Gap size : 86 (r=43)

Generated by program gapCounts : Mon Jun 27 12:44:35 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+030-0-0.00-0.00
3.7000e+030-0-0.00-0.00
3.8000e+030-0-0.00-0.00
3.9000e+030-0-0.00-0.00
4.0000e+030-0-0.00-0.00
4.1000e+030-0-0.00-0.00
4.2000e+030-0-0.00-0.00
4.3000e+030-0-0.00-0.00
4.4000e+030-0-0.00-0.00
4.5000e+030-0-0.00-0.00
4.6000e+030-0-0.00-0.00
4.7000e+030-0-0.00-0.00
4.8000e+030-0-0.00-0.00
4.9000e+030-0-0.00-0.00
5.0000e+030-0-0.00-0.00
5.2000e+030-0-0.00-0.00
5.4000e+030-0-0.00-0.00
5.6000e+030-0-0.00-0.00
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+04000.000.00
1.3000e+04000.000.00
1.3500e+04000.000.00
1.4000e+04000.000.00
1.4500e+04000.000.00
1.5000e+04000.000.00
1.5500e+04000.000.00
1.6000e+04000.000.00
1.6500e+04000.000.00
1.7000e+04000.000.00
1.7500e+04000.000.00
1.8000e+04000.000.00
1.8500e+04000.000.00
1.9000e+04000.000.00
1.9500e+04000.000.00
2.0000e+04000.000.00
2.1000e+04000.000.00
2.2000e+04000.000.00
2.3000e+04000.000.00
2.4000e+04000.000.00
2.5000e+04000.000.00
2.6000e+04000.000.00
2.7000e+04000.000.00
2.8000e+04000.000.00
2.9000e+04000.000.00
3.0000e+04000.000.00
3.1000e+04000.000.00
3.2000e+04000.000.00
3.3000e+04000.000.00
3.4000e+04000.000.00
3.5000e+04000.000.00
3.6000e+04000.000.00
3.7000e+04000.000.00
3.8000e+04000.000.00
3.9000e+04000.000.00
4.0000e+04000.000.00
4.1000e+04000.000.00
4.2000e+04000.000.00
4.3000e+04000.000.00
4.4000e+04000.000.00
4.5000e+04000.000.00
4.6000e+04000.000.00
4.7000e+04000.000.00
4.8000e+04000.000.00
4.9000e+04000.000.00
5.0000e+04000.000.00
5.2000e+04000.000.00
5.4000e+04000.000.00
5.6000e+04000.000.00
5.8000e+04000.000.00
6.0000e+04000.010.00
6.2000e+04000.010.00
6.4000e+04000.010.00
6.6000e+04000.010.00
6.8000e+04000.010.00
7.0000e+04000.010.00
7.2000e+04000.010.00
7.4000e+04000.010.00
7.6000e+04000.010.00
7.8000e+04000.010.00
8.0000e+04000.010.00
8.2000e+04000.010.00
8.4000e+04000.010.00
8.6000e+04000.010.00
8.8000e+04000.010.00
9.0000e+04000.010.00
9.2000e+04000.020.00
9.4000e+04000.020.00
9.6000e+04000.020.00
9.8000e+04000.020.00
1.0000e+05000.020.00
1.0500e+05000.020.00
1.1000e+05000.020.00
1.1500e+05000.030.00
1.2000e+05000.030.00
1.2500e+05000.030.00
1.3000e+05000.040.00
1.3500e+05000.040.00
1.4000e+05000.040.00
1.4500e+05000.040.00
1.5000e+05000.050.00
1.5500e+05000.050.00
1.6000e+0510-0.94-0.03
1.6500e+0510-0.94-0.03
1.7000e+0510-0.94-0.03
1.7500e+0510-0.93-0.03
1.8000e+0510-0.93-0.03
1.8500e+0510-0.92-0.03
1.9000e+0510-0.92-0.03
1.9500e+0510-0.91-0.03
2.0000e+0510-0.91-0.02
2.1000e+0510-0.90-0.02
2.2000e+0510-0.89-0.02
2.3000e+0510-0.88-0.02
2.4000e+0510-0.87-0.02
2.5000e+0510-0.85-0.02
2.6000e+0510-0.84-0.02
2.7000e+0510-0.83-0.02
2.8000e+0510-0.82-0.02
2.9000e+0510-0.80-0.02
3.0000e+0510-0.79-0.02
3.1000e+0510-0.78-0.02
3.2000e+0510-0.76-0.02
3.3000e+0510-0.75-0.02
3.4000e+0520-1.73-0.04
