Gap size : 84 (r=42)

Generated by program gapCounts : Mon Jun 27 12:44:32 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+02000.000.00
3.0000e+02000.000.00
4.0000e+02000.000.00
5.0000e+02000.000.00
6.0000e+02000.000.00
7.0000e+02000.000.00
8.0000e+02000.000.00
9.0000e+02000.000.00
1.0000e+03000.000.00
1.1000e+03000.000.00
1.2000e+03000.000.00
1.3000e+03000.000.00
1.4000e+03000.000.00
1.5000e+03000.000.00
1.6000e+03000.000.00
1.7000e+03000.000.00
1.8000e+03000.000.00
1.9000e+03000.000.00
2.0000e+03000.000.00
2.1000e+03000.000.00
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+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+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+04000.000.00
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+04000.010.00
3.8000e+04000.010.00
3.9000e+04000.010.00
4.0000e+04000.010.00
4.1000e+04000.010.00
4.2000e+04000.010.00
4.3000e+04000.010.00
4.4000e+04000.010.00
4.5000e+04000.010.00
4.6000e+04000.010.00
4.7000e+04000.010.00
4.8000e+04000.010.00
4.9000e+04000.010.00
5.0000e+04000.010.00
5.2000e+04000.010.00
5.4000e+04000.020.00
5.6000e+04000.020.00
5.8000e+04000.020.00
6.0000e+04000.020.00
6.2000e+04000.020.00
6.4000e+04000.020.00
6.6000e+04000.030.00
6.8000e+04000.030.00
7.0000e+04000.030.00
7.2000e+04000.030.00
7.4000e+04000.030.00
7.6000e+04000.040.00
7.8000e+04000.040.00
8.0000e+04000.040.00
8.2000e+04000.040.00
8.4000e+04000.050.00
8.6000e+04000.050.00
8.8000e+04000.050.00
9.0000e+04000.050.00
9.2000e+04000.060.00
9.4000e+04000.060.00
9.6000e+04000.060.00
9.8000e+04000.070.00
1.0000e+05000.070.00
1.0500e+05000.080.00
1.1000e+05000.090.00
1.1500e+05000.100.00
1.2000e+05000.110.00
1.2500e+05000.120.00
1.3000e+05000.130.00
1.3500e+05000.140.00
1.4000e+05000.150.00
1.4500e+05000.160.01
1.5000e+05000.170.01
1.5500e+05000.190.01
1.6000e+05000.200.01
1.6500e+05000.210.01
1.7000e+05000.230.01
1.7500e+05000.240.01
1.8000e+05000.260.01
1.8500e+05000.270.01
1.9000e+05000.290.01
1.9500e+05000.300.01
2.0000e+05000.320.01
2.1000e+05000.350.01
2.2000e+05000.390.01
2.3000e+05000.430.01
2.4000e+05000.460.01
2.5000e+05010.500.01
2.6000e+05010.550.01
2.7000e+05010.590.01
2.8000e+05010.630.01
2.9000e+05010.680.02
3.0000e+05010.720.02
3.1000e+05010.770.02
3.2000e+05010.820.02
3.3000e+05010.870.02
3.4000e+05010.920.02
3.5000e+05010.970.02
3.6000e+05011.030.02
3.7000e+05011.080.02
3.8000e+05011.140.02
3.9000e+05011.190.02
4.0000e+05011.250.03
4.1000e+05011.310.03
4.2000e+05011.370.03
4.3000e+05011.430.03
4.4000e+05011.490.03
4.5000e+05021.560.03
4.6000e+05021.620.03
4.7000e+05120.690.01
4.8000e+05120.750.01
4.9000e+05120.820.02
5.0000e+05120.890.02
5.2000e+05121.030.02
5.4000e+05220.170.00
5.6000e+05220.320.01
5.8000e+05220.470.01
6.0000e+05230.630.01
6.2000e+05230.780.01
6.4000e+0533-0.05-0.00
