Gap size : 112 (r=56)

Generated by program gapCounts : Mon Jun 27 12:45:11 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+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+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+030-0-0.00-0.00
6.6000e+030-0-0.00-0.00
6.8000e+030-0-0.00-0.00
7.0000e+030-0-0.00-0.00
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+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+04000.000.00
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+05000.010.00
2.3000e+05000.010.00
2.4000e+05000.010.00
2.5000e+05000.010.00
2.6000e+05000.010.00
2.7000e+05000.010.00
2.8000e+05000.010.00
2.9000e+05000.010.00
3.0000e+05000.010.00
3.1000e+05000.010.00
3.2000e+05000.010.00
3.3000e+05000.010.00
3.4000e+05000.020.00
3.5000e+05000.020.00
3.6000e+05000.020.00
3.7000e+05000.020.00
3.8000e+0510-0.98-0.02
3.9000e+0510-0.98-0.02
4.0000e+0510-0.98-0.02
4.1000e+0510-0.98-0.02
4.2000e+0510-0.98-0.02
4.3000e+0510-0.97-0.02
4.4000e+0510-0.97-0.02
4.5000e+0510-0.97-0.02
4.6000e+0510-0.97-0.02
4.7000e+0510-0.97-0.02
4.8000e+0510-0.97-0.02
4.9000e+0510-0.96-0.02
5.0000e+0510-0.96-0.02
5.2000e+0510-0.96-0.02
5.4000e+0510-0.96-0.02
5.6000e+0510-0.95-0.02
5.8000e+0510-0.95-0.02
6.0000e+0510-0.94-0.02
6.2000e+0510-0.94-0.02
6.4000e+0510-0.94-0.02
6.6000e+0510-0.93-0.02
6.8000e+0510-0.93-0.02
7.0000e+0510-0.92-0.01
7.2000e+0510-0.92-0.01
7.4000e+0510-0.91-0.01
7.6000e+0510-0.91-0.01
7.8000e+0510-0.90-0.01
8.0000e+0510-0.90-0.01
8.2000e+0510-0.89-0.01
8.4000e+0510-0.89-0.01
8.6000e+0510-0.88-0.01
8.8000e+0510-0.88-0.01
9.0000e+0510-0.87-0.01
9.2000e+0510-0.86-0.01
9.4000e+0510-0.86-0.01
9.6000e+0510-0.85-0.01
9.8000e+0510-0.85-0.01
1.0000e+0610-0.84-0.01
1.0500e+0610-0.82-0.01
1.1000e+0610-0.81-0.01
1.1500e+0610-0.79-0.01
1.2000e+0610-0.77-0.01
1.2500e+0610-0.75-0.01
1.3000e+0610-0.73-0.01
1.3500e+0610-0.71-0.01
1.4000e+0610-0.69-0.01
1.4500e+0610-0.66-0.01
1.5000e+0610-0.64-0.01
1.5500e+0610-0.62-0.01
1.6000e+0610-0.59-0.01
1.6500e+0610-0.57-0.01
1.7000e+0610-0.54-0.01
1.7500e+0610-0.52-0.01
1.8000e+0611-0.49-0.01
1.8500e+0611-0.47-0.00
1.9000e+0611-0.44-0.00
1.9500e+0611-0.41-0.00
2.0000e+0611-0.38-0.00
2.1000e+0611-0.32-0.00
2.2000e+0611-0.26-0.00
2.3000e+0611-0.20-0.00
2.4000e+0611-0.13-0.00
2.5000e+0611-0.07-0.00
2.6000e+06110.000.00
2.7000e+0621-0.92-0.01
2.8000e+0621-0.85-0.01
2.9000e+0621-0.78-0.01
3.0000e+0621-0.70-0.01
3.1000e+0621-0.62-0.01
3.2000e+0621-0.54-0.00
3.3000e+0622-0.46-0.00
3.4000e+0622-0.37-0.00
3.5000e+0622-0.29-0.00
3.6000e+0632-1.20-0.01
3.7000e+0632-1.11-0.01
3.8000e+0632-1.02-0.01
3.9000e+0632-0.93-0.01
4.0000e+0632-0.83-0.01
4.1000e+0632-0.74-0.01
4.2000e+0632-0.64-0.00
4.3000e+0632-0.54-0.00
4.4000e+0633-0.44-0.00
4.5000e+0633-0.34-0.00
4.6000e+0633-0.24-0.00
4.7000e+0633-0.14-0.00
4.8000e+0633-0.03-0.00
4.9000e+06330.080.00
5.0000e+06330.190.00
5.2000e+06330.410.00
5.4000e+06340.630.00
5.6000e+0644-0.13-0.00
5.8000e+06440.100.00
