Gap size : 110 (r=55)

Generated by program gapCounts : Mon Jun 27 12:45:08 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+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+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+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+05000.010.00
2.0000e+05000.010.00
2.1000e+05000.010.00
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+05000.020.00
3.1000e+05000.020.00
3.2000e+05000.020.00
3.3000e+05000.020.00
3.4000e+05000.020.00
3.5000e+05000.020.00
3.6000e+05000.020.00
3.7000e+05000.030.00
3.8000e+05000.030.00
3.9000e+05000.030.00
4.0000e+05000.030.00
4.1000e+05000.030.00
4.2000e+05000.030.00
4.3000e+05000.040.00
4.4000e+05000.040.00
4.5000e+05000.040.00
4.6000e+05000.040.00
4.7000e+05000.040.00
4.8000e+05000.050.00
4.9000e+05000.050.00
5.0000e+05000.050.00
5.2000e+05000.050.00
5.4000e+05000.060.00
5.6000e+05000.060.00
5.8000e+05000.070.00
6.0000e+05000.070.00
6.2000e+05000.080.00
6.4000e+05000.090.00
6.6000e+05000.090.00
6.8000e+05000.100.00
7.0000e+05000.100.00
7.2000e+05000.110.00
7.4000e+05000.120.00
7.6000e+05000.120.00
7.8000e+05000.130.00
8.0000e+05000.140.00
8.2000e+05000.140.00
8.4000e+05000.150.00
8.6000e+05000.160.00
8.8000e+05000.170.00
9.0000e+05000.170.00
9.2000e+05000.180.00
9.4000e+05000.190.00
9.6000e+05000.200.00
9.8000e+05000.210.00
1.0000e+06000.210.00
1.0500e+06000.240.00
1.1000e+06000.260.00
1.1500e+06000.280.00
1.2000e+06000.310.00
1.2500e+06000.330.00
1.3000e+06000.360.00
1.3500e+06000.390.00
1.4000e+06000.420.00
1.4500e+06000.450.01
1.5000e+0610-0.52-0.01
1.5500e+0611-0.49-0.01
1.6000e+0611-0.46-0.01
1.6500e+0611-0.43-0.00
1.7000e+0611-0.40-0.00
1.7500e+0611-0.36-0.00
1.8000e+0611-0.33-0.00
1.8500e+0611-0.29-0.00
1.9000e+0611-0.26-0.00
1.9500e+0611-0.22-0.00
2.0000e+0611-0.18-0.00
2.1000e+0611-0.10-0.00
2.2000e+0611-0.02-0.00
2.3000e+06110.060.00
2.4000e+06110.150.00
2.5000e+06110.230.00
2.6000e+0621-0.68-0.01
2.7000e+0621-0.58-0.01
2.8000e+0622-0.49-0.00
2.9000e+0622-0.39-0.00
3.0000e+0622-0.29-0.00
3.1000e+0632-1.18-0.01
3.2000e+0632-1.08-0.01
3.3000e+0642-1.97-0.02
3.4000e+0642-1.86-0.02
3.5000e+0652-2.75-0.02
3.6000e+0652-2.63-0.02
3.7000e+0652-2.52-0.02
3.8000e+0653-2.40-0.02
3.9000e+0653-2.28-0.02
4.0000e+0653-2.15-0.02
4.1000e+0653-2.03-0.02
4.2000e+0653-1.90-0.01
4.3000e+0653-1.77-0.01
4.4000e+0653-1.64-0.01
4.5000e+0653-1.51-0.01
4.6000e+0654-1.37-0.01
4.7000e+0654-1.24-0.01
4.8000e+0654-1.10-0.01
4.9000e+0654-0.96-0.01
5.0000e+0664-1.82-0.01
5.2000e+0664-1.53-0.01
5.4000e+0665-1.23-0.01
5.6000e+0665-0.93-0.01
5.8000e+0665-0.62-0.00
6.0000e+0676-1.30-0.01
6.2000e+0676-0.98-0.01
6.4000e+0686-1.65-0.01
6.6000e+0687-1.32-0.01
6.8000e+0687-0.98-0.01
7.0000e+0697-1.63-0.01
7.2000e+0698-1.28-0.01
7.4000e+0698-0.92-0.01
7.6000e+0698-0.56-0.00
7.8000e+0699-0.19-0.00
8.0000e+06990.190.00
8.2000e+069100.570.00
8.4000e+069100.950.01
8.6000e+069101.340.01
8.8000e+0610110.740.00
9.0000e+0610111.140.01
