Gap size : 66 (r=33)

Generated by program gapCounts : Mon Jun 27 12:44:07 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+030-0-0.00-0.00
2.3000e+030-0-0.00-0.00
2.4000e+030-0-0.00-0.00
2.5000e+030-0-0.00-0.00
2.6000e+030-0-0.00-0.00
2.7000e+030-0-0.00-0.00
2.8000e+030-0-0.00-0.00
2.9000e+030-0-0.00-0.00
3.0000e+030-0-0.00-0.00
3.1000e+030-0-0.00-0.00
3.2000e+030-0-0.00-0.00
3.3000e+030-0-0.00-0.00
3.4000e+030-0-0.00-0.00
3.5000e+030-0-0.00-0.00
3.6000e+03000.000.00
3.7000e+03000.000.00
3.8000e+03000.000.00
3.9000e+03000.000.00
4.0000e+03000.000.00
4.1000e+03000.000.00
4.2000e+03000.000.00
4.3000e+03000.000.00
4.4000e+03000.000.00
4.5000e+03000.000.00
4.6000e+03000.000.00
4.7000e+03000.000.00
4.8000e+03000.000.00
4.9000e+03000.000.00
5.0000e+03000.000.00
5.2000e+03000.000.00
5.4000e+03000.000.00
5.6000e+03000.000.00
5.8000e+03000.000.00
6.0000e+03000.000.00
6.2000e+03000.000.00
6.4000e+03000.000.00
6.6000e+03000.000.00
6.8000e+03000.000.00
7.0000e+03000.000.00
7.2000e+03000.000.00
7.4000e+03000.000.00
7.6000e+03000.000.00
7.8000e+03000.000.00
8.0000e+03000.000.00
8.2000e+03000.000.00
8.4000e+03000.000.00
8.6000e+03000.000.00
8.8000e+03000.000.00
9.0000e+03000.000.00
9.2000e+03000.000.00
9.4000e+03000.000.00
9.6000e+03000.000.00
9.8000e+03000.000.00
1.0000e+04000.000.00
1.0500e+04000.000.00
1.1000e+04000.000.00
1.1500e+04000.000.00
1.2000e+04000.000.00
1.2500e+04000.010.00
1.3000e+04000.010.00
1.3500e+04000.010.00
1.4000e+04000.010.00
1.4500e+04000.010.00
1.5000e+04000.010.00
1.5500e+04000.010.00
1.6000e+04000.010.00
1.6500e+04000.010.00
1.7000e+04000.010.00
1.7500e+04000.010.00
1.8000e+04000.020.00
1.8500e+04000.020.00
1.9000e+04000.020.00
1.9500e+04000.020.00
2.0000e+04000.020.00
2.1000e+04000.020.00
2.2000e+04000.030.00
2.3000e+04000.030.00
2.4000e+04000.030.00
2.5000e+04000.040.00
2.6000e+04000.040.00
2.7000e+04000.050.00
2.8000e+04000.050.00
2.9000e+04000.060.00
3.0000e+04000.060.00
3.1000e+04000.070.00
3.2000e+04000.070.00
3.3000e+04000.080.00
3.4000e+04000.080.00
3.5000e+04000.090.01
3.6000e+04000.100.01
3.7000e+04000.100.01
3.8000e+04000.110.01
3.9000e+04000.120.01
4.0000e+04000.120.01
4.1000e+04000.130.01
4.2000e+04000.140.01
4.3000e+04000.140.01
4.4000e+04000.150.01
4.5000e+04000.160.01
4.6000e+04000.170.01
4.7000e+04000.180.01
4.8000e+04000.180.01
4.9000e+04000.190.01
5.0000e+04000.200.01
5.2000e+04000.220.01
5.4000e+04000.240.01
5.6000e+04000.260.01
5.8000e+04000.280.01
6.0000e+04000.300.01
6.2000e+04000.320.01
6.4000e+04000.340.02
6.6000e+04000.370.02
6.8000e+04000.390.02
7.0000e+04000.410.02
7.2000e+04000.440.02
7.4000e+04000.460.02
7.6000e+04000.490.02
7.8000e+04010.520.02
8.0000e+04010.540.02
8.2000e+04010.570.02
8.4000e+04010.600.02
8.6000e+04010.630.02
8.8000e+04010.660.03
9.0000e+04010.690.03
9.2000e+04010.720.03
9.4000e+04010.750.03
9.6000e+04010.780.03
9.8000e+04010.810.03
1.0000e+05010.840.03
1.0500e+05010.930.03
1.1000e+05011.010.04
1.1500e+05011.100.04
1.2000e+05011.190.04
1.2500e+05011.290.04
1.3000e+05011.390.05
