Gap size : 130 (r=65)

Generated by program gapCounts : Mon Jun 27 12:45:36 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+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+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+05000.010.00
5.4000e+05000.010.00
5.6000e+05000.010.00
5.8000e+05000.010.00
6.0000e+05000.010.00
6.2000e+05000.010.00
6.4000e+05000.010.00
6.6000e+05000.010.00
6.8000e+05000.010.00
7.0000e+05000.010.00
7.2000e+05000.010.00
7.4000e+05000.010.00
7.6000e+05000.010.00
7.8000e+05000.010.00
8.0000e+05000.020.00
8.2000e+05000.020.00
8.4000e+05000.020.00
8.6000e+05000.020.00
8.8000e+05000.020.00
9.0000e+05000.020.00
9.2000e+05000.020.00
9.4000e+05000.020.00
9.6000e+05000.020.00
9.8000e+05000.020.00
1.0000e+06000.030.00
1.0500e+06000.030.00
1.1000e+06000.030.00
1.1500e+06000.040.00
1.2000e+06000.040.00
1.2500e+06000.040.00
1.3000e+06000.050.00
1.3500e+06000.050.00
1.4000e+06000.050.00
1.4500e+06000.060.00
1.5000e+06000.060.00
1.5500e+06000.070.00
1.6000e+06000.070.00
1.6500e+06000.080.00
1.7000e+06000.080.00
1.7500e+06000.090.00
1.8000e+06000.090.00
1.8500e+06000.100.00
1.9000e+06000.100.00
1.9500e+06000.110.00
2.0000e+06000.110.00
2.1000e+06000.130.00
2.2000e+06000.140.00
2.3000e+06000.150.00
2.4000e+06000.170.00
2.5000e+06000.180.00
2.6000e+06000.200.00
2.7000e+06000.210.00
2.8000e+06000.230.00
2.9000e+06000.240.00
3.0000e+06000.260.00
3.1000e+06000.280.00
3.2000e+06000.300.00
3.3000e+06000.310.00
3.4000e+06000.330.00
3.5000e+06000.350.00
3.6000e+06000.370.00
3.7000e+06000.390.00
3.8000e+06000.410.00
3.9000e+06000.440.00
4.0000e+06000.460.00
4.1000e+06000.480.00
4.2000e+06010.500.00
4.3000e+06010.520.00
4.4000e+06010.550.00
4.5000e+06010.570.00
4.6000e+06010.600.00
4.7000e+06010.620.00
4.8000e+06010.650.00
4.9000e+06010.670.00
5.0000e+06010.700.00
5.2000e+06010.750.01
5.4000e+06010.810.01
5.6000e+0611-0.14-0.00
5.8000e+0611-0.08-0.00
6.0000e+0611-0.02-0.00
6.2000e+06110.040.00
6.4000e+06110.100.00
6.6000e+06110.170.00
6.8000e+06110.230.00
7.0000e+06110.300.00
7.2000e+06110.370.00
7.4000e+06110.440.00
7.6000e+06120.510.00
7.8000e+06120.580.00
8.0000e+06120.650.00
8.2000e+06120.730.00
8.4000e+06120.810.00
8.6000e+06120.880.00
8.8000e+06120.960.01
9.0000e+06121.040.01
9.2000e+06121.120.01
9.4000e+06121.210.01
9.6000e+06121.290.01
9.8000e+06121.380.01
1.0000e+07121.460.01
1.0500e+07131.680.01
1.1000e+07131.910.01
1.1500e+07231.150.01
1.2000e+07231.390.01
1.2500e+07241.640.01
1.3000e+07241.890.01
1.3500e+07242.160.01
1.4000e+07242.420.01
1.4500e+07252.700.01
1.5000e+07252.980.01
1.5500e+07253.270.01
1.6000e+07263.560.01
1.6500e+07263.860.02
1.7000e+07264.160.02
1.7500e+07264.470.02
1.8000e+07274.780.02
1.8500e+07275.100.02
1.9000e+07275.430.02
1.9500e+07285.760.02
2.0000e+07286.100.02
2.1000e+07296.780.02
2.2000e+07396.490.02
