Gap size : 48 (r=24)

Generated by program gapCounts : Mon Jun 27 12:41:27 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+03000.000.00
2.3000e+03000.000.00
2.4000e+03000.000.00
2.5000e+03000.000.00
2.6000e+03000.000.00
2.7000e+03000.000.00
2.8000e+03000.000.00
2.9000e+03000.000.00
3.0000e+03000.000.00
3.1000e+03000.000.00
3.2000e+03000.000.00
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+03000.010.00
3.9000e+03000.010.00
4.0000e+03000.010.00
4.1000e+03000.010.00
4.2000e+03000.010.00
4.3000e+03000.010.00
4.4000e+03000.010.00
4.5000e+03000.010.00
4.6000e+03000.010.00
4.7000e+03000.010.00
4.8000e+03000.010.00
4.9000e+03000.010.00
5.0000e+03000.020.00
5.2000e+03000.020.00
5.4000e+03000.020.00
5.6000e+03000.020.00
5.8000e+03000.030.00
6.0000e+03000.030.00
6.2000e+03000.030.00
6.4000e+03000.030.00
6.6000e+03000.040.00
6.8000e+03000.040.00
7.0000e+03000.040.00
7.2000e+03000.050.01
7.4000e+03000.050.01
7.6000e+03000.060.01
7.8000e+03000.060.01
8.0000e+03000.060.01
8.2000e+03000.070.01
8.4000e+03000.070.01
8.6000e+03000.080.01
8.8000e+03000.080.01
9.0000e+03000.090.01
9.2000e+03000.090.01
9.4000e+03000.100.01
9.6000e+03000.100.01
9.8000e+03000.110.01
1.0000e+04000.110.01
1.0500e+04000.130.01
1.1000e+04000.140.01
1.1500e+04000.160.01
1.2000e+04000.180.02
1.2500e+04000.200.02
1.3000e+04000.210.02
1.3500e+04000.230.02
1.4000e+04000.250.02
1.4500e+04000.270.02
1.5000e+04000.300.02
1.5500e+04000.320.02
1.6000e+04000.340.03
1.6500e+04000.360.03
1.7000e+04000.390.03
1.7500e+04000.410.03
1.8000e+04000.440.03
1.8500e+04000.460.03
1.9000e+04000.490.03
1.9500e+04010.520.04
2.0000e+04010.540.04
2.1000e+04010.600.04
2.2000e+04010.660.04
2.3000e+04010.720.05
2.4000e+04010.790.05
2.5000e+04010.850.05
2.6000e+04010.920.06
2.7000e+04010.990.06
2.8000e+04011.060.06
2.9000e+04110.130.01
3.0000e+04110.210.01
3.1000e+04110.280.02
3.2000e+04110.360.02
3.3000e+04110.440.03
3.4000e+04120.520.03
3.5000e+04120.610.03
3.6000e+04120.690.04
3.7000e+04120.780.04
3.8000e+04120.870.05
3.9000e+04120.960.05
4.0000e+04121.050.06
4.1000e+04121.140.06
4.2000e+04121.230.06
4.3000e+04121.330.07
4.4000e+04121.420.07
4.5000e+04131.520.08
4.6000e+04131.620.08
4.7000e+04131.720.09
4.8000e+04131.820.09
4.9000e+04131.930.09
5.0000e+04132.030.10
5.2000e+04132.240.11
5.4000e+04132.460.12
5.6000e+04142.680.12
5.8000e+04142.900.13
6.0000e+04143.130.14
6.2000e+04143.360.15
6.4000e+04153.600.16
6.6000e+04153.840.17
6.8000e+04154.080.17
7.0000e+04154.330.18
7.2000e+04164.580.19
7.4000e+04263.840.16
7.6000e+04264.100.17
7.8000e+04264.360.18
8.0000e+04274.620.18
8.2000e+04274.890.19
8.4000e+04275.160.20
8.6000e+04275.440.21
8.8000e+04384.710.18
9.0000e+04384.990.19
9.2000e+04385.280.20
9.4000e+04395.560.21
9.6000e+04395.850.22
9.8000e+04396.140.23
1.0000e+05396.440.23
1.0500e+053107.180.26
1.1000e+055115.950.21
1.1500e+056125.720.20
1.2000e+056136.510.22
1.2500e+056137.320.24
1.3000e+056148.140.27
1.3500e+056158.970.29
1.4000e+057168.810.28
1.4500e+057179.670.30
1.5000e+0571810.530.32
1.5500e+0571811.410.35
1.6000e+0591910.300.31
1.6500e+05102010.200.30
1.7000e+0512219.110.27
1.7500e+0513229.030.26
1.8000e+0516236.960.20
1.8500e+0518245.900.17
1.9000e+0518256.850.19
1.9500e+0518267.810.22
2.0000e+0518278.770.24
2.1000e+0521297.730.21