6.0000e+06440.340.00
6.2000e+06450.590.00
6.4000e+06450.840.01
6.6000e+06451.100.01
6.8000e+06451.360.01
7.0000e+06560.630.00
7.2000e+06560.900.01
7.4000e+06660.170.00
7.6000e+0686-1.55-0.01
7.8000e+0687-1.27-0.01
8.0000e+0687-0.98-0.01
8.2000e+0687-0.69-0.00
8.4000e+0688-0.39-0.00
8.6000e+0688-0.09-0.00
8.8000e+06880.210.00
9.0000e+0699-0.48-0.00
9.2000e+0699-0.17-0.00
9.4000e+06109-0.85-0.00
9.6000e+06119-1.53-0.01
9.8000e+061110-1.21-0.01
1.0000e+071110-0.88-0.00
1.0500e+071111-0.05-0.00
1.1000e+071312-1.20-0.01
1.1500e+071413-1.33-0.01
1.2000e+071514-1.43-0.01
1.2500e+071514-0.52-0.00
1.3000e+071615-0.58-0.00
1.3500e+0716160.370.00
1.4000e+0716171.340.01
1.4500e+0717181.330.01
1.5000e+0717192.340.01
1.5500e+0719201.360.01
1.6000e+0720211.400.01
1.6500e+072322-0.54-0.00
1.7000e+072524-1.47-0.01
1.7500e+072825-3.38-0.01
1.8000e+073126-5.27-0.02
1.8500e+073227-5.15-0.02
1.9000e+073228-4.02-0.02
1.9500e+073329-3.87-0.01
2.0000e+073430-3.71-0.01
2.1000e+073833-5.34-0.02
2.2000e+074135-5.92-0.02
2.3000e+074338-5.44-0.02
2.4000e+074540-4.91-0.02
2.5000e+074643-3.34-0.01
2.6000e+074845-2.72-0.01
2.7000e+075148-3.05-0.01
2.8000e+075451-3.33-0.01
2.9000e+075853-4.57-0.01
3.0000e+076056-3.77-0.01
3.1000e+076559-5.93-0.02
3.2000e+076762-5.04-0.02
3.3000e+077165-6.11-0.02
3.4000e+077468-6.15-0.02
3.5000e+077671-5.15-0.02
3.6000e+077774-3.11-0.01
3.7000e+078077-3.03-0.01
3.8000e+078580-4.92-0.01
3.9000e+078883-4.77-0.01
4.0000e+078986-2.59-0.01
4.1000e+079290-2.37-0.01
4.2000e+079393-0.12-0.00
4.3000e+079896-1.84-0.00
4.4000e+0710299-2.52-0.01
4.5000e+07106103-3.18-0.01
4.6000e+07108106-1.80-0.00
4.7000e+07114110-4.39-0.01
4.8000e+07119113-5.95-0.02
4.9000e+07125117-8.49-0.02
5.0000e+07126120-5.99-0.02
5.2000e+07136127-8.91-0.02
5.4000e+07140134-5.72-0.01
5.6000e+07153142-11.42-0.03
5.8000e+07156149-7.02-0.02
6.0000e+07165156-8.52-0.02
6.2000e+07180164-15.91-0.04
6.4000e+07185172-13.21-0.03
6.6000e+07189180-9.42-0.02
6.8000e+07193187-5.53-0.01
7.0000e+07197195-1.55-0.00
7.2000e+07206204-2.48-0.01
7.4000e+07214212-2.33-0.00
7.6000e+072182201.910.00
7.8000e+072272281.230.00
8.0000e+072342372.630.01
8.2000e+072432452.110.00
8.4000e+07258254-4.33-0.01
8.6000e+072602622.300.00
8.8000e+072672714.010.01
9.0000e+072792800.800.00
9.2000e+072832895.650.01
9.4000e+072932984.580.01
9.6000e+07309307-2.42-0.00
9.8000e+07319316-3.36-0.01
1.0000e+08330325-5.22-0.01
1.0500e+08357348-9.10-0.02
1.1000e+08378371-6.58-0.01
1.1500e+083953950.330.00
1.2000e+084184201.610.00
1.2500e+084414443.240.01
1.3000e+084664693.230.01
1.3500e+084854959.550.02
1.4000e+085185202.200.00
1.4500e+085435463.160.00
1.5000e+085695723.430.01
1.5500e+085945995.000.01
1.6000e+0861462611.860.02
1.6500e+0863565318.000.03
1.7000e+0865968021.420.03
1.7500e+0868670822.110.03
1.8000e+0871373623.070.03
1.8500e+0874876416.280.02
1.9000e+0877979313.740.02
1.9500e+0880482117.450.02
2.0000e+088428508.400.01
2.1000e+089089090.990.00
2.2000e+08969968-0.50-0.00