6.6000e+05330.110.00
6.8000e+05330.280.00
7.0000e+05330.450.01
7.2000e+05340.620.01
7.4000e+05340.800.01
7.6000e+05340.980.02
7.8000e+05341.170.02
8.0000e+05341.350.02
8.2000e+05351.540.02
8.4000e+05450.740.01
8.6000e+05450.930.01
8.8000e+05451.130.02
9.0000e+05451.330.02
9.2000e+05461.530.02
9.4000e+05461.740.02
9.6000e+05461.950.03
9.8000e+05561.160.02
1.0000e+06660.370.01
1.0500e+0677-0.08-0.00
1.1000e+0687-0.52-0.01
1.1500e+06880.060.00
1.2000e+06890.650.01
1.2500e+06109-0.74-0.01
1.3000e+061010-0.13-0.00
1.3500e+0610110.510.01
1.4000e+0610111.150.01
1.4500e+061212-0.19-0.00
1.5000e+0612120.480.01
1.5500e+061413-0.84-0.01
1.6000e+061514-1.14-0.01
1.6500e+061715-2.44-0.03
1.7000e+061915-3.72-0.04
1.7500e+062116-4.99-0.05
1.8000e+062217-5.25-0.06
1.8500e+062217-4.51-0.05
1.9000e+062318-4.75-0.05
1.9500e+062319-3.98-0.04
2.0000e+062320-3.20-0.03
2.1000e+062321-1.61-0.02
2.2000e+062623-2.98-0.03
2.3000e+062725-2.32-0.02
2.4000e+063126-4.62-0.04
2.5000e+063328-4.89-0.05
2.6000e+063530-5.12-0.05
2.7000e+063832-6.32-0.06
2.8000e+064134-7.49-0.07
2.9000e+064235-6.63-0.06
3.0000e+064337-5.74-0.05
3.1000e+064939-9.82-0.08
3.2000e+065041-8.87-0.07
3.3000e+065343-9.90-0.08
3.4000e+065545-9.90-0.08
3.5000e+065747-9.87-0.08
3.6000e+066149-11.81-0.09
3.7000e+066151-9.74-0.08
3.8000e+066353-9.63-0.07
3.9000e+066555-9.50-0.07
4.0000e+066758-9.35-0.07
4.1000e+067060-10.18-0.08
4.2000e+067362-10.98-0.08
4.3000e+067764-12.76-0.09
4.4000e+067966-12.52-0.09
4.5000e+068069-11.26-0.08
4.6000e+068071-8.97-0.06
4.7000e+068473-10.67-0.08
4.8000e+068776-11.34-0.08
4.9000e+068778-9.00-0.06
5.0000e+069380-12.63-0.09
5.2000e+0610185-15.84-0.11
5.4000e+0610390-12.98-0.09
5.6000e+0611295-17.04-0.11
5.8000e+06121100-21.03-0.14
6.0000e+06129105-23.96-0.15
6.2000e+06134110-23.81-0.15
6.4000e+06136115-20.61-0.13
6.6000e+06139121-18.33-0.11
6.8000e+06144126-18.00-0.11
7.0000e+06153131-21.61-0.13
7.2000e+06156137-19.15-0.11
7.4000e+06165142-22.64-0.13
7.6000e+06172148-24.07-0.14
7.8000e+06177154-23.45-0.13
8.0000e+06185159-25.78-0.14
8.2000e+06192165-27.05-0.15
8.4000e+06199171-28.27-0.16
8.6000e+06207177-30.43-0.17
8.8000e+06213182-30.55-0.16
9.0000e+06219188-30.62-0.16
9.2000e+06223194-28.64-0.15
9.4000e+06225200-24.62-0.13
9.6000e+06233206-26.55-0.14
9.8000e+06238213-25.43-0.13
1.0000e+07247219-28.27-0.14
1.0500e+07263234-28.68-0.14
1.1000e+07284250-33.83-0.17
1.1500e+07307266-40.72-0.20
1.2000e+07325283-42.37-0.20
1.2500e+07337299-37.78-0.17
1.3000e+07348316-31.97-0.15
1.3500e+07369333-35.94-0.16
1.4000e+07387350-36.70-0.16
1.4500e+07399368-31.26-0.14
1.5000e+07415385-29.61-0.13
1.5500e+07429403-25.78-0.11
1.6000e+07445421-23.75-0.10
1.6500e+07468439-28.54-0.12
1.7000e+07480458-22.16-0.09
1.7500e+07498476-21.60-0.09
1.8000e+07522495-26.87-0.11
1.8500e+07538514-23.98-0.09
