Gap size : 136 (r=68)

Generated by program gapCounts : Mon Jun 27 12:45:44 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+030-0-0.00-0.00
6.0000e+030-0-0.00-0.00
6.2000e+030-0-0.00-0.00
6.4000e+03000.000.00
6.6000e+03000.000.00
6.8000e+03000.000.00
7.0000e+03000.000.00
7.2000e+030-0-0.00-0.00
7.4000e+030-0-0.00-0.00
7.6000e+030-0-0.00-0.00
7.8000e+030-0-0.00-0.00
8.0000e+030-0-0.00-0.00
8.2000e+030-0-0.00-0.00
8.4000e+030-0-0.00-0.00
8.6000e+030-0-0.00-0.00
8.8000e+030-0-0.00-0.00
9.0000e+030-0-0.00-0.00
9.2000e+030-0-0.00-0.00
9.4000e+030-0-0.00-0.00
9.6000e+030-0-0.00-0.00
9.8000e+030-0-0.00-0.00
1.0000e+040-0-0.00-0.00
1.0500e+040-0-0.00-0.00
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+04000.000.00
6.2000e+04000.000.00
6.4000e+04000.000.00
6.6000e+04000.000.00
6.8000e+04000.000.00
7.0000e+04000.000.00
7.2000e+04000.000.00
7.4000e+04000.000.00
7.6000e+04000.000.00
7.8000e+04000.000.00
8.0000e+04000.000.00
8.2000e+04000.000.00
8.4000e+04000.000.00
8.6000e+04000.000.00
8.8000e+04000.000.00
9.0000e+04000.000.00
9.2000e+04000.000.00
9.4000e+04000.000.00
9.6000e+04000.000.00
9.8000e+04000.000.00
1.0000e+05000.000.00
1.0500e+05000.000.00
1.1000e+05000.000.00
1.1500e+05000.000.00
1.2000e+05000.000.00
1.2500e+05000.000.00
1.3000e+05000.000.00
1.3500e+05000.000.00
1.4000e+05000.000.00
1.4500e+05000.000.00
1.5000e+05000.000.00
1.5500e+05000.000.00
1.6000e+05000.000.00
1.6500e+05000.000.00
1.7000e+05000.000.00
1.7500e+05000.000.00
1.8000e+05000.000.00
1.8500e+05000.000.00
1.9000e+05000.000.00
1.9500e+05000.000.00
2.0000e+05000.000.00
2.1000e+05000.000.00
2.2000e+05000.000.00
2.3000e+05000.000.00
2.4000e+05000.000.00
2.5000e+05000.000.00
2.6000e+05000.000.00
2.7000e+05000.000.00
2.8000e+05000.000.00
2.9000e+05000.000.00
3.0000e+05000.000.00
3.1000e+05000.000.00
3.2000e+05000.000.00
3.3000e+05000.000.00
3.4000e+05000.000.00
3.5000e+05000.000.00
3.6000e+05000.000.00
3.7000e+05000.000.00
3.8000e+05000.000.00
3.9000e+05000.000.00
4.0000e+05000.000.00
4.1000e+05000.000.00
4.2000e+05000.000.00
4.3000e+05000.000.00
4.4000e+05000.000.00
4.5000e+05000.000.00
4.6000e+05000.000.00
4.7000e+05000.000.00
4.8000e+05000.000.00
4.9000e+05000.000.00
5.0000e+05000.000.00
5.2000e+05000.000.00
5.4000e+05000.000.00
5.6000e+05000.000.00
5.8000e+05000.000.00
6.0000e+05000.000.00
6.2000e+05000.000.00
6.4000e+05000.000.00
6.6000e+05000.000.00
6.8000e+05000.000.00
7.0000e+05000.000.00
7.2000e+05000.000.00
7.4000e+05000.000.00
7.6000e+05000.000.00
7.8000e+05000.010.00
8.0000e+05000.010.00
8.2000e+05000.010.00
8.4000e+05000.010.00
