Gap size : 30 (r=15)

Generated by program gapCounts : Mon Jun 27 12:41:03 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+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+020-0-0.01-0.00
6.0000e+020-0-0.01-0.00
7.0000e+020-0-0.01-0.00
8.0000e+020-0-0.01-0.00
9.0000e+020-0-0.00-0.00
1.0000e+03000.000.00
1.1000e+03000.010.00
1.2000e+03000.020.00
1.3000e+03000.040.01
1.4000e+03000.050.01
1.5000e+03000.070.01
1.6000e+03000.090.02
1.7000e+03000.110.02
1.8000e+03000.130.02
1.9000e+03000.160.03
2.0000e+03000.180.03
2.1000e+03000.210.04
2.2000e+03000.240.04
2.3000e+03000.270.04
2.4000e+03000.310.05
2.5000e+03000.340.05
2.6000e+03000.380.06
2.7000e+03000.410.06
2.8000e+03000.450.07
2.9000e+03000.490.07
3.0000e+03010.530.08
3.1000e+03010.580.08
3.2000e+03010.620.09
3.3000e+03010.660.09
3.4000e+03010.710.10
3.5000e+03010.760.10
3.6000e+03010.810.11
3.7000e+03010.860.12
3.8000e+03010.910.12
3.9000e+03010.960.13
4.0000e+03011.010.13
4.1000e+03011.070.14
4.2000e+03011.120.14
4.3000e+03011.180.15
4.4000e+03110.230.03
4.5000e+03110.290.04
4.6000e+03110.350.04
4.7000e+03110.410.05
4.8000e+03110.470.06
4.9000e+0322-0.47-0.06
5.0000e+0322-0.41-0.05
5.2000e+0322-0.28-0.03
5.4000e+0332-1.16-0.14
5.6000e+0332-1.02-0.12
5.8000e+0342-1.89-0.21
6.0000e+0342-1.75-0.20
6.2000e+0342-1.61-0.18
6.4000e+0343-1.47-0.16
6.6000e+0353-2.32-0.25
6.8000e+0353-2.17-0.23
7.0000e+0363-3.02-0.32
7.2000e+0363-2.87-0.30
7.4000e+0373-3.72-0.38
7.6000e+0373-3.56-0.36
7.8000e+0384-4.40-0.45
8.0000e+0394-5.24-0.53
8.2000e+0394-5.08-0.51
8.4000e+0394-4.91-0.48
8.6000e+03104-5.74-0.56
8.8000e+03104-5.58-0.54
9.0000e+03115-6.40-0.61
9.2000e+03115-6.23-0.59
9.4000e+03115-6.06-0.57
9.6000e+03115-5.88-0.55
9.8000e+03115-5.70-0.53
1.0000e+04115-5.52-0.51
1.0500e+04116-5.07-0.46
1.1000e+04116-4.61-0.41
1.1500e+04117-4.13-0.36
1.2000e+04117-3.65-0.31
1.2500e+04118-3.16-0.27
1.3000e+04118-2.66-0.22
1.3500e+04139-4.16-0.34
1.4000e+04159-5.64-0.46
1.4500e+041610-6.12-0.49
1.5000e+041610-5.60-0.44
1.5500e+041711-6.07-0.47
1.6000e+041711-5.53-0.42
1.6500e+041812-5.98-0.45
1.7000e+041913-6.43-0.48
1.7500e+041913-5.88-0.43
1.8000e+042014-6.32-0.46
1.8500e+042014-5.75-0.42
1.9000e+042215-7.18-0.51
1.9500e+042215-6.61-0.47
2.0000e+042216-6.03-0.42
2.1000e+042317-5.85-0.40
2.2000e+042618-7.66-0.52
2.3000e+042620-6.45-0.43
2.4000e+042821-7.23-0.47
2.5000e+042922-6.99-0.45
2.6000e+043023-6.74-0.42
2.7000e+043225-7.47-0.46
2.8000e+043526-9.19-0.56
2.9000e+043627-8.90-0.54
3.0000e+043828-9.60-0.57
3.1000e+043930-9.28-0.55
3.2000e+044331-11.96-0.69
3.3000e+044432-11.62-0.67
3.4000e+044734-13.28-0.75
3.5000e+044735-11.92-0.67
3.6000e+044936-12.56-0.69
3.7000e+044938-11.19-0.61
3.8000e+045139-11.80-0.64
3.9000e+045341-12.41-0.66
4.0000e+045342-11.01-0.58
4.1000e+045443-10.60-0.56
4.2000e+045745-12.19-0.63
4.3000e+045946-12.77-0.66
4.4000e+046048-12.34-0.63
4.5000e+046249-12.90-0.65
4.6000e+046351-12.46-0.62
4.7000e+046552-13.00-0.65
4.8000e+046553-11.55-0.57
4.9000e+046555-10.08-0.49
5.0000e+046656-9.61-0.47
5.2000e+047059-10.65-0.51
5.4000e+047262-9.67-0.45
5.6000e+047665-10.67-0.49
5.8000e+047968-10.64-0.48
6.0000e+048271-10.60-0.48
6.2000e+048374-8.53-0.38
6.4000e+048778-9.45-0.41
6.6000e+049281-11.35-0.49
6.8000e+049584-11.23-0.48