1.9000e+07559533-25.93-0.10
1.9500e+07581552-28.72-0.11
2.0000e+07601572-29.35-0.11
2.1000e+07648611-37.18-0.14
2.2000e+07695651-44.43-0.16
2.3000e+07738691-47.13-0.17
2.4000e+07769732-37.30-0.13
2.5000e+07809773-35.95-0.12
2.6000e+07836815-21.12-0.07
2.7000e+07876857-18.81-0.06
2.8000e+07920900-20.04-0.06
2.9000e+07964943-20.83-0.07
3.0000e+071014987-27.18-0.09
3.1000e+0710561031-25.12-0.08
3.2000e+0710891075-13.65-0.04
3.3000e+0711251120-4.79-0.01
3.4000e+07116111654.460.01
3.5000e+07120312118.080.02
3.6000e+07125012577.060.02
3.7000e+07130013033.400.01
3.8000e+07134913501.080.00
3.9000e+07139313974.100.01
4.0000e+07143814446.450.02
4.1000e+071479149213.130.04
4.2000e+071518154022.110.06
4.3000e+071568158820.410.05
4.4000e+071610163727.000.07
4.5000e+071661168624.890.07
4.6000e+071711173524.070.06
4.7000e+071755178529.530.08
4.8000e+071801183433.270.08
4.9000e+071849188435.290.09
5.0000e+071897193537.570.09
5.2000e+071984203651.910.13
5.4000e+072085213853.260.13
5.6000e+072200224241.590.10
5.8000e+072324234621.860.05
6.0000e+072425245126.050.06
6.2000e+072531255726.130.06
6.4000e+072643266421.060.05
6.6000e+072760277211.830.03
6.8000e+072853288027.410.06
7.0000e+072961299028.780.06
7.2000e+073068310031.910.07
7.4000e+073171321139.790.08
7.6000e+073293332229.400.06
7.8000e+073402343532.730.07
8.0000e+073526354821.740.04
8.2000e+073636366125.430.05
8.4000e+073765377610.790.02
8.6000e+07388138919.790.02
8.8000e+07399740069.420.02
9.0000e+074107412315.680.03
9.2000e+074220424019.540.04
9.4000e+074329435727.990.05
9.6000e+074428447547.020.09
9.8000e+074564459429.630.06
1.0000e+084668471344.790.08
1.0500e+084938501375.080.14
1.1000e+085247531769.640.12
1.1500e+085562562361.340.11
1.2000e+085888593345.040.08
1.2500e+086196624649.630.08
1.3000e+086542656118.990.03
1.3500e+08687368796.030.01
1.4000e+08719472005.640.01
1.4500e+0875267523-3.26-0.01
1.5000e+0878527848-3.75-0.01
1.5500e+088164817612.100.02
1.6000e+088484850622.200.03
1.6500e+088820883818.490.03
1.7000e+0891829173-9.09-0.01
1.7500e+0895249509-14.61-0.02
1.8000e+0898629848-14.11-0.02
1.8500e+0810179101889.340.01
1.9000e+081056010531-29.31-0.04
1.9500e+081087610875-1.10-0.00
2.0000e+0811215112215.930.01
2.1000e+0811915119183.230.00
2.2000e+081265212622-29.72-0.04
2.3000e+081339013333-57.23-0.07
2.4000e+081415214049-102.56-0.13
2.5000e+081482514772-52.97-0.06
2.6000e+0815495155005.320.01
2.7000e+081625416234-19.92-0.02
2.8000e+081698416973-10.88-0.01
2.9000e+0817717177170.270.00
3.0000e+08184511846615.340.02
3.1000e+081923519220-14.83-0.02
3.2000e+0819976199792.620.00
3.3000e+082077420742-32.46-0.04
3.4000e+082153221509-23.19-0.02
3.5000e+08222672228013.290.01
3.6000e+082306623056-10.13-0.01
3.7000e+082384623835-10.57-0.01
3.8000e+08246062461912.870.01
3.9000e+08253922540614.100.01