2.2000e+0521319.720.25
2.3000e+0525337.740.20
2.4000e+0527357.790.20
2.5000e+0529377.870.20
2.6000e+0529399.980.24
2.7000e+05314110.110.24
2.8000e+05324311.270.27
2.9000e+05344511.450.27
3.0000e+05374810.660.25
3.1000e+05375012.890.29
3.2000e+05385214.140.32
3.3000e+05415413.420.30
3.4000e+05435713.710.30
3.5000e+05455914.030.30
3.6000e+05476114.360.31
3.7000e+05516412.720.27
3.8000e+05526614.090.29
3.9000e+05536815.480.32
4.0000e+05547116.890.34
4.1000e+05547319.310.39
4.2000e+05557620.750.41
4.3000e+05567822.210.44
4.4000e+05578123.690.46
4.5000e+05608323.180.45
4.6000e+05608625.680.49
4.7000e+05618827.200.52
4.8000e+05649126.730.50
4.9000e+05679326.280.49
5.0000e+05679628.850.54
5.2000e+057010131.010.57
5.4000e+057310633.230.60
5.6000e+058111130.500.54
5.8000e+058711729.820.52
6.0000e+059312229.180.50
6.2000e+059912828.590.48
6.4000e+0510513328.050.47
6.6000e+0510913929.540.49
6.8000e+0511214432.080.52
7.0000e+0511615033.660.54
7.2000e+0511815537.270.59
7.4000e+0512316137.930.60
7.6000e+0513316733.620.52
7.8000e+0513717235.340.54
8.0000e+0514417834.100.52
8.2000e+0514818435.890.54
8.4000e+0515219037.720.56
8.6000e+0515919636.580.54
8.8000e+0516320138.470.56
9.0000e+0516520742.390.61
9.2000e+0517321340.330.58
9.4000e+0517721942.310.60
9.6000e+0518322542.320.59
9.8000e+0518923142.350.59
1.0000e+0619623741.410.57
1.0500e+0621925333.680.46
1.1000e+0623326835.100.47
1.1500e+0624428439.680.52
1.2000e+0625529944.390.57
1.2500e+0627331542.250.53
1.3000e+0629033141.230.51
1.3500e+0630434743.340.53
1.4000e+0631136452.570.63
1.4500e+0632638053.910.64
1.5000e+0634139655.370.64
1.5500e+0635441358.930.67
1.6000e+0636243067.600.76
1.6500e+0637744669.360.77
1.7000e+0639246371.230.78
1.7500e+0641348067.180.73
1.8000e+0642849769.230.74
1.8500e+0644951465.370.69
1.9000e+0646953262.590.66
1.9500e+0648354965.890.68
2.0000e+0649756669.280.71
2.1000e+0652760174.280.75
2.2000e+0655863778.590.77
2.3000e+0659667276.170.74
2.4000e+0663470874.020.70
2.5000e+0666874476.140.71
2.6000e+0670178079.490.73
2.7000e+0673481783.090.75
2.8000e+0677585478.910.70
2.9000e+0681589175.940.66
3.0000e+0685692872.190.62
3.1000e+0688896677.640.66
3.2000e+06934100369.280.58
3.3000e+06976104165.100.54
3.4000e+061016107963.110.51
3.5000e+061053111764.300.52
3.6000e+061098115657.650.46
3.7000e+061140119454.170.43
3.8000e+061184123348.850.38
3.9000e+061234127237.680.29
4.0000e+061275131135.660.27
4.1000e+061316135033.790.25
4.2000e+061354138935.060.26
4.3000e+061388142840.470.30
4.4000e+061416146852.020.38
4.5000e+061450150857.690.42
4.6000e+061485154762.500.45
4.7000e+061530158757.430.41
4.8000e+061561162766.480.47
4.9000e+061600166867.650.47
5.0000e+061634170873.930.51
5.2000e+061707178981.850.56
5.4000e+061788187082.200.55
5.6000e+061882195269.960.46
5.8000e+061957203477.130.50
6.0000e+062050211766.690.42
6.2000e+062121220078.610.49
6.4000e+062202228380.900.50
6.6000e+062296236770.520.43
6.8000e+062391245059.490.36
7.0000e+062488253546.770.28
7.2000e+062578261941.370.24
7.4000e+062664270440.260.23
7.6000e+062764278925.450.15
7.8000e+062838287536.930.21
8.0000e+062928296132.680.18
8.2000e+063012304734.700.19
8.4000e+063083313349.980.27
8.6000e+063176322043.510.24
8.8000e+063259330647.290.25
9.0000e+063341339352.310.28