2.3000e+074106.220.02
2.4000e+075115.960.02
2.5000e+076125.720.02
2.6000e+076136.500.02
2.7000e+076137.300.02
2.8000e+077147.110.02
2.9000e+077157.950.03
3.0000e+079166.790.02
3.1000e+0711175.660.02
3.2000e+0714183.530.01
3.3000e+0715183.430.01
3.4000e+0717192.340.01
3.5000e+0717203.260.01
3.6000e+0717214.200.01
3.7000e+0717225.150.01
3.8000e+0717236.120.02
3.9000e+0718246.100.02
4.0000e+0718257.090.02
4.1000e+0718268.100.02
4.2000e+0718279.110.02
4.3000e+07182810.150.03
4.4000e+07192910.190.03
4.5000e+07193011.250.03
4.6000e+07193112.320.03
4.7000e+07193213.400.03
4.8000e+07193314.490.04
4.9000e+07193515.600.04
5.0000e+07193616.720.04
5.2000e+07203817.980.04
5.4000e+07204020.300.05
5.6000e+07224320.650.05
5.8000e+07244521.050.05
6.0000e+07254722.490.05
6.2000e+07265023.970.05
6.4000e+07305222.490.05
6.6000e+07325523.050.05
6.8000e+07335824.650.05
7.0000e+07386022.280.05
7.2000e+07396323.950.05
7.4000e+07396626.660.06
7.6000e+07446824.400.05
7.8000e+07467125.170.05
8.0000e+07477426.980.05
8.2000e+07507726.830.05
8.4000e+07558024.700.05
8.6000e+07588324.610.05
8.8000e+07628623.550.05
9.0000e+07668922.520.04
9.2000e+07689223.520.04
9.4000e+07739521.550.04
9.6000e+07749823.610.04
9.8000e+077510125.700.05
1.0000e+087810425.820.05
1.0500e+088411227.750.05
1.1000e+089312026.840.05
1.1500e+0810312825.100.04
1.2000e+0810713729.520.05
1.2500e+0811714528.100.05
1.3000e+0812315430.830.05
1.3500e+0813216330.700.05
1.4000e+0814517226.720.04
1.4500e+0815118129.880.05
1.5000e+0815819032.180.05
1.5500e+0816720032.610.05
1.6000e+0817520934.170.05
1.6500e+0818821930.850.05
1.7000e+0819422934.660.05
1.7500e+0820523933.590.05
1.8000e+0821124937.640.05
1.8500e+0822025938.800.05
1.9000e+0822926940.080.06
1.9500e+0824027939.470.05
2.0000e+0825129038.970.05
2.1000e+0827031141.290.05
2.2000e+0828733346.030.06
2.3000e+0830935546.160.06
2.4000e+0833437843.680.05
2.5000e+0835940141.570.05
2.6000e+0838542438.830.05
2.7000e+0840944738.440.05
2.8000e+0843147140.390.05
2.9000e+0845949636.670.04
3.0000e+0847952041.280.05
3.1000e+0850654539.200.04
3.2000e+0852557045.430.05
3.3000e+0854559650.960.06
3.4000e+0857162250.790.05
3.5000e+0860264845.900.05
3.6000e+0862567449.290.05
3.7000e+0865370147.960.05
3.8000e+0867972848.890.05
3.9000e+0870975546.090.05
4.0000e+0873778345.540.05
4.1000e+0876581045.250.04
4.2000e+0879783841.200.04
4.3000e+0882786639.400.04
4.4000e+0885689538.840.04
4.5000e+0888492439.510.04
4.6000e+0891195241.410.04
4.7000e+0894098241.530.04
4.8000e+08971101139.880.04
4.9000e+08995104045.450.04
5.0000e+081030107040.230.04
5.2000e+081085113045.430.04
5.4000e+081138119153.450.05
5.6000e+081200125353.260.05
5.8000e+081267131648.850.04
6.0000e+081347137932.190.03
6.2000e+081412144331.270.03
6.4000e+081475150833.060.03
6.6000e+081548157425.540.02
6.8000e+081613164026.700.02