1.3500e+05011.490.05
1.4000e+05021.590.05
1.4500e+05021.690.05
1.5000e+05021.800.06
1.5500e+05021.910.06
1.6000e+05022.030.06
1.6500e+05121.140.03
1.7000e+05121.260.04
1.7500e+05121.380.04
1.8000e+05131.500.04
1.8500e+05131.630.05
1.9000e+05131.750.05
1.9500e+05131.880.05
2.0000e+05132.010.05
2.1000e+05132.280.06
2.2000e+05142.560.07
2.3000e+05241.840.05
2.4000e+05242.130.05
2.5000e+05242.430.06
2.6000e+05351.730.04
2.7000e+05352.050.05
2.8000e+05451.370.03
2.9000e+0576-1.31-0.03
3.0000e+0596-2.98-0.07
3.1000e+0596-2.64-0.06
3.2000e+0597-2.30-0.05
3.3000e+0597-1.95-0.04
3.4000e+0597-1.59-0.03
3.5000e+05108-2.23-0.05
3.6000e+05108-1.86-0.04
3.7000e+05109-1.49-0.03
3.8000e+05129-3.12-0.06
3.9000e+05129-2.73-0.06
4.0000e+051310-3.35-0.07
4.1000e+051310-2.95-0.06
4.2000e+051310-2.56-0.05
4.3000e+051411-3.15-0.06
4.4000e+051511-3.75-0.07
4.5000e+051512-3.34-0.06
4.6000e+051612-3.92-0.08
4.7000e+051612-3.50-0.07
4.8000e+051613-3.08-0.06
4.9000e+051613-2.65-0.05
5.0000e+051614-2.21-0.04
5.2000e+051615-1.34-0.02
5.4000e+051616-0.44-0.01
5.6000e+051816-1.53-0.03
5.8000e+051917-1.61-0.03
6.0000e+051918-0.66-0.01
6.2000e+0519190.290.00
6.4000e+0519201.260.02
6.6000e+052221-0.76-0.01
6.8000e+0522220.240.00
7.0000e+052423-0.75-0.01
7.2000e+052524-0.73-0.01
7.4000e+052925-3.70-0.06
7.6000e+052926-2.65-0.04
7.8000e+053027-2.59-0.04
8.0000e+053328-4.52-0.07
8.2000e+053330-3.44-0.05
8.4000e+053731-6.35-0.09
8.6000e+053732-5.25-0.08
8.8000e+053833-5.13-0.07
9.0000e+054034-6.01-0.09
9.2000e+054035-4.87-0.07
9.4000e+054336-6.73-0.10
9.6000e+054537-7.57-0.11
9.8000e+054639-7.41-0.10
1.0000e+064840-8.24-0.11
1.0500e+065143-8.26-0.11
1.1000e+065346-7.23-0.10
1.1500e+065949-10.14-0.13
1.2000e+066152-9.00-0.12
1.2500e+066355-7.81-0.10
1.3000e+066558-6.57-0.08
1.3500e+066862-6.29-0.08
1.4000e+067265-6.96-0.08
1.4500e+067468-5.58-0.07
1.5000e+067672-4.17-0.05
1.5500e+067975-3.71-0.04
1.6000e+068679-7.21-0.08
1.6500e+069282-9.67-0.11
1.7000e+069386-7.10-0.08
1.7500e+069790-7.48-0.08
1.8000e+069893-4.83-0.05
1.8500e+0610197-4.15-0.04
1.9000e+06104101-3.43-0.04
1.9500e+06110104-5.68-0.06
2.0000e+06116108-7.89-0.08
2.1000e+06122116-6.23-0.06
2.2000e+06126124-2.44-0.02
2.3000e+06133131-1.54-0.01
2.4000e+06142139-2.52-0.02
2.5000e+06149148-1.39-0.01
2.6000e+06158156-2.16-0.02
2.7000e+061641640.170.00
2.8000e+061711731.600.01
2.9000e+061791812.120.02
3.0000e+06190190-0.26-0.00
3.1000e+061961982.440.02
3.2000e+062002077.230.06
3.3000e+062112165.100.04
3.4000e+06226225-0.94-0.01
3.5000e+06235234-0.91-0.01
3.6000e+06244243-0.80-0.01
3.7000e+062522520.380.00
3.8000e+06262262-0.36-0.00
3.9000e+06274271-3.04-0.02
4.0000e+06289280-8.64-0.07
4.1000e+06302290-12.18-0.09
4.2000e+06312299-12.65-0.09
4.3000e+06320309-11.05-0.08
4.4000e+06330319-11.39-0.08
4.5000e+06335328-6.67-0.05
4.6000e+06352338-13.89-0.10
4.7000e+06363348-15.06-0.11
4.8000e+06379358-21.16-0.15
4.9000e+06389368-21.20-0.15
5.0000e+06394378-16.20-0.11
5.2000e+06416398-18.01-0.12
5.4000e+06431418-12.62-0.08
5.6000e+06464439-25.02-0.16