8.6000e+05000.010.00
8.8000e+05000.010.00
9.0000e+05000.010.00
9.2000e+05000.010.00
9.4000e+05000.010.00
9.6000e+05000.010.00
9.8000e+05000.010.00
1.0000e+06000.010.00
1.0500e+06000.010.00
1.1000e+06000.010.00
1.1500e+06000.010.00
1.2000e+06000.010.00
1.2500e+06000.020.00
1.3000e+06000.020.00
1.3500e+06000.020.00
1.4000e+06000.020.00
1.4500e+06000.020.00
1.5000e+06000.020.00
1.5500e+06000.020.00
1.6000e+06000.030.00
1.6500e+06000.030.00
1.7000e+06000.030.00
1.7500e+06000.030.00
1.8000e+06000.030.00
1.8500e+06000.040.00
1.9000e+06000.040.00
1.9500e+06000.040.00
2.0000e+06000.040.00
2.1000e+06000.050.00
2.2000e+06000.050.00
2.3000e+06000.060.00
2.4000e+06000.060.00
2.5000e+06000.070.00
2.6000e+06000.080.00
2.7000e+06000.080.00
2.8000e+06000.090.00
2.9000e+06000.090.00
3.0000e+06000.100.00
3.1000e+06000.110.00
3.2000e+06000.120.00
3.3000e+06000.120.00
3.4000e+06000.130.00
3.5000e+06000.140.00
3.6000e+06000.150.00
3.7000e+06000.150.00
3.8000e+06000.160.00
3.9000e+06000.170.00
4.0000e+06000.180.00
4.1000e+06000.190.00
4.2000e+06000.200.00
4.3000e+06000.210.00
4.4000e+06000.220.00
4.5000e+06000.230.00
4.6000e+06000.240.00
4.7000e+06000.250.00
4.8000e+06000.260.00
4.9000e+06000.270.00
5.0000e+06000.280.00
5.2000e+06000.300.00
5.4000e+06000.320.00
5.6000e+06000.350.00
5.8000e+06000.370.00
6.0000e+06000.390.00
6.2000e+06000.420.00
6.4000e+0610-0.55-0.00
6.6000e+0610-0.53-0.00
6.8000e+0611-0.50-0.00
7.0000e+0611-0.47-0.00
7.2000e+0611-0.44-0.00
7.4000e+0611-0.41-0.00
7.6000e+0611-0.38-0.00
7.8000e+0611-0.35-0.00
8.0000e+0611-0.32-0.00
8.2000e+0611-0.29-0.00
8.4000e+0611-0.26-0.00
8.6000e+0611-0.23-0.00
8.8000e+0611-0.19-0.00
9.0000e+0611-0.16-0.00
9.2000e+0611-0.13-0.00
9.4000e+0621-1.09-0.01
9.6000e+0621-1.05-0.01
9.8000e+0621-1.02-0.01
1.0000e+0721-0.98-0.01
1.0500e+0721-0.89-0.00
1.1000e+0721-0.79-0.00
1.1500e+0721-0.69-0.00
1.2000e+0731-1.59-0.01
1.2500e+0742-2.48-0.01
1.3000e+0742-2.37-0.01
1.3500e+0742-2.26-0.01
1.4000e+0742-2.14-0.01
1.4500e+0742-2.02-0.01
1.5000e+0742-1.90-0.01
1.5500e+0742-1.78-0.01
1.6000e+0742-1.65-0.01
1.6500e+0742-1.52-0.01
1.7000e+0743-1.39-0.01
1.7500e+0743-1.26-0.01
1.8000e+0743-1.12-0.00
1.8500e+0743-0.98-0.00
1.9000e+0743-0.84-0.00
1.9500e+0743-0.69-0.00
2.0000e+0743-0.55-0.00
2.1000e+0744-0.25-0.00
2.2000e+0754-0.94-0.00
2.3000e+0754-0.62-0.00
2.4000e+0765-1.29-0.00
2.5000e+0775-1.95-0.01
2.6000e+0775-1.61-0.01
2.7000e+0776-1.26-0.00
2.8000e+0776-0.90-0.00
2.9000e+0776-0.53-0.00
3.0000e+0787-1.15-0.00
3.1000e+0797-1.77-0.01
3.2000e+07108-2.38-0.01
3.3000e+07108-1.98-0.01
3.4000e+07108-1.57-0.00