9.2000e+0610121.550.01
9.4000e+0610121.960.01
9.6000e+0610122.370.01
9.8000e+0610132.790.01
1.0000e+0711132.220.01
1.0500e+0713141.300.01
1.1000e+0715150.410.00
1.1500e+0716170.540.00
1.2000e+0717180.710.00
1.2500e+072019-1.10-0.01
1.3000e+072120-0.89-0.00
1.3500e+072221-0.65-0.00
1.4000e+072423-1.39-0.01
1.4500e+072424-0.11-0.00
1.5000e+0724251.200.01
1.5500e+0726270.530.00
1.6000e+072928-1.12-0.00
1.6500e+073229-2.75-0.01
1.7000e+073431-3.35-0.01
1.7500e+073932-6.94-0.03
1.8000e+073933-5.51-0.02
1.8500e+074135-6.06-0.02
1.9000e+074236-5.59-0.02
1.9500e+074338-5.10-0.02
2.0000e+074439-4.59-0.02
2.1000e+074442-1.52-0.01
2.2000e+0745460.620.00
2.3000e+075049-1.17-0.00
2.4000e+075552-2.90-0.01
2.5000e+076155-5.57-0.02
2.6000e+076759-8.17-0.03
2.7000e+076962-6.71-0.02
2.8000e+077666-10.20-0.03
2.9000e+077769-7.63-0.02
3.0000e+077973-6.00-0.02
3.1000e+078277-5.32-0.02
3.2000e+078680-5.59-0.02
3.3000e+078884-3.81-0.01
3.4000e+079488-5.97-0.02
3.5000e+079892-6.09-0.02
3.6000e+0710496-8.16-0.02
3.7000e+07106100-6.18-0.02
3.8000e+07113104-9.16-0.03
3.9000e+07120108-12.09-0.03
4.0000e+07123112-10.98-0.03
4.1000e+07132116-15.82-0.04
4.2000e+07133120-12.63-0.03
4.3000e+07138125-13.38-0.04
4.4000e+07143129-14.10-0.04
4.5000e+07147133-13.78-0.04
4.6000e+07149138-11.42-0.03
4.7000e+07152142-10.02-0.03
4.8000e+07160146-13.58-0.03
4.9000e+07163151-12.11-0.03
5.0000e+07169155-13.59-0.03
5.2000e+07178165-13.46-0.03
5.4000e+07193174-19.18-0.05
5.6000e+07201183-17.76-0.04
5.8000e+07215193-22.21-0.05
6.0000e+07226202-23.53-0.05
6.2000e+07239212-26.73-0.06
6.4000e+07247222-24.80-0.06
6.6000e+07255232-22.74-0.05
6.8000e+07267242-24.57-0.05
7.0000e+07278253-25.29-0.05
7.2000e+07292263-28.89-0.06
7.4000e+07299274-25.39-0.05
7.6000e+07310284-25.77-0.05
7.8000e+07318295-23.05-0.05
8.0000e+07329306-23.23-0.05
8.2000e+07345317-28.30-0.06
8.4000e+07361328-33.28-0.07
8.6000e+07376339-37.15-0.07
8.8000e+07390350-39.94-0.08
9.0000e+07401361-39.62-0.08
9.2000e+07419373-46.22-0.09
9.4000e+07430384-45.73-0.09
9.6000e+07441396-45.14-0.08
9.8000e+07448408-40.47-0.08
1.0000e+08454419-34.72-0.06
1.0500e+08472449-22.96-0.04
1.1000e+08505479-25.69-0.05
1.1500e+08527510-16.93-0.03
1.2000e+08549541-7.70-0.01
1.2500e+08576573-3.01-0.01
1.3000e+086046051.120.00
1.3500e+08644638-6.32-0.01
1.4000e+08675671-4.34-0.01
1.4500e+08705704-0.97-0.00
1.5000e+087357382.800.00
1.5500e+08780772-8.05-0.01
1.6000e+08817806-10.54-0.02
1.6500e+08848841-6.66-0.01
1.7000e+088748772.570.00
1.7500e+089109122.140.00
1.8000e+089469482.050.00
1.8500e+089809844.290.01
1.9000e+081010102110.840.01
1.9500e+081044105813.700.02
2.0000e+08108910955.880.01
2.1000e+08116511705.110.01
2.2000e+0812551246-8.50-0.01
2.3000e+0813421324-18.01-0.02
2.4000e+0814131403-10.45-0.01
2.5000e+08148214820.130.00
2.6000e+0815651563-2.29-0.00
2.7000e+0816501644-5.76-0.01
2.8000e+08171917277.710.01
2.9000e+0818141810-3.92-0.00
3.0000e+08189018944.320.00
3.1000e+081963197916.410.02