9.2000e+063430348150.570.27
9.4000e+063519356849.050.26
9.6000e+063613365642.760.22
9.8000e+063693374450.680.26
1.0000e+073784383247.820.24
1.0500e+074009405344.070.22
1.1000e+074227427648.540.24
1.1500e+074455449944.180.21
1.2000e+074673472450.930.24
1.2500e+074912495037.730.17
1.3000e+075143517733.540.15
1.3500e+075366540438.310.17
1.4000e+075622563311.000.05
1.4500e+07585958633.580.02
1.5000e+076064609329.010.12
1.5500e+076312632412.250.05
1.6000e+07655465562.280.01
1.6500e+076771678918.070.07
1.7000e+077002702320.590.08
1.7500e+077234725722.820.09
1.8000e+077469749222.730.09
1.8500e+077700772727.300.11
1.9000e+077927796436.510.14
1.9500e+078144820056.340.21
2.0000e+078369843868.780.26
2.1000e+0788038914111.390.41
2.2000e+079311939382.220.30
2.3000e+079820987454.140.19
2.4000e+07103281035729.060.10
2.5000e+07107781084263.870.22
2.6000e+0711320113288.490.03
2.7000e+07117881181728.830.09
2.8000e+07122961230710.830.04
2.9000e+07127651279833.410.11
3.0000e+07132451329246.520.15
3.1000e+07137681378618.080.06
3.2000e+07142391428243.050.13
3.3000e+071479214779-12.63-0.04
3.4000e+071533415278-56.00-0.17
3.5000e+071587015778-92.10-0.27
3.6000e+071638116279-101.99-0.30
3.7000e+071689316781-111.70-0.32
3.8000e+071741617285-131.26-0.37
3.9000e+071789517789-105.72-0.30
4.0000e+071840318295-108.11-0.30
4.1000e+071894118802-139.45-0.38
4.2000e+071941719309-107.77-0.29
4.3000e+071995019818-132.12-0.35
4.4000e+072048820327-160.50-0.43
4.5000e+072101020838-171.96-0.45
4.6000e+072150021349-150.50-0.39
4.7000e+072199021862-128.17-0.33
4.8000e+072250522375-129.97-0.33
4.9000e+072301722889-127.93-0.32
5.0000e+072351623404-112.06-0.28
5.2000e+072456124436-124.96-0.31
5.4000e+072558525471-113.78-0.28
5.6000e+072665926509-149.69-0.36
5.8000e+072766627550-115.78-0.27
6.0000e+072866828594-74.19-0.17
6.2000e+072971229640-72.02-0.16
6.4000e+073070130689-12.35-0.03
6.6000e+07316993174040.700.09
6.8000e+07327303279363.060.14
7.0000e+07338083384940.650.09
7.2000e+07348673490639.400.08
7.4000e+07359053596661.220.13
7.6000e+07369553702873.050.15
7.8000e+07380023809289.840.18
8.0000e+07391023915855.520.11
8.2000e+0740223402252.030.00
8.4000e+074130441294-9.67-0.02
8.6000e+07423284236537.350.07
8.8000e+07433794343859.060.12
9.0000e+07444524451260.410.12
9.2000e+07455584558830.350.06
9.4000e+0746664466661.850.00
9.6000e+07476944774550.850.10
9.8000e+07487524882573.340.14
1.0000e+08498244990783.260.15
1.0500e+085246852618150.150.27
1.1000e+085520955337128.320.23
1.1500e+085793258064132.340.23
1.2000e+086068660799112.780.19
1.2500e+086340763540133.280.22
1.3000e+086616966289119.510.20
1.3500e+086888369043160.140.26
1.4000e+087166671804137.900.22
1.4500e+087446074571110.520.17
1.5000e+08772747734368.760.11
1.5500e+08800998012021.400.03
1.6000e+08828348290369.220.10
1.6500e+08856168569175.020.11
1.7000e+088854388484-59.36-0.09
1.7500e+0891273912817.890.01
1.8000e+08940069408376.610.11
1.8500e+089674196889147.660.21
1.9000e+089959599699103.900.14
1.9500e+08102375102513138.180.19
2.0000e+08105182105331149.390.20
2.1000e+08110827110979152.110.20
2.2000e+08116466116641175.180.23
2.3000e+08122050122317266.820.34
2.4000e+08127833128005172.290.21
2.5000e+0813367813370627.960.03
2.6000e+0813935213941866.230.08
2.7000e+08145031145142110.560.13
