Gap size : 42 (r=21)

Generated by program gapCounts : Mon Jun 27 12:41:19 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+03000.000.00
1.8000e+03000.000.00
1.9000e+03000.000.00
2.0000e+03000.000.00
2.1000e+03000.000.00
2.2000e+03000.000.00
2.3000e+03000.000.00
2.4000e+03000.010.00
2.5000e+03000.010.00
2.6000e+03000.010.00
2.7000e+03000.010.00
2.8000e+03000.010.00
2.9000e+03000.010.00
3.0000e+03000.010.00
3.1000e+03000.020.00
3.2000e+03000.020.00
3.3000e+03000.020.00
3.4000e+03000.020.00
3.5000e+03000.030.00
3.6000e+03000.030.00
3.7000e+03000.030.00
3.8000e+03000.030.00
3.9000e+03000.040.00
4.0000e+03000.040.01
4.1000e+03000.040.01
4.2000e+03000.050.01
4.3000e+03000.050.01
4.4000e+03000.050.01
4.5000e+03000.060.01
4.6000e+03000.060.01
4.7000e+03000.060.01
4.8000e+03000.070.01
4.9000e+03000.070.01
5.0000e+03000.080.01
5.2000e+03000.090.01
5.4000e+03000.090.01
5.6000e+03000.100.01
5.8000e+03000.110.01
6.0000e+03000.130.01
6.2000e+03000.140.02
6.4000e+03000.150.02
6.6000e+03000.160.02
6.8000e+03000.170.02
7.0000e+03000.190.02
7.2000e+03000.200.02
7.4000e+03000.210.02
7.6000e+03000.230.02
7.8000e+03000.240.02
8.0000e+03000.260.03
8.2000e+03000.270.03
8.4000e+03000.290.03
8.6000e+03000.300.03
8.8000e+03000.320.03
9.0000e+03000.340.03
9.2000e+03000.350.03
9.4000e+03000.370.04
9.6000e+03000.390.04
9.8000e+03000.410.04
1.0000e+04000.430.04
1.0500e+04000.470.04
1.1000e+04010.520.05
1.1500e+04010.580.05
1.2000e+04010.630.05
1.2500e+04010.690.06
1.3000e+04010.740.06
1.3500e+04010.800.07
1.4000e+04010.860.07
1.4500e+04010.930.07
1.5000e+04010.990.08
1.5500e+04011.060.08
1.6000e+04011.120.09
1.6500e+04110.190.01
1.7000e+04110.260.02
1.7500e+04110.340.02
1.8000e+04110.410.03
1.8500e+04110.490.04
1.9000e+04120.560.04
1.9500e+04120.640.05
2.0000e+04120.720.05
2.1000e+04120.880.06
2.2000e+04121.050.07
2.3000e+04121.220.08
2.4000e+04121.400.09
2.5000e+04131.580.10
2.6000e+04131.760.11
2.7000e+04131.950.12
2.8000e+04132.150.13
2.9000e+04132.340.14
3.0000e+04142.550.15
3.1000e+04142.750.16
3.2000e+04142.960.17
3.3000e+04143.170.18
3.4000e+04143.390.19
3.5000e+04153.610.20
3.6000e+04252.830.16
3.7000e+04253.060.17
3.8000e+04253.280.18
3.9000e+04362.520.13
4.0000e+04461.750.09
4.1000e+04461.990.10
4.2000e+04462.230.12
4.3000e+04462.470.13
4.4000e+04472.720.14
4.5000e+04472.970.15
4.6000e+04572.220.11
4.7000e+04572.470.12
4.8000e+04582.730.13
4.9000e+04582.990.15
5.0000e+04583.250.16
5.2000e+04593.780.18
5.4000e+04693.310.16
5.6000e+046103.860.18
5.8000e+046104.420.20
6.0000e+047113.980.18
6.2000e+048123.550.16
6.4000e+048124.130.18
6.6000e+048134.720.20
6.8000e+048135.310.23
7.0000e+049144.910.21
7.2000e+049155.520.23
7.4000e+049156.130.25
7.6000e+0410165.750.23
7.8000e+0410166.380.26
8.0000e+0412175.020.20
8.2000e+0414183.650.14
8.4000e+0415183.300.13
8.6000e+0416192.950.11
8.8000e+0416203.610.14
9.0000e+0417203.270.12
9.2000e+0417213.940.15
9.4000e+0417224.610.17
9.6000e+0417225.290.20
9.8000e+0419233.970.15
1.0000e+0519244.660.17
1.0500e+0520255.400.19
1.1000e+0522275.160.18
1.1500e+0522296.960.24
1.2000e+0526314.780.16
1.2500e+0529333.630.12
1.3000e+0533341.500.05
1.3500e+0535361.390.04
1.4000e+0535383.310.10
1.4500e+0536404.250.13
1.5000e+0537425.210.16
1.5500e+0537447.180.22
1.6000e+0538468.180.25
1.6500e+0541487.200.21
1.7000e+0542508.230.24
1.7500e+0544528.280.24