3.5000e+0520-1.71-0.04
3.6000e+0520-1.70-0.04
3.7000e+0520-1.68-0.04
3.8000e+0520-1.67-0.03
3.9000e+0520-1.65-0.03
4.0000e+0520-1.63-0.03
4.1000e+0520-1.61-0.03
4.2000e+0520-1.59-0.03
4.3000e+0520-1.58-0.03
4.4000e+0520-1.56-0.03
4.5000e+0520-1.54-0.03
4.6000e+0520-1.52-0.03
4.7000e+0521-1.50-0.03
4.8000e+0521-1.48-0.03
4.9000e+0521-1.46-0.03
5.0000e+0521-1.44-0.03
5.2000e+0521-1.39-0.03
5.4000e+0521-1.35-0.02
5.6000e+0521-1.30-0.02
5.8000e+0521-1.26-0.02
6.0000e+0521-1.21-0.02
6.2000e+0521-1.16-0.02
6.4000e+0521-1.11-0.02
6.6000e+0521-1.06-0.02
6.8000e+0521-1.01-0.02
7.0000e+0521-0.95-0.02
7.2000e+0521-0.90-0.01
7.4000e+0521-0.84-0.01
7.6000e+0521-0.79-0.01
7.8000e+0521-0.73-0.01
8.0000e+0521-0.67-0.01
8.2000e+0521-0.61-0.01
8.4000e+0521-0.55-0.01
8.6000e+0532-1.49-0.02
8.8000e+0542-2.43-0.04
9.0000e+0542-2.37-0.03
9.2000e+0542-2.30-0.03
9.4000e+0542-2.24-0.03
9.6000e+0542-2.17-0.03
9.8000e+0542-2.11-0.03
1.0000e+0642-2.04-0.03
1.0500e+0642-1.87-0.03
1.1000e+0642-1.69-0.02
1.1500e+0642-1.51-0.02
1.2000e+0643-1.32-0.02
1.2500e+0653-2.13-0.03
1.3000e+0653-1.93-0.02
1.3500e+0653-1.73-0.02
1.4000e+0653-1.52-0.02
1.4500e+0654-1.31-0.02
1.5000e+0664-2.10-0.02
1.5500e+0664-1.88-0.02
1.6000e+0664-1.66-0.02
1.6500e+0675-2.43-0.03
1.7000e+0675-2.20-0.02
1.7500e+0675-1.97-0.02
1.8000e+0675-1.73-0.02
1.8500e+0676-1.49-0.02
1.9000e+0676-1.25-0.01
1.9500e+0676-1.00-0.01
2.0000e+0676-0.75-0.01
2.1000e+0677-0.24-0.00
2.2000e+06770.290.00
2.3000e+06780.830.01
2.4000e+06880.380.00
2.5000e+06890.940.01
2.6000e+068101.510.01
2.7000e+061110-0.90-0.01
2.8000e+061211-1.31-0.01
2.9000e+061311-1.70-0.01
3.0000e+061512-3.08-0.03
3.1000e+061513-2.46-0.02
3.2000e+061613-2.82-0.02
3.3000e+061614-2.18-0.02
3.4000e+061614-1.52-0.01
3.5000e+061815-2.86-0.02
3.6000e+061816-2.18-0.02
3.7000e+061816-1.50-0.01
3.8000e+061917-1.81-0.01
3.9000e+061918-1.11-0.01
4.0000e+061919-0.40-0.00
4.1000e+0619190.310.00
4.2000e+0619201.030.01
4.3000e+0619211.770.01
4.4000e+0619222.500.02
4.5000e+0620222.250.02
4.6000e+0621232.000.01
4.7000e+0621242.760.02
4.8000e+0621253.530.02
4.9000e+0621254.310.03
5.0000e+0621265.090.04
5.2000e+0623284.670.03
5.4000e+0624295.280.04
5.6000e+0624316.920.05
5.8000e+0626336.580.04
6.0000e+0630344.270.03
6.2000e+0631364.980.03
6.4000e+0632385.710.04
6.6000e+0632397.460.05
6.8000e+0632419.240.06
7.0000e+0634439.040.05
7.2000e+0636458.850.05
7.4000e+0639477.690.04
7.6000e+0640498.550.05
7.8000e+0641509.430.05
8.0000e+0643529.330.05
8.2000e+06435411.250.06
8.4000e+06435613.180.07
8.6000e+06465812.130.07
8.8000e+06506010.100.05
9.0000e+0653629.090.05
9.2000e+06536411.100.06
9.4000e+06566610.120.05
9.6000e+06586810.160.05
9.8000e+06607010.210.05
1.0000e+0766726.280.03
1.0500e+0773784.520.02
1.1000e+0777835.860.03
1.1500e+0780888.290.04
1.2000e+0784949.800.05
1.2500e+07889911.400.05
1.3000e+07961059.080.04
