Gap size : 14 (r=7)

Generated by program gapCounts : Mon Jun 27 12:32:58 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+020-0-0.14-0.06
2.0000e+021-0-1.01-0.38
3.0000e+0210-0.73-0.24
4.0000e+0231-2.37-0.71
5.0000e+0231-1.97-0.55
6.0000e+0231-1.54-0.40
7.0000e+0232-1.09-0.27
8.0000e+0242-1.62-0.38
9.0000e+0263-3.14-0.71
1.0000e+0373-3.66-0.80
1.1000e+0374-3.16-0.67
1.2000e+0374-2.66-0.54
1.3000e+0375-2.15-0.43
1.4000e+0375-1.64-0.32
1.5000e+0386-2.12-0.40
1.6000e+0396-2.60-0.48
1.7000e+0397-2.08-0.37
1.8000e+0397-1.55-0.27
1.9000e+03108-2.03-0.35
2.0000e+03109-1.50-0.25
2.1000e+03119-1.97-0.33
2.2000e+031110-1.44-0.24
2.3000e+031110-0.91-0.15
2.4000e+031211-1.37-0.22
2.5000e+031311-1.84-0.29
2.6000e+031312-1.30-0.20
2.7000e+031412-1.77-0.27
2.8000e+031513-2.23-0.33
2.9000e+031613-2.69-0.40
3.0000e+031714-3.16-0.46
3.1000e+031814-3.62-0.52
3.2000e+031815-3.08-0.44
3.3000e+031815-2.54-0.36
3.4000e+031816-2.00-0.28
3.5000e+031817-1.47-0.20
3.6000e+031817-0.93-0.13
3.7000e+032018-2.39-0.32
3.8000e+032118-2.85-0.38
3.9000e+032319-4.31-0.57
4.0000e+032319-3.77-0.49
4.1000e+032320-3.23-0.42
4.2000e+032420-3.69-0.47
4.3000e+032421-3.15-0.40
4.4000e+032421-2.61-0.33
4.5000e+032422-2.07-0.26
4.6000e+032522-2.53-0.31
4.7000e+032523-1.99-0.25
4.8000e+032524-1.45-0.18
4.9000e+032624-1.91-0.23
5.0000e+032825-3.37-0.41
5.2000e+032926-3.29-0.39
5.4000e+033127-4.21-0.49
5.6000e+033128-3.14-0.36
5.8000e+033229-3.06-0.35
6.0000e+033330-2.98-0.33
6.2000e+033431-2.91-0.32
6.4000e+033432-1.83-0.20
6.6000e+033433-0.75-0.08
6.8000e+033534-0.68-0.07
7.0000e+0335350.390.04
7.2000e+0336360.470.05
7.4000e+033838-0.46-0.05
7.6000e+0338390.610.06
7.8000e+034140-1.32-0.13
8.0000e+034241-1.25-0.13
8.2000e+034442-2.18-0.22
8.4000e+034643-3.11-0.31
8.6000e+034744-3.04-0.30
8.8000e+034845-2.98-0.29
9.0000e+034846-1.91-0.18
9.2000e+034947-1.84-0.18
9.4000e+035148-2.78-0.26
9.6000e+035249-2.71-0.25
9.8000e+035350-2.65-0.25
1.0000e+045451-2.59-0.24
1.0500e+045654-1.94-0.17
1.1000e+045857-1.29-0.11
1.1500e+046059-0.64-0.06
1.2000e+0461621.000.09
1.2500e+0463651.630.14
1.3000e+0464673.260.27
1.3500e+0467702.890.24
1.4000e+0472730.510.04
1.4500e+047675-0.87-0.07
1.5000e+048378-5.26-0.41
1.5500e+048780-6.65-0.52
1.6000e+049183-8.04-0.62
1.6500e+049586-9.44-0.71
1.7000e+049588-6.84-0.51
1.7500e+049691-5.25-0.39
1.8000e+049793-3.66-0.27
1.8500e+049996-3.07-0.22
1.9000e+0410299-3.49-0.25
1.9500e+04105101-3.91-0.28
2.0000e+04107104-3.33-0.23
2.1000e+04110109-1.19-0.08
2.2000e+04118114-4.06-0.27
2.3000e+04121119-1.94-0.13
2.4000e+04128124-3.83-0.25
2.5000e+04134129-4.74-0.30
2.6000e+04141134-6.66-0.42
2.7000e+04144139-4.59-0.28
2.8000e+04149144-4.53-0.28
2.9000e+04152150-2.48-0.15
3.0000e+04157155-2.44-0.15
3.1000e+04161160-1.41-0.08
3.2000e+041641650.600.04
3.3000e+041691700.610.04
3.4000e+041731751.610.09
3.5000e+041771802.600.15
3.6000e+041801854.590.25
3.7000e+041851904.560.25
3.8000e+041871957.520.41
3.9000e+041931996.480.35
4.0000e+041962048.430.45
4.1000e+0419920910.370.54
4.2000e+042052149.300.48
4.3000e+0420921910.230.53
4.4000e+042162248.150.42
4.5000e+042202299.060.46
4.6000e+042272346.960.35
4.7000e+042312397.860.39
4.8000e+042362447.750.38