1.8000e+0545549.350.27
1.8500e+0549567.440.21
1.9000e+0550598.540.24
1.9500e+0551619.650.27
2.0000e+0557635.780.16
2.1000e+0560677.090.19
2.2000e+0566715.450.14
2.3000e+0570765.870.15
2.4000e+0574806.340.16
2.5000e+0579855.850.15
2.6000e+0585894.420.11
2.7000e+0592942.020.05
2.8000e+0597991.670.04
2.9000e+051011032.360.06
3.0000e+051071081.100.03
3.1000e+051091133.860.09
3.2000e+051131184.670.10
3.3000e+051211231.510.03
3.4000e+051231274.390.10
3.5000e+051251327.300.16
3.6000e+051301377.240.15
3.7000e+0513214210.210.22
3.8000e+051391478.220.17
3.9000e+0514115211.250.23
4.0000e+0514515712.320.25
4.1000e+051531629.410.19
4.2000e+051591688.520.17
4.3000e+051681734.670.09
4.4000e+051741783.840.08
4.5000e+051781835.030.10
4.6000e+051851883.250.06
4.7000e+051881935.500.10
4.8000e+051901998.770.17
4.9000e+051962048.060.15
5.0000e+052002099.370.17
5.2000e+0520922011.060.20
5.4000e+0521623114.830.27
5.6000e+0522824213.690.24
5.8000e+0523725315.620.27
6.0000e+0524326420.630.35
6.2000e+0525627518.710.32
6.4000e+0526928616.860.28
6.6000e+0528329714.070.23
6.8000e+0528830820.350.33
7.0000e+0529732022.690.37
7.2000e+0530633125.090.40
7.4000e+0531334329.550.46
7.6000e+0532635428.070.44
7.8000e+0533536630.640.47
8.0000e+0534637731.270.48
8.2000e+0535938929.940.45
8.4000e+0537240128.670.43
8.6000e+0538841224.450.36
8.8000e+0539842426.270.38
9.0000e+0540943627.140.39
9.2000e+0542144827.060.39
9.4000e+0543846022.020.31
9.6000e+0545247220.030.28
9.8000e+0546148423.070.32
1.0000e+0647649620.160.28
1.0500e+0650852718.550.25
1.1000e+0653655721.190.28
1.1500e+0657158817.040.22
1.2000e+0659861921.120.27
1.2500e+0663165019.400.24
1.3000e+0666168220.870.26
1.3500e+0668971424.530.30
1.4000e+0670974536.370.44
1.4500e+0674277735.380.42
1.5000e+0677081039.560.46
1.5500e+0681884223.900.27
1.6000e+0684487430.380.34
1.6500e+0688390724.020.27
1.7000e+0691194028.800.32
1.7500e+0694597327.710.30
1.8000e+06983100622.760.24
1.8500e+061009103929.940.32
1.9000e+061035107237.240.39
1.9500e+061075110630.660.32
2.0000e+061105113934.200.35
2.1000e+061172120734.620.35
2.2000e+061245127429.460.29
2.3000e+061312134330.720.30
2.4000e+061376141135.360.34
2.5000e+061456148024.370.23
2.6000e+061518155031.730.29
2.7000e+061587161932.430.29
2.8000e+061648168941.450.37
2.9000e+061714176045.770.40
3.0000e+061801183029.390.25
3.1000e+061880190121.300.18
3.2000e+061947197225.470.21
3.3000e+062027204416.910.14
3.4000e+06210621169.610.08
3.5000e+062176218811.540.09
3.6000e+062240226019.720.16
3.7000e+062312233220.120.16
3.8000e+06239524059.750.08
3.9000e+06247224785.590.04
4.0000e+062539255111.640.09
4.1000e+06261426249.890.07
4.2000e+062684269713.340.10
4.3000e+062753277117.970.13
4.4000e+062833284511.800.09
4.5000e+06291129197.800.06
4.6000e+062981299311.980.09
4.7000e+063045306722.330.16
4.8000e+063116314225.850.18
4.9000e+063192321724.530.17
5.0000e+063271329120.370.14
5.2000e+06343234429.510.06
5.4000e+0635953592-2.76-0.02
5.6000e+06374037443.540.02
5.8000e+0639063895-10.62-0.07
6.0000e+0640624048-14.26-0.09
6.2000e+0642134201-12.40-0.08
6.4000e+0643684354-14.06-0.09
6.6000e+0645284508-20.25-0.12
6.8000e+0646704662-8.00-0.05
7.0000e+06481548171.670.01
7.2000e+064959497212.770.08
7.4000e+06512051277.260.04
7.6000e+0652905283-6.86-0.04
7.8000e+0654405439-0.60-0.00
8.0000e+065582559614.020.08
8.2000e+065741575312.000.07