3.5000e+07139-4.16-0.01
3.6000e+07139-3.74-0.01
3.7000e+071310-3.31-0.01
3.8000e+071310-2.88-0.01
3.9000e+071311-2.44-0.01
4.0000e+071311-2.00-0.01
4.1000e+071311-1.54-0.00
4.2000e+071312-1.09-0.00
4.3000e+071312-0.62-0.00
4.4000e+071313-0.15-0.00
4.5000e+0713130.330.00
4.6000e+0713140.810.00
4.7000e+0713141.300.00
4.8000e+0714150.790.00
4.9000e+0715150.290.00
5.0000e+0715160.800.00
5.2000e+071717-0.18-0.00
5.4000e+0717180.870.00
5.6000e+0718190.940.00
5.8000e+0720200.030.00
6.0000e+0721210.140.00
6.2000e+072422-1.73-0.00
6.4000e+072423-0.58-0.00
6.6000e+072625-1.41-0.00
6.8000e+072626-0.22-0.00
7.0000e+072927-2.01-0.00
7.2000e+072928-0.79-0.00
7.4000e+0729290.450.00
7.6000e+0730310.710.00
7.8000e+0731320.980.00
8.0000e+0732331.280.00
8.2000e+0733351.580.00
8.4000e+0733362.910.01
8.6000e+0734373.250.01
8.8000e+0735393.600.01
9.0000e+0737402.980.01
9.2000e+0737414.360.01
9.4000e+0739433.760.01
9.6000e+0740444.180.01
9.8000e+0740465.610.01
1.0000e+0840477.050.01
1.0500e+0846514.730.01
1.1000e+0848546.490.01
1.1500e+0849589.330.02
1.2000e+0854628.250.01
1.2500e+0858668.250.01
1.3000e+0863707.320.01
1.3500e+0868746.470.01
1.4000e+0870798.690.01
1.4500e+0874838.980.01
1.5000e+0878879.340.01
1.5500e+08809211.760.02
1.6000e+08839613.250.02
1.6500e+088810112.810.02
1.7000e+089210513.430.02
1.7500e+089511015.100.02
1.8000e+0810011514.840.02
1.8500e+0810412015.640.02
1.9000e+0810812416.490.02
1.9500e+0811312916.400.02
2.0000e+0811913415.370.02
2.1000e+0812314421.460.03
2.2000e+0813415520.760.03
2.3000e+0814416521.270.03
2.4000e+0815417621.970.03
2.5000e+0816818718.860.02
2.6000e+0817819819.940.02
2.7000e+0818920920.200.02
2.8000e+0820222118.630.02
2.9000e+0821523217.230.02
3.0000e+0822524419.000.02
3.1000e+0824425611.930.01
3.2000e+082592689.020.01
3.3000e+082722808.270.01
3.4000e+0828029312.660.01
3.5000e+0829130514.200.01
3.6000e+0829831819.890.02
3.7000e+0830833122.710.02
3.8000e+0831734426.680.03
3.9000e+0833035726.780.03
4.0000e+0834137029.010.03
4.1000e+0835938324.380.02
4.2000e+0837239724.870.02
4.3000e+0838841022.490.02
4.4000e+0840942415.230.01
4.5000e+0842143817.090.02
4.6000e+0843345219.070.02
4.7000e+0844446622.170.02
4.8000e+0845448026.390.02
4.9000e+0847449520.710.02
5.0000e+0848450925.150.02
5.2000e+0850453834.360.03
5.4000e+0853156837.000.03
5.6000e+0856259836.050.03
5.8000e+0858462944.510.04
6.0000e+0861465945.350.04
6.2000e+0864269148.580.04
6.4000e+0867172251.190.04
6.6000e+0870775447.160.04
6.8000e+0873878648.480.04
7.0000e+0877381946.150.04
7.2000e+0880385249.160.04
7.4000e+0882988656.500.04
7.6000e+0886891951.170.04