4.0000e+08261262619771.000.07
4.1000e+08269202699271.510.07
4.2000e+08277232779066.510.06
4.3000e+08284972859193.950.09
4.4000e+08293062939689.730.09
4.5000e+083005130204152.780.14
4.6000e+083084731015168.030.16
4.7000e+083162231829207.410.19
4.8000e+083244732647199.860.18
4.9000e+083325333467214.310.19
5.0000e+083407034291220.700.20
5.2000e+083572935946217.080.19
5.4000e+083735137613261.550.23
5.6000e+083896339290326.710.28
5.8000e+084068040977297.180.25
6.0000e+084239442675280.610.23
6.2000e+084411444382267.660.22
6.4000e+084576646098332.030.27
6.6000e+084743347823390.430.31
6.8000e+084921449558343.590.27
7.0000e+085086751300433.250.33
7.2000e+085266953051382.160.29
7.4000e+085443854810372.110.28
7.6000e+085619256577384.870.29
7.8000e+085796158351390.230.29
8.0000e+085981260133321.010.23
8.2000e+086158261922340.010.24
8.4000e+086344263718276.070.20
8.6000e+086523065521291.010.20
8.8000e+086708367331247.670.17
9.0000e+086884069147306.900.21
9.2000e+087066370970306.560.21
9.4000e+087249172798307.500.21
9.6000e+087437874634255.590.17
9.8000e+087624276475232.700.15
1.0000e+097807778322244.700.16
1.0500e+098274482964220.260.14
1.1000e+098751387641128.230.08
1.1500e+099221392351138.030.08
1.2000e+099696697092126.220.08
1.2500e+0910182710186336.490.02
1.3000e+0910659410666469.630.04
1.3500e+09111505111492-13.49-0.01
1.4000e+0911633511634611.110.01
1.4500e+0912116512122661.440.03
1.5000e+0912609712613234.630.02
1.5500e+0913098213106178.820.04
1.6000e+09135843136013170.240.09
1.6500e+09140818140988170.150.09
1.7000e+09145826145985158.860.08
1.7500e+09150866151003136.730.07
1.8000e+0915598615604155.130.03
1.8500e+0916104216109957.490.03
1.9000e+091661721661775.270.00
1.9500e+0917123717127436.930.02
2.0000e+0917632817638961.000.03
2.1000e+09186549186672123.490.06
2.2000e+09197070197024-45.73-0.02
2.3000e+09207556207441-114.83-0.05
2.4000e+09218084217920-163.69-0.07
2.5000e+09228610228459-150.96-0.07
2.6000e+09239335239055-280.07-0.12
2.7000e+09250077249706-371.25-0.16
2.8000e+09260791260409-381.60-0.16
2.9000e+09271544271164-380.02-0.15
3.0000e+09282380281968-412.34-0.16
3.1000e+09293387292819-568.20-0.22
3.2000e+09304244303716-528.19-0.20
3.3000e+09315148314657-490.77-0.19
3.4000e+09325997325642-355.32-0.13
3.5000e+09337025336668-357.13-0.13
3.6000e+09348104347735-369.43-0.14
3.7000e+09359303358841-462.37-0.17
3.8000e+09370265369985-280.05-0.10
3.9000e+09381348381167-181.49-0.06
4.0000e+09392546392384-161.68-0.06
4.1000e+09403910403637-272.55-0.09
4.2000e+09415091414925-165.99-0.06
4.3000e+09426439426246-192.83-0.07
4.4000e+09437715437600-114.88-0.04
4.5000e+09449275448986-288.91-0.10
4.6000e+09460794460403-390.65-0.13
4.7000e+09472034471851-182.80-0.06
4.8000e+09483688483329-359.03-0.12
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