8.4000e+06590459106.320.03
8.6000e+0660766068-8.03-0.04
8.8000e+0662496226-23.05-0.12
9.0000e+0663976384-12.76-0.07
9.2000e+0665436543-0.16-0.00
9.4000e+06670067021.740.01
9.6000e+06685568615.930.03
9.8000e+0670497020-28.60-0.15
1.0000e+07718071800.150.00
1.0500e+07757375817.690.04
1.1000e+077971798311.820.06
1.1500e+078363838623.450.11
1.2000e+0788068792-14.49-0.07
1.2500e+07919291985.920.03
1.3000e+0796099606-3.38-0.02
1.3500e+071003010015-15.45-0.07
1.4000e+071043310425-8.35-0.04
1.4500e+0710829108366.870.03
1.5000e+07112331124815.160.06
1.5500e+071166411661-2.51-0.01
1.6000e+07120581207617.800.07
1.6500e+07124731249118.070.07
1.7000e+07128661290741.250.17
1.7500e+071322313324101.320.40
1.8000e+071362713742115.240.45
1.8500e+071404914161111.980.44
1.9000e+071447614581104.520.40
1.9500e+071488615001114.840.44
2.0000e+071531815422103.890.39
2.1000e+07161981626668.160.25
2.2000e+071699617113117.150.42
2.3000e+071783317963129.720.46
2.4000e+071869518815119.720.42
2.5000e+071953819669131.040.45
2.6000e+072042220526103.550.35
2.7000e+07213042138480.160.26
2.8000e+07221542224590.760.29
2.9000e+07230562310751.280.16
3.0000e+07239082397263.620.20
3.1000e+072473724838100.710.31
3.2000e+072560025705105.480.32
3.3000e+072644326575131.870.40
3.4000e+072730627446139.820.42
3.5000e+072813028318188.260.55
3.6000e+072905129192141.150.41
3.7000e+072993330067134.430.39
3.8000e+07308713094473.060.21
3.9000e+073170831822114.000.32
4.0000e+073258132701120.190.33
4.1000e+073344233582139.610.38
4.2000e+07343793446384.220.23
4.3000e+07352463534699.970.27
4.4000e+073612936230100.840.27
4.5000e+073696437115150.790.40
4.6000e+073780738001193.800.50
4.7000e+073866738888220.840.57
4.8000e+073954539776230.870.59
4.9000e+074045440665210.870.53
5.0000e+074136541555189.820.48
5.2000e+074318443337153.460.38
5.4000e+074493545124188.620.46
5.6000e+074669846913215.120.51
5.8000e+074854148706164.830.39
6.0000e+075028350502218.590.51
6.2000e+075209552300205.290.47
6.4000e+075385354102248.790.56
6.6000e+075570455906201.990.45
6.8000e+075743657713276.790.61
7.0000e+075926159522261.080.56
7.2000e+076109661334237.790.51
7.4000e+076295263148195.810.41
7.6000e+076478664964178.080.37
7.8000e+076663266783150.510.31
8.0000e+076844668603157.040.32
8.2000e+077029570426130.600.26
8.4000e+077213072250120.130.24
8.6000e+077390474077172.560.34
8.8000e+077572575905179.840.35
9.0000e+077755677735178.920.35
9.2000e+077936679567200.740.38
9.4000e+078116081400240.250.45
9.6000e+078295483235281.420.53
9.8000e+078478585072287.180.53
1.0000e+088663786911273.520.50
1.0500e+089106291513450.920.81
1.1000e+089570696124418.260.74
1.1500e+08100318100744426.020.74
1.2000e+08104960105372411.720.70
1.2500e+08109575110007431.930.72
1.3000e+08114183114649466.270.76
1.3500e+08118763119298535.380.86
1.4000e+08123388123954565.930.90
1.4500e+08127887128616728.631.14
1.5000e+08132641133283642.190.99
1.5500e+08137224137956732.371.11
1.6000e+08141869142635765.931.14
1.6500e+08146526147319792.641.17
1.7000e+08151264152007743.301.08
1.7500e+08155851156701849.731.22
1.8000e+08160525161399873.741.24
1.8500e+08165270166101831.161.16
1.9000e+08169898170808909.841.26
1.9500e+08174552175519966.631.32
2.0000e+08179248180233985.391.33
2.1000e+08188687189674987.311.31
2.2000e+081980391991301090.631.41
2.3000e+082075482085981050.481.33
