402766403607840.641.52
1.1000e+08421019421641621.521.10
1.1500e+08438869439624755.261.31
1.2000e+08456940457560620.181.05
1.2500e+08474899475450551.400.92
1.3000e+08492768493297528.850.87
1.3500e+08510549511101552.330.89
1.4000e+08528303528865562.470.89
1.4500e+08546057546591533.820.83
1.5000e+08563801564279477.800.73
1.5500e+08581404581931526.720.80
1.6000e+08599155599548392.830.59
1.6500e+08616930617131201.280.30
1.7000e+0863458463468298.160.14
1.7500e+0865216065220141.490.06
1.8000e+08669735669690-44.78-0.06
1.8500e+0868710468714945.260.06
1.9000e+087045797045790.470.00
1.9500e+08722123721982-141.35-0.19
2.0000e+08739453739357-96.44-0.13
2.1000e+0877395177402776.480.10
2.2000e+08808652808598-54.41-0.07
2.3000e+08843201843072-129.22-0.16
2.4000e+08877459877454-4.51-0.01
2.5000e+0891173091175019.790.02
2.6000e+0894586394596198.400.12
2.7000e+0898001698009376.750.09
2.8000e+0810138581014147289.020.34
2.9000e+0810478101048127317.130.36
3.0000e+0810818791082036156.820.18
3.1000e+0811154311115876444.620.49
3.2000e+0811490641149649584.920.64
3.3000e+0811827981183358559.910.60
3.4000e+0812165081217005496.700.53
3.5000e+0812500541250591537.220.56
3.6000e+0812835121284119607.310.63
3.7000e+0813170711317591519.710.53
3.8000e+0813503301351007677.060.69
3.9000e+0813839061384370463.900.46
4.0000e+0814173351417681345.700.34
4.1000e+0814505311450941409.850.40
4.2000e+0814837921484152359.660.35
4.3000e+0815168601517314454.400.44
4.4000e+0815499721550430458.250.43
4.5000e+0815831061583500394.360.37
4.6000e+0816162631616526262.820.24
4.7000e+081649449164950858.650.05
4.8000e+081682415168244731.850.03
4.9000e+081715327171534417.380.02
5.0000e+081748160174820141.140.04
5.2000e+0818133031813796492.800.43
5.4000e+0818786871879237550.400.48
5.6000e+0819438781944532654.000.56
5.8000e+0820089692009685716.220.60
6.0000e+08207369220747021010.270.83
6.2000e+0821386262139588962.000.78
6.4000e+0822034902204347856.950.69
6.6000e+0822680452268983938.360.74
6.8000e+0823326892333501812.190.63
7.0000e+0823972052397904699.190.54
7.2000e+0824616842462196511.860.39
7.4000e+0825256332526380746.510.56
7.6000e+08258939425904581064.270.79
7.8000e+08265309326544351342.090.98
8.0000e+08271702827183131284.770.93
8.2000e+08278088327820941210.970.87
8.4000e+08284472628457811055.200.75
8.6000e+08290806129093771315.860.92
8.8000e+08297164029728831243.240.86
9.0000e+08303510030363021202.500.83
9.2000e+08309833530996371301.720.89
9.4000e+08316164131628881246.870.84
9.6000e+08322456932260581488.860.99
9.8000e+08328791332891481235.500.82
1.0000e+09335103233521621129.510.74
1.0500e+0935083823509365983.200.63
1.1000e+0936654113666118707.200.44
1.1500e+0938217363822442706.460.43
1.2000e+0939779193978358438.940.26
1.2500e+0941332814133883601.900.36
1.3000e+0942883914289034643.080.37
1.3500e+0944429934443827833.880.48
1.4000e+0945974284598276847.550.48
1.4500e+09475136847523931025.240.57
1.5000e+09490465649061921536.210.84
1.5500e+09505783750596841846.830.99
1.6000e+09521113552128791743.740.92
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