7.8000e+0889895355.150.04
8.0000e+0892998758.450.04
8.2000e+08956102266.050.05
8.4000e+08993105763.950.05
8.6000e+081041109251.150.04
8.8000e+081074112853.640.04
9.0000e+081108116355.400.04
9.2000e+081145119954.450.04
9.4000e+081183123652.770.04
9.6000e+081220127252.360.03
9.8000e+081258130951.220.03
1.0000e+091297134649.330.03
1.0500e+091396144044.230.03
1.1000e+091480153655.670.03
1.1500e+091575163357.590.04
1.2000e+091689173141.950.03
1.2500e+091773183157.690.03
1.3000e+091873193258.770.03
1.3500e+091983203451.140.03
1.4000e+092106213831.780.02
1.4500e+092219224323.630.01
1.5000e+092317234931.680.02
1.5500e+092410245645.870.02
1.6000e+092500256464.200.03
1.6500e+092602267471.620.04
1.7000e+092703278481.110.04
1.7500e+092813289682.640.04
1.8000e+092912300896.190.05
1.8500e+093028312293.740.05
1.9000e+093145323691.260.04
1.9500e+093270335281.730.04
2.0000e+093380346888.130.04
2.1000e+093609370494.660.04
2.2000e+093869394373.700.03
2.3000e+094101418584.120.04
2.4000e+094360443170.790.03
2.5000e+094616468063.600.03
2.6000e+094888493143.450.02
2.7000e+095159518627.240.01
2.8000e+0954625444-18.12-0.01
2.9000e+09570457040.280.00
3.0000e+09595859679.360.00
3.1000e+096208623325.050.01
3.2000e+096459650142.290.02
3.3000e+096708677263.990.02
3.4000e+096956704589.100.03
3.5000e+097228732192.560.03
3.6000e+097502759896.310.04
3.7000e+0977397878139.290.05
3.8000e+0979928160168.470.06
3.9000e+0982448445200.780.07
4.0000e+0985268731205.190.07
4.1000e+0988099020210.640.07
4.2000e+0991329310178.100.06
4.3000e+0994099603193.520.07
4.4000e+0996999897197.860.07
4.5000e+09997910193214.100.07
4.6000e+091026110491230.190.08
4.7000e+091060310791188.100.06
4.8000e+091090511093187.790.06
4.9000e+091123011396166.230.05
5.0000e+091153511701166.400.05
5.2000e+091217212317144.790.04
5.4000e+091280512939133.740.04
5.6000e+091342413567143.020.04
5.8000e+091404114201160.460.05
6.0000e+091469014842151.860.04
6.2000e+091534115488147.070.04
6.4000e+091597716140162.900.05
6.6000e+091663816797159.220.04
6.8000e+091727517460184.880.05
7.0000e+091793618128191.750.05
7.2000e+091863818801162.690.04
7.4000e+091929819479180.580.05
7.6000e+091994020161221.320.06
7.8000e+092061620849232.780.06
8.0000e+092130821541232.860.06
8.2000e+092205122237186.460.05
8.4000e+092272722938211.490.05
8.6000e+092349023644153.860.04
8.8000e+092419124353162.470.04
9.0000e+092489825067169.250.04
9.2000e+092561225785173.110.04
9.4000e+092635226507154.970.04
9.6000e+092705427233178.760.04
9.8000e+092784427962118.420.03
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