5.8000e+06491460-31.23-0.20
6.0000e+06513481-32.25-0.21
6.2000e+06530502-28.08-0.18
6.4000e+06555523-31.73-0.20
6.6000e+06579545-34.22-0.21
6.8000e+06606566-39.53-0.24
7.0000e+06625588-36.68-0.22
7.2000e+06646610-35.67-0.21
7.4000e+06667632-34.51-0.20
7.6000e+06689655-34.20-0.20
7.8000e+06715677-37.74-0.21
8.0000e+06738700-38.14-0.21
8.2000e+06758723-35.40-0.20
8.4000e+06790745-44.52-0.24
8.6000e+06812768-43.51-0.24
8.8000e+06834792-42.38-0.23
9.0000e+06861815-46.11-0.25
9.2000e+06886838-47.72-0.25
9.4000e+06904862-42.21-0.22
9.6000e+06926885-40.58-0.21
9.8000e+06951909-41.83-0.22
1.0000e+07973933-39.97-0.20
1.0500e+071037993-43.83-0.22
1.1000e+0710901054-36.03-0.18
1.1500e+0711521115-36.58-0.18
1.2000e+0712041177-26.53-0.12
1.2500e+0712791240-38.89-0.18
1.3000e+0713461303-42.69-0.19
1.3500e+0714111367-43.95-0.20
1.4000e+0714641431-32.69-0.14
1.4500e+0715311496-34.93-0.15
1.5000e+0715951561-33.68-0.14
1.5500e+0716641627-36.96-0.16
1.6000e+0717261693-32.79-0.14
1.6500e+0717931760-33.18-0.14
1.7000e+0718531827-26.14-0.11
1.7500e+0719221894-27.69-0.11
1.8000e+0719851962-22.84-0.09
1.8500e+0720562030-25.60-0.10
1.9000e+0721432099-43.98-0.17
1.9500e+0722062168-37.98-0.14
2.0000e+0722782237-40.63-0.15
2.1000e+0724482377-70.88-0.26
2.2000e+0725832518-64.78-0.23
2.3000e+0727342661-73.41-0.26
2.4000e+0728792804-74.82-0.26
2.5000e+0730302949-81.06-0.28
2.6000e+0731673095-72.18-0.24
2.7000e+0733103242-68.22-0.22
2.8000e+0734443390-54.22-0.18
2.9000e+0735923539-53.21-0.17
3.0000e+0737393689-50.25-0.16
3.1000e+0738973840-57.35-0.18
3.2000e+0740453991-53.55-0.16
3.3000e+0742104144-65.87-0.20
3.4000e+0743554298-57.35-0.17
3.5000e+0745114452-59.00-0.17
3.6000e+0746574607-49.86-0.14
3.7000e+0748174763-53.95-0.15
3.8000e+0749734920-53.28-0.15
3.9000e+0751345077-56.88-0.16
4.0000e+0752725235-36.77-0.10
4.1000e+0754245394-29.96-0.08
4.2000e+0755885554-34.47-0.09
4.3000e+0757405714-26.32-0.07
4.4000e+0758875874-12.53-0.03
4.5000e+076024603611.890.03
4.6000e+076165619832.930.09
4.7000e+07635563615.580.01
4.8000e+07651965244.810.01
4.9000e+0767006688-12.39-0.03
5.0000e+07684868523.990.01
5.2000e+0772007182-17.63-0.04
5.4000e+07751375151.890.00
5.6000e+0778577849-7.56-0.02
5.8000e+0782028186-16.04-0.04
6.0000e+0785478524-22.63-0.05
6.2000e+0788748865-9.38-0.02
6.4000e+0792139207-6.37-0.01
6.6000e+07954795503.360.01
6.8000e+079870989625.750.06
7.0000e+07102101024332.740.07
7.2000e+07105511059140.290.09
7.4000e+07108881094153.360.11
7.6000e+07112401129352.900.11
7.8000e+07115541164691.870.19
8.0000e+07119031200097.230.20
8.2000e+071223212356123.950.25
8.4000e+07126271271386.000.17
8.6000e+07129841307187.330.17
8.8000e+07133321343198.920.19
9.0000e+07136941379297.740.19
9.2000e+07140591415494.760.18
9.4000e+07144181451798.950.19
9.6000e+07147941488187.290.16
9.8000e+07151831524763.750.12
1.0000e+08155791561334.310.06
1.0500e+08164751653459.350.11
1.1000e+08173981746263.780.11
1.1500e+0818386183959.290.02
1.2000e+08193211933513.600.02
1.2500e+0820277202792.450.00
1.3000e+082127721230-47.38-0.08