1.3500e+071031117.830.04
1.4000e+071091177.670.03
1.4500e+0711212310.580.05
1.5000e+0711712911.550.05
1.5500e+0712213512.600.05
1.6000e+0712414116.720.07
1.6500e+0713214714.900.06
1.7000e+0713515318.150.07
1.7500e+0713915920.450.08
1.8000e+0714416621.820.09
1.8500e+0715417218.250.07
1.9000e+0716417914.740.06
1.9500e+0716918516.280.06
2.0000e+0717419217.880.07
2.1000e+0717920526.240.10
2.2000e+0719321925.810.09
2.3000e+0720523327.580.10
2.4000e+0722024726.540.09
2.5000e+0723326127.690.09
2.6000e+0724827527.010.09
2.7000e+0726229027.510.09
2.8000e+0727630428.180.09
2.9000e+0729331926.010.08
3.0000e+0730633427.990.09
3.1000e+0731634933.130.10
3.2000e+0733136433.420.10
3.3000e+0734438035.850.11
3.4000e+0736039535.420.11
3.5000e+0737641135.130.10
3.6000e+0739142735.970.10
3.7000e+0740544337.940.11
3.8000e+0742045939.030.11
3.9000e+0743147544.250.12
4.0000e+0744949242.600.12
4.1000e+0746550843.050.12
4.2000e+0748852536.630.10
4.3000e+0750154140.320.11
4.4000e+0751855840.120.11
4.5000e+0753757538.020.10
4.6000e+0755859234.040.09
4.7000e+0757660933.150.09
4.8000e+0759162635.370.09
4.9000e+0760864435.690.09
5.0000e+0762566136.110.09
5.2000e+0766069636.240.09
5.4000e+0769773234.730.08
5.6000e+0774176826.590.06
5.8000e+0777880425.800.06
6.0000e+0780984031.340.07
6.2000e+0784687731.210.07
6.4000e+0788791427.400.06
6.6000e+0791895233.900.08
6.8000e+0796499025.700.06
7.0000e+071003102824.790.05
7.2000e+071040106626.170.06
7.4000e+071069110535.820.08
7.6000e+071112114431.740.07
7.8000e+071146118336.930.08
8.0000e+071178122244.370.09
8.2000e+071229126233.060.07
8.4000e+071280130222.010.04
8.6000e+071320134222.190.04
8.8000e+071360138322.600.04
9.0000e+071404142319.250.04
9.2000e+071442146422.120.04
9.4000e+071481150524.210.05
9.6000e+071520154726.520.05
9.8000e+071559158829.050.05
1.0000e+081597163032.780.06
1.0500e+081705173529.990.05
1.1000e+081798184143.430.08
1.1500e+081917194932.030.06
1.2000e+082024205833.760.06
1.2500e+082133216834.560.06
1.3000e+082242227836.410.06
1.3500e+082342239048.250.08
1.4000e+082461250342.060.07
1.4500e+082578261738.800.06
1.5000e+082692273139.450.06
1.5500e+082803284743.970.07
1.6000e+082929296334.330.05
1.6500e+083045308135.520.05
1.7000e+083179319919.510.03
1.7500e+08330833179.280.01
1.8000e+08342934377.800.01
1.8500e+08355735570.060.00
1.9000e+0836833678-4.97-0.01
1.9500e+08379838001.700.00
2.0000e+08392239220.060.00
2.1000e+0841854169-16.25-0.02
2.2000e+0844304418-12.02-0.02
2.3000e+0847154670-45.35-0.06
2.4000e+0849544924-30.36-0.04
2.5000e+0851835180-3.12-0.00
2.6000e+08543454384.260.01
2.7000e+085682569916.720.02
2.8000e+08595859613.170.00
2.9000e+0862306226-4.44-0.01
3.0000e+086451649240.810.05
3.1000e+086703676056.870.06
3.2000e+086970703059.680.07
3.3000e+087233730168.180.07
3.4000e+087524757450.340.05
3.5000e+087776784973.090.08
3.6000e+088062812563.400.07