2.8000e+08150712150875163.450.19
2.9000e+08156380156619239.430.27
3.0000e+08162113162373260.090.29
3.1000e+08167793168136343.020.38
3.2000e+08173468173908439.870.48
3.3000e+08179318179688370.290.40
3.4000e+08185053185477423.960.45
3.5000e+08190887191274386.590.41
3.6000e+08196620197078457.890.48
3.7000e+08202407202890482.620.50
3.8000e+08208352208709356.500.36
3.9000e+08214175214534359.330.36
4.0000e+08219981220367385.870.38
4.1000e+08225913226206292.930.29
4.2000e+08231693232051358.300.35
4.3000e+08237518237903384.800.37
4.4000e+08243450243760310.260.29
4.5000e+08249255249623368.500.35
4.6000e+08255147255492345.370.32
4.7000e+08260894261367472.710.44
4.8000e+08266644267246602.390.55
4.9000e+08272465273131666.270.60
5.0000e+08278400279021621.210.56
5.2000e+08290187290816628.780.55
5.4000e+08301776302629853.180.74
5.6000e+08313711314461749.530.64
5.8000e+08325847326309462.040.39
6.0000e+08337640338174533.970.44
6.2000e+08349487350055567.660.46
6.4000e+08361264361950686.450.55
6.6000e+08373260373861600.780.47
6.8000e+08385058385785727.080.57
7.0000e+08397034397723688.850.53
7.2000e+08408833409674840.600.64
7.4000e+08420835421637801.880.60
7.6000e+08432826433612786.280.58
7.8000e+08444835445599764.380.56
8.0000e+08456902457598695.820.50
8.2000e+08468875469607732.250.52
8.4000e+08480813481627814.310.58
8.6000e+08492948493658709.710.50
8.8000e+08504865505698833.130.58
9.0000e+08516998517748750.280.52
9.2000e+08529062529808745.900.51
9.4000e+08540971541877905.730.61
9.6000e+08553119553955835.520.56
9.8000e+08565119566041922.040.61
1.0000e+09577247578136889.050.58
1.0500e+09607612608409797.390.51
1.1000e+09637842638731889.430.56
1.1500e+096680986690991001.390.62
1.2000e+09698635699511875.730.53
1.2500e+097288917299631072.170.64
1.3000e+09759544760455910.630.53
1.3500e+097898847909831099.200.63
1.4000e+098204578215471090.140.61
1.4500e+098510508521451094.830.61
1.5000e+09881948882775826.800.45
1.5500e+09912697913436738.670.40
1.6000e+09943430944126696.170.37
1.6500e+09974167974845678.120.35
1.7000e+0910049551005591636.410.33
1.7500e+0910357581036364606.000.31
1.8000e+0910663441067162817.950.41
1.8500e+0910977631097984221.330.11
1.9000e+0911283571128830473.300.23
1.9500e+0911593171159699382.070.19
2.0000e+0911903421190590247.880.12
2.1000e+0912526091252435-174.20-0.08
2.2000e+0913144071314360-47.15-0.02
2.3000e+0913765611376360-200.69-0.09
2.4000e+0914385271438432-95.06-0.04
2.5000e+0915003631500571207.910.09
2.6000e+0915624591562774314.720.13
2.7000e+0916245881625037449.170.19
2.8000e+0916870081687358350.340.14
2.9000e+0917493811749735353.550.14
3.0000e+0918117931812163370.300.15
3.1000e+091874554187464288.320.03
3.2000e+0919369491937169220.470.09
3.3000e+0919995231999743219.770.08
3.4000e+0920620122062360348.400.13
3.5000e+0921253202125021-299.37-0.11
3.6000e+0921879812187722-259.14-0.10
3.7000e+0922507302250463-267.42-0.10
3.8000e+092313145231324196.390.03
3.9000e+0923757142376057342.950.12
4.0000e+0924386842438908224.020.08
4.1000e+0925015702501793223.420.08
4.2000e+0925645182564712194.040.07
4.3000e+092627627262766335.820.01
4.4000e+092690566269064578.770.03
4.5000e+0927540782753657-421.06-0.14
4.6000e+0928170452816698-346.56-0.11
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