1.3500e+082225322185-68.11-0.11
1.4000e+082319323145-47.95-0.08
1.4500e+08240842411025.930.04
1.5000e+08250512507928.350.04
1.5500e+08260432605310.150.02
1.6000e+082703927031-7.82-0.01
1.6500e+0828011280132.310.00
1.7000e+082904128999-41.60-0.06
1.7500e+083007529989-85.67-0.12
1.8000e+083107930983-96.02-0.14
1.8500e+083212531980-144.75-0.20
1.9000e+083312232981-140.98-0.19
1.9500e+083412333985-137.79-0.19
2.0000e+083510534993-112.29-0.15
2.1000e+083713937017-121.68-0.16
2.2000e+083919339054-138.79-0.18
2.3000e+084120441103-101.23-0.13
2.4000e+084327443162-111.53-0.14
2.5000e+084530545233-72.19-0.09
2.6000e+084735847313-44.65-0.05
2.7000e+084950049404-96.35-0.11
2.8000e+085157251503-68.66-0.08
2.9000e+085361653612-3.94-0.00
3.0000e+085577555729-45.53-0.05
3.1000e+085796157855-105.73-0.12
3.2000e+086008759989-97.84-0.11
3.3000e+086216962131-38.12-0.04
3.4000e+08642686428012.160.01
3.5000e+086644766437-10.22-0.01
3.6000e+086865368601-52.49-0.05
3.7000e+087091870771-146.87-0.15
3.8000e+087313372948-184.56-0.19
3.9000e+087535775132-224.73-0.23
4.0000e+087748777322-164.59-0.16
4.1000e+087972279519-203.28-0.20
4.2000e+088184981721-127.98-0.12
4.3000e+088400683929-76.83-0.07
4.4000e+088621086143-66.99-0.06
4.5000e+08883498836213.400.01
4.6000e+089062090587-32.78-0.03
4.7000e+089289792817-79.66-0.07
4.8000e+089512995053-76.37-0.07
4.9000e+089739597293-102.02-0.09
5.0000e+089969399538-154.72-0.14
5.2000e+08104352104043-308.71-0.27
5.4000e+08108986108567-419.13-0.36
5.6000e+08113522113108-413.72-0.35
5.8000e+08118046117667-379.18-0.32
6.0000e+08122711122242-469.15-0.39
6.2000e+08127308126833-475.21-0.39
6.4000e+08131846131439-406.93-0.33
6.6000e+08136474136060-413.82-0.33
6.8000e+08141050140696-354.36-0.28
7.0000e+08145703145345-358.03-0.28
7.2000e+08150355150008-347.23-0.26
7.4000e+08155134154684-450.39-0.34
7.6000e+08159759159372-386.88-0.29
7.8000e+08164527164073-454.06-0.33
8.0000e+08169160168786-374.28-0.27
8.2000e+08173825173510-314.87-0.23
8.4000e+08178537178246-291.12-0.21
8.6000e+08183348182993-355.33-0.25
8.8000e+08188014187750-263.79-0.18
9.0000e+08192867192518-348.76-0.24
9.2000e+08197598197297-301.49-0.21
9.4000e+08202401202085-316.22-0.21
9.6000e+08207193206883-310.18-0.21
9.8000e+08211987211690-296.61-0.20
1.0000e+09216787216507-279.70-0.18
1.0500e+09228851228589-261.92-0.17
1.1000e+0924070824072516.970.01
1.1500e+09252746252912166.290.10
1.2000e+09265039265149109.600.07
1.2500e+092774272774324.670.00
1.3000e+09289800289759-40.53-0.02
1.3500e+09302215302130-84.90-0.05
1.4000e+09314717314542-175.16-0.10
1.4500e+09327286326993-292.91-0.16
1.5000e+09339809339482-326.66-0.18
1.5500e+09352385352008-376.78-0.20
1.6000e+09364996364569-426.57-0.23
1.6500e+09377754377165-589.25-0.31
1.7000e+09390477389793-683.93-0.35
1.7500e+09403180402453-726.70-0.37
1.8000e+09415929415144-784.54-0.39
1.8500e+09428729427866-863.41-0.43
1.9000e+09441488440616-872.18-0.43
1.9500e+09454224453394-829.71-0.40
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