7.0000e+0410387-16.10-0.68
7.2000e+0410690-15.95-0.66
7.4000e+0411293-18.78-0.77
7.6000e+0411696-19.60-0.80
7.8000e+04118100-18.40-0.74
8.0000e+04119103-16.19-0.65
8.2000e+04121106-14.97-0.59
8.4000e+04123109-13.73-0.54
8.6000e+04128113-15.48-0.60
8.8000e+04131116-15.22-0.58
9.0000e+04131119-11.95-0.45
9.2000e+04138122-15.66-0.59
9.4000e+04140126-14.36-0.54
9.6000e+04143129-14.06-0.52
9.8000e+04144132-11.74-0.43
1.0000e+05146136-10.41-0.38
1.0500e+05154144-10.04-0.36
1.1000e+05161152-8.61-0.30
1.1500e+05175161-14.13-0.49
1.2000e+05182169-12.59-0.43
1.2500e+05191178-13.01-0.43
1.3000e+05195187-8.37-0.27
1.3500e+05209195-13.69-0.44
1.4000e+05215204-10.97-0.35
1.4500e+05226213-13.20-0.41
1.5000e+05234222-12.40-0.38
1.5500e+05243230-12.55-0.38
1.6000e+05245239-5.68-0.17
1.6500e+05252248-3.76-0.11
1.7000e+05266257-8.82-0.26
1.7500e+05275266-8.84-0.25
1.8000e+05283275-7.83-0.22
1.8500e+05288284-3.79-0.11
1.9000e+05297293-3.72-0.10
1.9500e+05312302-9.62-0.27
2.0000e+05319312-7.50-0.20
2.1000e+05342330-12.17-0.33
2.2000e+05359348-10.75-0.28
2.3000e+05379367-12.24-0.32
2.4000e+05396385-10.64-0.27
2.5000e+05408404-3.96-0.10
2.6000e+05430423-7.20-0.18
2.7000e+054384423.630.09
2.8000e+054574613.530.08
2.9000e+054704799.490.22
3.0000e+0548549913.520.31
3.1000e+055105187.610.17
3.2000e+055315375.760.13
3.3000e+055505565.960.13
3.4000e+0556057515.220.33
3.5000e+0558259512.530.27
3.6000e+0560261411.890.25
3.7000e+0562263311.290.24
3.8000e+0564265310.740.22
3.9000e+056696723.230.07
4.0000e+056896922.770.06
4.1000e+057037118.350.17
4.2000e+0571673114.960.30
4.3000e+0573675114.620.29
4.4000e+0575077020.310.40
4.5000e+0576879022.040.43
4.6000e+0579081019.800.38
4.7000e+0580683023.600.45
4.8000e+0582084929.420.56
4.9000e+0584086929.290.55
5.0000e+0586188928.180.52
5.2000e+0590592924.050.44
5.4000e+0594596924.040.43
5.6000e+05973100936.140.64
5.8000e+051011104938.340.67
6.0000e+051070109019.630.34
6.2000e+051106113024.020.41
6.4000e+051150117120.510.34
6.6000e+051197121114.070.23
6.8000e+05124412527.720.13
7.0000e+05128412928.450.14
7.2000e+0513341333-0.75-0.01
7.4000e+05137313741.130.02
7.6000e+0514181415-2.93-0.05
7.8000e+05145314563.080.05
8.0000e+0514981497-0.84-0.01
8.2000e+0515411538-2.70-0.04
8.4000e+05157215797.500.11
8.6000e+051610162110.750.16
8.8000e+051649166213.070.19
9.0000e+051687170316.440.24
9.2000e+051729174515.860.23
9.4000e+051764178622.330.32
9.6000e+051814182813.850.19
9.8000e+0518721869-2.58-0.04
1.0000e+0619141911-2.96-0.04
1.0500e+0620222015-6.72-0.09
1.1000e+0621372120-17.22-0.23
1.1500e+0622302225-5.46-0.07
1.2000e+06232023309.520.12
1.2500e+062423243511.720.15
1.3000e+062507254033.130.41
1.3500e+062616264629.730.36
1.4000e+062725275226.510.32
1.4500e+062833285724.470.29
1.5000e+062931296432.590.38
1.5500e+063033307036.870.42
1.6000e+063147317629.300.33
1.6500e+063242328340.870.46
1.7000e+063357339032.580.36
1.7500e+063465349631.420.34
1.8000e+063574360329.380.32
1.8500e+063679371031.460.33
1.9000e+063777381840.660.43
1.9500e+063898392526.970.28
2.0000e+064019403213.380.14
2.1000e+0642564248-8.50-0.09
2.2000e+06446144632.010.02
2.3000e+064642467936.870.36
2.4000e+064848489547.050.45
2.5000e+065060511251.540.48
2.6000e+065266532862.330.57
2.7000e+065494554551.380.46