4.9000e+0423824910.630.52
5.0000e+042442549.510.46
5.2000e+042582635.240.25
5.4000e+042672735.950.28
5.6000e+042762836.630.31
5.8000e+042882924.300.20
6.0000e+042953026.930.31
6.2000e+043063125.550.25
6.4000e+043173214.150.18
6.6000e+04331331-0.28-0.01
6.8000e+04344340-3.72-0.16
7.0000e+04352350-2.19-0.09
7.2000e+043573592.330.10
7.4000e+043633695.830.24
7.6000e+043733785.300.22
7.8000e+043823885.770.23
8.0000e+043903977.210.29
8.2000e+044004076.640.26
8.4000e+044084168.050.32
8.6000e+0441542510.450.40
8.8000e+044274357.830.30
9.0000e+044444440.190.01
9.2000e+04456454-2.46-0.09
9.4000e+04464463-1.12-0.04
9.6000e+044714721.200.04
9.8000e+044774824.510.17
1.0000e+054844916.800.25
1.0500e+05514514-0.02-0.00
1.1000e+05542537-4.93-0.17
1.1500e+05564560-3.91-0.13
1.2000e+05590583-6.97-0.24
1.2500e+05612606-6.09-0.20
1.3000e+05633629-4.29-0.14
1.3500e+05653651-1.55-0.05
1.4000e+05684674-9.87-0.31
1.4500e+05704697-7.25-0.23
1.5000e+05725719-5.69-0.18
1.5500e+05751742-9.19-0.28
1.6000e+05774764-9.74-0.29
1.6500e+05791787-4.34-0.13
1.7000e+05816809-7.00-0.20
1.7500e+05837831-5.70-0.16
1.8000e+05863854-9.46-0.27
1.8500e+05882876-6.26-0.18
1.9000e+05904898-6.10-0.17
1.9500e+05925920-4.99-0.14
2.0000e+05959942-16.93-0.46
2.1000e+051002986-15.92-0.43
2.2000e+0510571030-27.07-0.71
2.3000e+0510961074-22.38-0.58
2.4000e+0511501117-32.83-0.83
2.5000e+0511911161-30.42-0.76
2.6000e+0512421204-38.15-0.93
2.7000e+0512801247-33.00-0.79
2.8000e+0513161290-25.98-0.62
2.9000e+0513581333-25.08-0.59
3.0000e+0513961376-20.29-0.47
3.1000e+0514321418-13.62-0.31
3.2000e+0514741461-13.05-0.29
3.3000e+0515111503-7.58-0.17
3.4000e+0515601546-14.22-0.31
3.5000e+0516031588-14.95-0.32
3.6000e+0516371630-6.78-0.14
3.7000e+0516811672-8.70-0.18
3.8000e+0517361714-21.70-0.45
3.9000e+0517851756-28.80-0.59
4.0000e+0518371798-38.98-0.79
4.1000e+0518801840-40.24-0.81
4.2000e+0519241881-42.58-0.85
4.3000e+0519611923-38.00-0.75
4.4000e+0520111965-46.50-0.91
4.5000e+0520562006-50.07-0.97
4.6000e+0521012047-53.71-1.03
4.7000e+0521522089-63.42-1.21
4.8000e+0521932130-63.21-1.19
4.9000e+0522452171-74.06-1.39
5.0000e+0522812212-68.98-1.28
5.2000e+0523692294-75.00-1.37
5.4000e+0524442376-68.28-1.23
5.6000e+0525212457-63.80-1.13
5.8000e+0525992538-60.55-1.06
6.0000e+0526832619-63.52-1.09
6.2000e+0527572700-56.70-0.96
6.4000e+0528292781-48.10-0.80
6.6000e+0529142861-52.69-0.87
6.8000e+0529942942-52.48-0.85
7.0000e+0530883022-66.45-1.07
7.2000e+0531773101-75.61-1.20
7.4000e+0532623181-80.94-1.27
7.6000e+0533223261-61.44-0.95
7.8000e+0533963340-56.11-0.86
8.0000e+0534693419-49.95-0.76
8.2000e+0535473498-48.94-0.74
8.4000e+0536163577-39.08-0.58
8.6000e+0536893656-33.38-0.49
8.8000e+0537653734-30.82-0.45
9.0000e+0538323813-19.40-0.28
9.2000e+0539173891-26.12-0.37
9.4000e+0539913969-21.98-0.31
9.6000e+0540704047-22.97-0.32
9.8000e+0541454125-20.10-0.28
1.0000e+0642334203-30.34-0.42
1.0500e+0644104396-13.50-0.18
1.1000e+0646054590-15.40-0.20
1.1500e+0647974782-15.00-0.20
1.2000e+0649974974-23.27-0.30
1.2500e+0651665165-1.18-0.01
1.3000e+06535353552.300.03
1.3500e+06553955456.190.08
1.4000e+065721573513.520.16
1.4500e+06591459239.310.11
1.5000e+066101611210.580.12
1.5500e+066274629925.340.29