7.0000e+081675170731.530.02
7.2000e+081748177426.000.02
7.4000e+081825184217.100.01
7.6000e+081900191110.820.01
7.8000e+0819921980-11.85-0.01
8.0000e+0820592050-8.93-0.01
8.2000e+0821402121-19.43-0.01
8.4000e+0822172192-25.35-0.02
8.6000e+0822972263-33.73-0.02
8.8000e+0823662335-30.55-0.02
9.0000e+0824372408-28.84-0.02
9.2000e+0825082481-26.59-0.02
9.4000e+0825902555-34.84-0.02
9.6000e+0826622629-32.57-0.02
9.8000e+0827462704-41.80-0.03
1.0000e+0928132779-33.54-0.02
1.0500e+0930002970-30.29-0.02
1.1000e+0931823163-19.13-0.01
1.1500e+0933793359-20.17-0.01
1.2000e+0936043557-46.52-0.03
1.2500e+0937993759-40.27-0.02
1.3000e+0939853963-22.50-0.01
1.3500e+0941894169-20.29-0.01
1.4000e+0944014377-23.73-0.01
1.4500e+09458745881.120.00
1.5000e+0948274801-25.80-0.01
1.5500e+0950635016-46.56-0.03
1.6000e+0952875234-53.22-0.03
1.6500e+0955165453-62.83-0.03
1.7000e+0957525675-77.45-0.04
1.7500e+0959855898-87.12-0.04
1.8000e+0962346123-110.89-0.06
1.8500e+0964416350-90.81-0.05
1.9000e+0966586579-78.91-0.04
1.9500e+0968856810-75.24-0.04
2.0000e+0971117042-68.84-0.03
2.1000e+0975557512-42.99-0.02
2.2000e+0980247988-35.62-0.02
2.3000e+0984938471-22.00-0.01
2.4000e+0989998960-39.34-0.02
2.5000e+0995059454-50.87-0.02
2.6000e+09100079954-52.79-0.02
2.7000e+091055110460-91.28-0.04
2.8000e+091107510970-104.51-0.04
2.9000e+091156411486-77.64-0.03
3.0000e+091209812007-90.83-0.04
3.1000e+091265512533-122.22-0.05
3.2000e+091321413063-150.94-0.06
3.3000e+091372913598-131.11-0.05
3.4000e+091425514137-117.86-0.04
3.5000e+091481414681-133.30-0.05
3.6000e+091536215228-133.54-0.05
3.7000e+091590915780-128.67-0.05
3.8000e+091646016336-123.79-0.04
3.9000e+091701516896-119.00-0.04
4.0000e+091761317460-153.38-0.05
4.1000e+091821118027-184.01-0.06
4.2000e+091876518598-166.97-0.06
4.3000e+091934419173-171.35-0.06
4.4000e+091991319751-162.20-0.05
4.5000e+092046020332-127.61-0.04
4.6000e+092108920917-171.64-0.06
4.7000e+092166121506-155.35-0.05
4.8000e+092223522097-137.81-0.04
4.9000e+092284422692-152.07-0.05
5.0000e+092342623290-136.19-0.04
5.2000e+092459124495-96.23-0.03
5.4000e+092581925712-107.35-0.03
5.6000e+092707026940-129.93-0.04
5.8000e+092829428180-114.35-0.03
6.0000e+092951429430-83.93-0.02
6.2000e+093075330691-61.99-0.02
6.4000e+093202231962-59.84-0.02
6.6000e+093332733243-83.76-0.02
6.8000e+093461334534-79.00-0.02
7.0000e+093583535834-0.83-0.00
7.2000e+0937139371444.510.00
7.4000e+09384283846233.820.01
7.6000e+09396973978991.860.02
7.8000e+09410544112470.430.02
8.0000e+09424014246867.350.02
8.2000e+09437464382074.420.02
8.4000e+09451044518076.470.02
8.6000e+094644146548107.330.03
8.8000e+094782247924101.840.02
9.0000e+09492744930732.840.01
9.2000e+095069950697-1.81-0.00
9.4000e+09520655209529.740.01
9.6000e+095350953499-9.64-0.00
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