2.8000e+065731576331.690.28
2.9000e+065943598037.240.33
3.0000e+066153619845.020.39
3.1000e+066365641651.010.43
3.2000e+066593663441.210.35
3.3000e+066809685343.610.36
3.4000e+067002707169.190.56
3.5000e+067222729067.950.55
3.6000e+067440750968.870.55
3.7000e+067651772876.960.61
3.8000e+067895794752.200.41
3.9000e+068113816753.590.41
4.0000e+068323838663.120.48
4.1000e+068535860670.790.53
4.2000e+068768882657.580.43
4.3000e+068995904650.500.37
4.4000e+069243926622.540.16
4.5000e+069460948625.700.19
4.6000e+069659970646.960.34
4.7000e+069869992657.340.41
4.8000e+06100911014755.810.39
4.9000e+06103381036729.390.20
5.0000e+06105501058838.060.26
5.2000e+06109831103046.670.32
5.4000e+06114331147238.630.26
5.6000e+06118421191471.920.47
5.8000e+06123151235741.510.27
6.0000e+06127631279936.380.23
6.2000e+06131831324359.520.37
6.4000e+06136581368627.920.17
6.6000e+06140981413031.550.19
6.8000e+06145581457315.400.09
7.0000e+061504815017-30.53-0.18
7.2000e+06154441546217.740.10
7.4000e+06158871590619.200.11
7.6000e+06163341635116.850.10
7.8000e+06167741679621.660.12
8.0000e+06171951724145.640.26
8.2000e+06176551768630.770.17
8.4000e+06180821813149.060.27
8.6000e+06185451857631.480.17
8.8000e+06189941902228.040.15
9.0000e+0619466194681.720.01
9.2000e+061994319914-29.47-0.16
9.4000e+062038320359-23.54-0.12
9.6000e+062083220805-26.50-0.14
9.8000e+062127521252-23.36-0.12
1.0000e+072174121698-43.11-0.22
1.0500e+072286922814-55.06-0.27
1.1000e+072401923931-88.47-0.43
1.1500e+072510425048-56.38-0.27
1.2000e+072623326165-67.83-0.32
1.2500e+072741227283-128.88-0.60
1.3000e+072850528401-103.57-0.47
1.3500e+072959329520-72.92-0.33
1.4000e+073068730639-47.96-0.21
1.4500e+07317423175816.270.07
1.5000e+07328393287838.740.17
1.5500e+0733997339970.450.00
1.6000e+073514935117-31.64-0.13
1.6500e+073630336237-65.54-0.27
1.7000e+073747837358-120.27-0.49
1.7500e+073859938478-120.85-0.48
1.8000e+073977239599-173.28-0.68
1.8500e+074090240719-182.60-0.71
1.9000e+074199541840-154.79-0.60
1.9500e+074319242961-230.89-0.88
2.0000e+074427144082-188.89-0.71
2.1000e+074647446324-149.66-0.55
2.2000e+074871948567-152.18-0.55
2.3000e+075093150810-121.49-0.43
2.4000e+075317753052-124.66-0.43
2.5000e+075537155295-75.74-0.26
2.6000e+075765457538-115.75-0.39
2.7000e+075986659781-84.74-0.28
2.8000e+076211662024-91.74-0.30
2.9000e+076434064267-72.78-0.23
3.0000e+076659166510-80.88-0.25
3.1000e+076885868753-105.06-0.33
3.2000e+077110970996-113.34-0.35
3.3000e+077338373238-144.75-0.44
3.4000e+077558275481-101.29-0.30
3.5000e+077778577723-61.97-0.18
3.6000e+078000879965-42.82-0.12
3.7000e+078224482207-36.84-0.11
3.8000e+078447484449-25.05-0.07
3.9000e+078669286691-1.45-0.00
4.0000e+078899388932-61.04-0.17
4.1000e+079121391173-39.85-0.11
4.2000e+079343193414-16.87-0.05
4.3000e+07956389565516.890.05
4.4000e+079790697895-10.57-0.03
4.5000e+07100181100136-45.26-0.12
4.6000e+071023681023767.810.02
4.7000e+07104629104616-13.35-0.03
4.8000e+07106869106855-13.76-0.04
4.9000e+071090871090957.590.02
5.0000e+07111349111334-15.31-0.04
5.2000e+07115837115811-25.86-0.06
5.4000e+071202861202881.580.00
5.6000e+07124792124763-29.01-0.07
5.8000e+07129244129237-6.63-0.02
6.0000e+07133764133711-53.29-0.12
6.2000e+07138225138183-42.00-0.10