3.7000e+088322840381.220.08
3.8000e+088588868394.520.10
3.9000e+088877896386.250.09
4.0000e+0891309245115.390.11
4.1000e+0893999529129.890.13
4.2000e+0896879814126.730.12
4.3000e+08100051010094.880.09
4.4000e+081027710387110.290.10
4.5000e+081056810676107.960.10
4.6000e+081083510966130.840.12
4.7000e+081112311257133.920.12
4.8000e+081140911549140.160.13
4.9000e+081170011843142.560.13
5.0000e+081199412137143.070.13
5.2000e+081254012729189.380.17
5.4000e+081314313326182.920.16
5.6000e+081373713927189.550.16
5.8000e+081433714531194.120.16
6.0000e+081496515139174.490.14
6.2000e+081556915752182.550.15
6.4000e+081618216367185.180.15
6.6000e+081678616986200.260.16
6.8000e+081744517609163.700.13
7.0000e+081806218234172.390.13
7.2000e+081867718863186.250.14
7.4000e+081930819495187.190.14
7.6000e+081994720130183.130.14
7.8000e+082060520768162.990.12
8.0000e+082125921409149.690.11
8.2000e+082193822052114.170.08
8.4000e+082259722698101.360.07
8.6000e+082322823347119.190.08
8.8000e+082388023999118.600.08
9.0000e+08245592465393.540.06
9.2000e+082518725309121.960.08
9.4000e+082582025968147.790.10
9.6000e+082646426629164.980.11
9.8000e+082716527292127.500.08
1.0000e+092779327958165.290.11
1.0500e+092949629632136.390.09
1.1000e+093117931320140.760.09
1.1500e+093286333020156.790.10
1.2000e+093458334732148.930.09
1.2500e+093627336456182.680.11
1.3000e+093795038191240.570.14
1.3500e+093970739936229.190.13
1.4000e+094153041692162.130.09
1.4500e+094323843458220.030.12
1.5000e+094497345234260.550.14
1.5500e+094673247018286.350.15
1.6000e+094859548812217.150.12
1.6500e+095037450615240.670.13
1.7000e+095214752426278.630.14
1.7500e+095395854245286.790.15
1.8000e+095580056072271.920.14
1.8500e+095763257907274.790.14
1.9000e+095952259749227.190.11
1.9500e+096136261599236.920.11
2.0000e+096317463456281.810.13
2.1000e+096685667190334.300.16
2.2000e+097052070951431.320.20
2.3000e+097442874738309.670.14
2.4000e+097823678548312.240.14
2.5000e+098210682382276.000.12
2.6000e+098601986238219.030.09
2.7000e+098995790115158.450.07
2.8000e+099391094013103.470.04
2.9000e+09978519793180.350.03
3.0000e+09101754101868114.390.05
3.1000e+0910575510582468.940.03
3.2000e+09109610109797187.410.07
3.3000e+09113652113788136.220.05
3.4000e+09117663117796132.840.05
3.5000e+09121597121820222.780.08
3.6000e+09125638125860221.550.08
3.7000e+09129537129915377.720.14
3.8000e+09133670133985314.860.11
3.9000e+09137799138070270.570.10
4.0000e+09141955142168213.470.07
4.1000e+09146050146281231.200.08
4.2000e+09150174150407233.410.08
4.3000e+09154278154547268.790.09
4.4000e+09158462158699237.020.08
4.5000e+09162616162864247.800.08
4.6000e+09166891167041149.850.05
4.7000e+09171092171230137.900.04
4.8000e+09175290175431140.680.05
4.9000e+09179452179643190.960.06
5.0000e+09183633183866233.480.07
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