1.6000e+066472648714.620.17
1.6500e+066661667312.430.14
1.7000e+066847686012.790.14
1.7500e+067035704610.700.12
1.8000e+0672347231-2.80-0.03
1.8500e+06740774169.270.10
1.9000e+067574760126.950.28
1.9500e+067761778524.240.25
2.0000e+067941796928.150.29
2.1000e+068293833642.870.43
2.2000e+068649870152.190.51
2.3000e+069014906551.190.49
2.4000e+069383942844.920.43
2.5000e+069756978933.430.31
2.6000e+06101281015021.790.20
2.7000e+06104831050926.040.23
2.8000e+06108381086729.230.26
2.9000e+0611216112248.390.07
3.0000e+0611572115818.560.07
3.1000e+06119141193621.790.18
3.2000e+06122701229020.100.17
3.3000e+06126171264426.520.22
3.4000e+061301212996-15.91-0.13
3.5000e+061336613348-18.17-0.15
3.6000e+061374013699-41.24-0.33
3.7000e+061409814049-49.08-0.39
3.8000e+061442914398-30.68-0.24
3.9000e+061479814747-51.01-0.39
4.0000e+061513015095-35.06-0.27
4.1000e+061547515442-32.80-0.25
4.2000e+061583215789-43.22-0.32
4.3000e+061616616135-31.30-0.23
4.4000e+061651616480-36.02-0.26
4.5000e+061683816825-13.36-0.10
4.6000e+061718717169-18.32-0.13
4.7000e+061754017512-27.87-0.20
4.8000e+061788917855-34.00-0.24
4.9000e+061824418197-46.71-0.33
5.0000e+061857018539-30.97-0.21
5.2000e+061923119221-10.11-0.07
5.4000e+061991519901-14.34-0.10
5.6000e+062063220578-53.58-0.35
5.8000e+062134121254-86.74-0.56
6.0000e+062199421928-65.75-0.42
6.2000e+062267522600-74.55-0.47
6.4000e+062335323271-82.07-0.51
6.6000e+062405023940-110.25-0.67
6.8000e+062472624607-119.05-0.72
7.0000e+062540025273-127.40-0.76
7.2000e+062608425937-147.26-0.87
7.4000e+062676326599-163.58-0.95
7.6000e+062741327261-152.32-0.88
7.8000e+062804927921-128.44-0.73
8.0000e+062872828579-148.90-0.84
8.2000e+062938429236-147.67-0.82
8.4000e+063004529892-152.70-0.84
8.6000e+063072630547-178.97-0.97
8.8000e+063139331201-192.45-1.04
9.0000e+063209231853-239.10-1.28
9.2000e+063274732504-242.89-1.28
9.4000e+063343533154-280.81-1.47
9.6000e+063410833803-304.82-1.58
9.8000e+063474234451-290.89-1.50
1.0000e+073539435098-296.01-1.51
1.0500e+073696736711-256.23-1.28
1.1000e+073859938317-281.50-1.38
1.1500e+074020939918-290.53-1.39
1.2000e+074182241514-308.03-1.45
1.2500e+074341943104-314.77-1.45
1.3000e+074503244689-342.50-1.56
1.3500e+074662746270-357.02-1.60
1.4000e+074820547846-359.14-1.58
1.4500e+074979549417-377.68-1.64
1.5000e+075132350985-338.46-1.44
1.5500e+075287452548-326.34-1.37
1.6000e+075442554107-318.17-1.32
1.6500e+075596055662-297.81-1.22
1.7000e+075750957214-295.14-1.19
1.7500e+075906358762-301.04-1.20
1.8000e+076064160307-334.40-1.32
1.8500e+076216161848-313.11-1.22
1.9000e+076368163386-295.07-1.13
1.9500e+076519364921-272.19-1.03
2.0000e+076676266453-309.38-1.16
2.1000e+076981969507-311.65-1.15
2.2000e+077280772551-256.23-0.92
2.3000e+077583075583-246.58-0.87
2.4000e+077883478606-228.17-0.79
2.5000e+078172381618-104.55-0.36
2.6000e+078476284622-140.28-0.47
2.7000e+078775787616-140.96-0.46
2.8000e+079075290602-150.24-0.49
2.9000e+079367093579-90.77-0.29
3.0000e+079657196549-22.25-0.07
3.1000e+079954899511-37.39-0.12
3.2000e+0710242510246540.090.12
3.3000e+07105479105412-66.55-0.20
3.4000e+07108391108353-38.09-0.11
3.5000e+07111300111287-13.30-0.04
3.6000e+07114310114214-95.98-0.28