6.4000e+07142658142654-3.76-0.01
6.6000e+07147170147124-45.57-0.10
6.8000e+07151688151594-94.42-0.21
7.0000e+07156070156062-8.32-0.02
7.2000e+07160548160529-19.27-0.04
7.4000e+07165076164995-81.26-0.17
7.6000e+07169518169460-58.28-0.12
7.8000e+071739191739244.660.01
8.0000e+07178254178387132.580.27
8.2000e+07182567182848281.470.57
8.4000e+07187091187309218.350.43
8.6000e+07191587191769182.230.36
8.8000e+07196047196228181.100.35
9.0000e+07200556200686129.970.25
9.2000e+07204996205143146.860.28
9.4000e+07209495209599103.760.20
9.6000e+07213928214054125.690.24
9.8000e+07218337218508170.650.32
1.0000e+08222847222961113.660.21
1.0500e+08234105234089-15.98-0.03
1.1000e+08245304245212-92.47-0.16
1.1500e+08256396256328-67.67-0.12
1.2000e+08267647267440-207.50-0.35
1.2500e+08278831278545-285.82-0.48
1.3000e+08289960289645-314.54-0.52
1.3500e+08300903300740-162.56-0.26
1.4000e+08311622311830208.240.33
1.4500e+0832285632291558.950.09
1.5000e+08333819333995175.660.27
1.5500e+08344825345069244.470.37
1.6000e+08355911356139228.470.34
1.6500e+08366953367205251.740.37
1.7000e+08378046378265219.380.32
1.7500e+08388951389321370.450.53
1.8000e+08400003400373370.050.52
1.8500e+08411031411420389.240.54
1.9000e+08421861422463602.110.83
1.9500e+08432937433502564.720.77
2.0000e+08443840444536696.140.94
2.1000e+08466029466593563.680.75
2.2000e+08487960488633673.250.87
2.3000e+08510002510658656.340.83
2.4000e+08532156532668512.390.64
2.5000e+08554140554664523.840.64
2.6000e+08576248576645397.080.48
2.7000e+08598159598613453.500.54
2.8000e+08619965620566601.470.70
2.9000e+08641906642507601.320.69
3.0000e+08663724664435711.380.80
3.1000e+08685733686351617.960.69
3.2000e+08707653708254601.350.66
3.3000e+08729448730146697.830.75
3.4000e+08751451752026574.680.61
3.5000e+08773168773894726.140.76
3.6000e+08795266795751485.470.50
3.7000e+08817259817598338.880.35
3.8000e+08839106839434327.610.33
3.9000e+08860888861259370.870.37
4.0000e+08882823883074250.870.25
4.1000e+08904627904879251.800.25
4.2000e+0892662192667452.850.05
4.3000e+0894840794845952.210.05
4.4000e+08970115970235120.040.11
4.5000e+08992073992002-71.47-0.07
4.6000e+0810139211013759-162.17-0.15
4.7000e+0810356091035507-101.91-0.09
4.8000e+0810575991057246-352.52-0.32
4.9000e+0810792681078977-290.87-0.26
5.0000e+0811009901100699-290.81-0.26
5.2000e+0811444751144118-356.93-0.31
5.4000e+0811879751187504-470.82-0.41
5.6000e+0812314351230858-576.53-0.49
5.8000e+0812746591274182-477.12-0.40
6.0000e+0813182581317475-782.74-0.65
6.2000e+0813614551360739-715.56-0.58
6.4000e+0814042781403975-302.81-0.24
6.6000e+0814475331447183-349.77-0.28
6.8000e+0814908051490364-440.74-0.34
7.0000e+0815339461533519-427.06-0.33
7.2000e+0815771941576648-546.12-0.42
7.4000e+0816200181619752-266.30-0.20
7.6000e+0816632511662831-420.05-0.31
7.8000e+0817060051705886-118.83-0.09
8.0000e+0817487581748918159.890.12
8.2000e+0817919521791927-25.41-0.02
8.4000e+081834846183491366.760.05
8.6000e+0818781871877877-310.16-0.22
8.8000e+0819209161920819-96.73-0.07
9.0000e+0819635571963740183.470.13
9.2000e+0820063062006641334.850.23
9.4000e+0820491262049521394.770.27
9.6000e+0820924742092381-93.37-0.06
9.8000e+082135180213522140.770.03
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