2.3000e+08102410294.870.01
2.4000e+081070109020.090.03
2.5000e+081140115212.110.01
2.6000e+081194121520.910.03
2.7000e+081254127824.470.03
2.8000e+081314134328.760.03
2.9000e+081359140848.770.06
3.0000e+081436147337.460.04
3.1000e+081508154031.820.04
3.2000e+081576160730.830.03
3.3000e+081641167433.480.04
3.4000e+081701174341.740.04
3.5000e+081768181243.610.05
3.6000e+081840188141.060.04
3.7000e+081903195148.090.05
3.8000e+081984202237.670.04
3.9000e+082041209351.800.05
4.0000e+082098216466.470.07
4.1000e+082173223763.660.06
4.2000e+082256230953.370.05
4.3000e+082334238348.570.05
4.4000e+082416245640.270.04
4.5000e+082494253036.450.03
4.6000e+082574260531.100.03
4.7000e+082650268030.210.03
4.8000e+082721275634.790.03
4.9000e+082789283242.800.04
5.0000e+082854290854.260.05
5.2000e+083036306226.460.02
5.4000e+083208321810.330.01
5.6000e+0833783376-2.19-0.00
5.8000e+0835583535-23.14-0.02
6.0000e+0837203695-24.58-0.02
6.2000e+0838803857-22.54-0.02
6.4000e+0840494021-28.08-0.02
6.6000e+0842014186-15.22-0.01
6.8000e+0843544352-2.01-0.00
7.0000e+08451345206.520.01
7.2000e+0846974688-8.67-0.01
7.4000e+0848874858-28.60-0.02
7.6000e+0850795030-49.30-0.04
7.8000e+0852355202-32.82-0.02
8.0000e+0853875376-11.16-0.01
8.2000e+0855635551-12.36-0.01
8.4000e+08572157275.560.00
8.6000e+085882590421.570.02
8.8000e+086046608235.650.02
9.0000e+086223626137.780.03
9.2000e+086393644147.940.03
9.4000e+086568662254.110.04
9.6000e+086758680446.270.03
9.8000e+086932698755.400.04
1.0000e+097139717132.490.02
1.0500e+097595763640.770.03
1.1000e+098072810633.650.02
1.1500e+098534858146.920.03
1.2000e+099010906151.350.03
1.2500e+099473954773.760.04
1.3000e+0999641003772.960.04
1.3500e+09104411053290.790.05
1.4000e+09109491103182.100.05
1.4500e+09114471153587.740.05
1.5000e+09119711204371.570.04
1.5500e+09124721255482.470.04
1.6000e+09130101307060.320.03
1.6500e+09135311359059.010.03
1.7000e+09140671411346.430.02
1.7500e+09145931464047.490.02
1.8000e+09151251517146.080.02
1.8500e+0915697157058.120.00
1.9000e+0916237162435.520.00
1.9500e+09167561678327.210.01
2.0000e+09173161732711.100.01
2.1000e+09183731842451.210.02
2.2000e+0919533195330.320.00
2.3000e+092071320654-59.09-0.03
2.4000e+092179321786-7.46-0.00
2.5000e+092294322928-15.23-0.01
2.6000e+092408224080-1.77-0.00
2.7000e+092526425243-21.46-0.01
2.8000e+092647126414-56.62-0.02
2.9000e+092767527595-79.58-0.03
3.0000e+092892828785-142.62-0.06
3.1000e+093007129984-87.02-0.03
3.2000e+093127531191-84.03-0.03
3.3000e+093248632406-79.91-0.03
3.4000e+093370533629-75.87-0.03
3.5000e+093491334860-53.13-0.02
3.6000e+093612336098-24.90-0.01
3.7000e+093738537344-41.37-0.01
3.8000e+093863838596-41.73-0.01
3.9000e+093988639856-30.13-0.01
4.0000e+094115241122-29.76-0.01
4.1000e+09423794239516.230.01
4.2000e+094369043675-15.31-0.01
4.3000e+09449084496052.470.02
4.4000e+09462304625222.450.01
4.5000e+09475024755048.490.02
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