3.7000e+07117219117135-83.91-0.24
3.8000e+07120119120050-68.93-0.20
3.9000e+07122984122959-24.85-0.07
4.0000e+07125873125862-10.51-0.03
4.1000e+071287531287607.250.02
4.2000e+07131724131653-71.41-0.19
4.3000e+071345361345403.630.01
4.4000e+0713738413742237.520.10
4.5000e+0714022514029873.390.19
4.6000e+07142994143170176.350.46
4.7000e+07145915146038122.530.32
4.8000e+0714881114890089.030.23
4.9000e+07151651151758106.970.27
5.0000e+07154462154611149.450.37
5.2000e+07160191160305114.390.28
5.4000e+07165852165983130.600.32
5.6000e+07171541171644102.760.24
5.8000e+07177167177289122.500.29
6.0000e+07182794182920126.400.29
6.2000e+0718847518853762.000.14
6.4000e+0719412019414019.820.04
6.6000e+0719969119972938.310.08
6.8000e+0720522320530682.940.18
7.0000e+0721077321087097.110.21
7.2000e+0721639121642231.210.07
7.4000e+07222001221963-38.39-0.08
7.6000e+07227580227492-88.34-0.18
7.8000e+07233203233010-193.31-0.40
8.0000e+07238762238517-244.99-0.50
8.2000e+07244248244014-234.10-0.47
8.4000e+07249612249501-111.34-0.22
8.6000e+07255082254978-104.46-0.21
8.8000e+0726041026044534.800.07
9.0000e+0726585026590352.680.10
9.2000e+072713482713513.410.01
9.4000e+07276915276791-123.80-0.23
9.6000e+07282403282222-180.74-0.34
9.8000e+07287934287645-289.20-0.54
1.0000e+08293201293059-141.99-0.26
1.0500e+08306749306559-189.76-0.34
1.1000e+08320289320011-277.84-0.49
1.1500e+08333806333417-388.81-0.67
1.2000e+08347108346780-328.48-0.56
1.2500e+08360569360100-468.85-0.78
1.3000e+08373796373381-415.10-0.68
1.3500e+08387058386623-434.54-0.70
1.4000e+08400409399829-579.61-0.92
1.4500e+08413522413000-521.88-0.81
1.5000e+08426708426137-571.02-0.88
1.5500e+08439908439241-666.79-1.01
1.6000e+08452926452314-612.02-0.91
1.6500e+08466046465356-689.65-1.02
1.7000e+08479076478369-706.66-1.03
1.7500e+08492137491354-783.09-1.12
1.8000e+08504954504311-643.07-0.91
1.8500e+08518005517241-763.74-1.07
1.9000e+08530898530146-752.32-1.04
1.9500e+08543651543025-626.06-0.86
2.0000e+08556481555880-601.25-0.81
2.1000e+08582078581519-559.31-0.74
2.2000e+08607923607067-855.55-1.11
2.3000e+08633520632531-989.46-1.26
2.4000e+08658878657912-965.95-1.20
2.5000e+08684205683216-989.29-1.21
2.6000e+08709819708445-1374.06-1.65
2.7000e+08734948733603-1345.13-1.59
2.8000e+08760262758692-1569.58-1.82
2.9000e+08785125783716-1408.75-1.61
3.0000e+08809904808677-1227.13-1.38
3.1000e+08834885833577-1308.43-1.45
3.2000e+08859645858418-1227.48-1.34
3.3000e+08884292883202-1090.26-1.18
3.4000e+08908993907931-1061.89-1.13
3.5000e+08933403932607-795.60-0.84
3.6000e+08957930957232-697.72-0.72
3.7000e+08982432981807-624.68-0.64
3.8000e+0810068091006334-475.01-0.48
3.9000e+0810312241030814-410.31-0.41
4.0000e+0810555881055248-340.26-0.34
4.1000e+0810797171079637-79.59-0.08
4.2000e+0811040081103984-24.14-0.02
4.3000e+0811282901128288-1.75-0.00
4.4000e+0811526001152552-48.37-0.05
4.5000e+0811768551176775-79.96-0.08
4.6000e+0812010081200959-48.56-0.05
4.7000e+0812251651225106-59.23-0.05
4.8000e+0812492831249215-68.08-0.06
4.9000e+0812733781273288-90.26-0.08
5.0000e+081297259129732566.040.06
5.2000e+0813451101345296186.180.16
5.4000e+081393115139313419.200.02
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