3.2000e+082050206515.330.02
3.3000e+082138215214.060.02
3.4000e+082217224022.560.02
3.5000e+0823352328-7.17-0.01
3.6000e+0824372417-20.15-0.02
3.7000e+0825212507-14.41-0.01
3.8000e+0826052597-7.96-0.01
3.9000e+0826992688-10.81-0.01
4.0000e+0828002780-19.99-0.02
4.1000e+0828912872-18.50-0.02
4.2000e+0829792966-13.37-0.01
4.3000e+0830633059-3.59-0.00
4.4000e+08314831545.800.01
4.5000e+08324432494.810.00
4.6000e+08334033444.420.00
4.7000e+083427344113.610.01
4.8000e+083518353719.380.02
4.9000e+08363236352.720.00
5.0000e+08372337339.610.01
5.2000e+0839313930-0.97-0.00
5.4000e+08412941300.570.00
5.6000e+084304433127.150.02
5.8000e+084513453521.700.02
6.0000e+084713474027.180.02
6.2000e+084899494848.530.04
6.4000e+085114515742.680.03
6.6000e+085302536865.600.05
6.8000e+085508558072.230.06
7.0000e+085716579578.530.06
7.2000e+085925601085.460.06
7.4000e+086149622878.970.06
7.6000e+0863316447116.040.09
7.8000e+0865516668116.610.09
8.0000e+0867786890111.670.08
8.2000e+0870017113112.170.08
8.4000e+087240733898.090.07
8.6000e+0874517564113.390.08
8.8000e+0876457792147.040.10
9.0000e+0878748021147.030.10
9.2000e+0881128251139.310.09
9.4000e+0883518483131.880.09
9.6000e+0885938716122.690.08
9.8000e+0888398950110.740.07
1.0000e+0990659185119.990.08
1.0500e+0996749778104.250.07
1.1000e+091022210379156.610.10
1.1500e+091078910986196.770.12
1.2000e+091140711599192.460.12
1.2500e+091206612219153.440.09
1.3000e+091268612845159.480.09
1.3500e+091332713477150.380.09
1.4000e+091396614115148.920.08
1.4500e+091460614758151.940.08
1.5000e+091523415406172.270.09
1.5500e+091585416060205.730.11
1.6000e+091649516718223.180.12
1.6500e+091714117381240.480.13
1.7000e+091783318049216.490.11
1.7500e+091849818722224.090.11
1.8000e+091916919399230.160.12
1.8500e+091986820081212.590.11
1.9000e+092053220766234.260.11
1.9500e+092124821456208.080.10
2.0000e+092189422150255.940.12
2.1000e+092327423549275.450.13
2.2000e+092464624964318.100.15
2.3000e+092610426393289.250.13
2.4000e+092756227836274.320.12
2.5000e+092897929293313.780.14
2.6000e+093045030762312.140.13
2.7000e+093191932244324.940.14
2.8000e+093342833738309.750.13
2.9000e+093494235243301.180.12
3.0000e+093645636760303.860.12
3.1000e+093797038287317.430.12
3.2000e+093953639826289.580.11
3.3000e+094104841374325.990.12
3.4000e+094257342932359.390.14
3.5000e+094410144500399.490.15
3.6000e+094566446078414.040.15
3.7000e+094728547665379.800.14
3.8000e+094890549261355.530.13
3.9000e+095054850865317.010.11
4.0000e+095212452478354.040.12
4.1000e+095375654099343.410.12
4.2000e+095535055729378.940.13
4.3000e+095700157366365.440.12
4.4000e+095865659012355.750.12
4.5000e+096033260665332.690.11
4.6000e+096201362325312.110.10
4.7000e+096373763993255.860.08
4.8000e+096543665668231.780.07
4.9000e+096719867350151.740.05
5.0000e+096883469039204.610.06
5.2000e+097220672437230.560.07
5.4000e+097557775861283.630.09
5.6000e+097898479310325.920.10
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