2.4000e+08217113218080967.081.20
2.5000e+08226743227574830.741.02
2.6000e+08236355237079723.800.87
2.7000e+08245887246595707.680.84
2.8000e+08255250256121870.841.01
2.9000e+08264872265657784.800.90
3.0000e+08274378275202824.090.93
3.1000e+08283977284756779.310.87
3.2000e+08293568294319751.060.82
3.3000e+08303243303890646.980.70
3.4000e+08312822313469646.730.69
3.5000e+08322520323055535.020.56
3.6000e+08332063332649585.540.61
3.7000e+08341569342249680.010.70
3.8000e+08351082351856774.200.78
3.9000e+08360862361470607.840.61
4.0000e+08370523371090566.720.56
4.1000e+08380117380716598.630.59
4.2000e+08389691390347656.360.64
4.3000e+08399222399985762.720.73
4.4000e+08408993409628634.540.60
4.5000e+08418583419276692.640.65
4.6000e+08428221428929707.850.66
4.7000e+08437912438587675.040.62
4.8000e+08447495448250755.040.69
4.9000e+08457171457918746.720.68
5.0000e+08466941467590648.960.58
5.2000e+08486252486948695.570.61
5.4000e+08505594506322727.940.63
5.6000e+08524935525712777.200.66
5.8000e+08544426545118691.560.58
6.0000e+08563749564537788.290.65
6.2000e+08583050583971920.710.75
6.4000e+08602660603417757.220.61
6.6000e+08622099622876777.240.61
6.8000e+08641694642347653.220.51
7.0000e+08661022661830807.670.62
7.2000e+08680413681323910.130.69
7.4000e+08699914700827913.160.69
7.6000e+08719381720341960.360.71
7.8000e+08738872739865993.340.73
8.0000e+087581947593991204.740.87
8.2000e+087776947789411247.220.89
8.4000e+087972837984921209.480.86
8.6000e+088168648180521188.200.83
8.8000e+088364428376201178.100.82
9.0000e+088560998571961096.910.75
9.2000e+088756828767791097.380.75
9.4000e+08895449896370921.270.62
9.6000e+08915001915968967.340.65
9.8000e+08934815935573758.380.50
1.0000e+09954456955185729.180.48
1.0500e+0910034801004243762.970.49
1.1000e+0910525501053339788.950.50
1.1500e+0911021541102471316.550.19
1.2000e+0911512421151635393.500.24
1.2500e+0912003971200832434.720.26
1.3000e+0912495111250057546.370.32
1.3500e+0912986411299311669.740.38
1.4000e+09134752713485901063.300.60
1.4500e+09139673813978951156.610.64
1.5000e+0914463781447222844.400.46
1.5500e+09149511014965721462.470.79
1.6000e+09154437815459441565.710.83
1.6500e+09159371615953351619.110.85
1.7000e+09164342716447461318.720.68
1.7500e+09169294116941751233.670.63
1.8000e+09174234717436211274.140.64
1.8500e+09179187617930841208.370.60
1.9000e+0918416211842564942.650.46
1.9500e+0918911301892058928.310.45
2.0000e+0919408941941568673.720.32
2.1000e+0920398982040629730.510.34
2.2000e+09213842821397421313.700.60
2.3000e+09223766622389031237.480.56
2.4000e+0923372322338110878.440.39
2.5000e+0924366612437359698.500.30
2.6000e+092536557253664890.900.04
2.7000e+0926357342635973239.120.10
2.8000e+0927352082735333124.900.05
2.9000e+092834661283472564.140.03
3.0000e+0929338612934148286.960.11
3.1000e+0930328603033600739.600.29
3.2000e+0931322833133078795.460.31
3.3000e+09323120932325831374.070.52
3.4000e+09333041033321121702.050.64
3.5000e+09343044834316641216.130.45
3.6000e+09352994435312381294.140.47
3.7000e+09362935136308331481.990.54
3.8000e+09372887137304481576.660.56
3.9000e+09382868838300811393.190.49
4.0000e+09392835839297331374.690.48
4.1000e+09402804240294011359.340.47
4.2000e+0941280894129086997.340.34
4.3000e+0942278764228787910.960.31
4.4000e+0943277874328503715.510.24
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