Gap size : 122 (r=61)

Generated by program gapCounts : Mon Jun 27 12:45:25 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+03000.000.00
3.4000e+03000.000.00
3.5000e+03000.000.00
3.6000e+03000.000.00
3.7000e+03000.000.00
3.8000e+03000.000.00
3.9000e+03000.000.00
4.0000e+03000.000.00
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+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+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+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+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+05000.000.00
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+05000.010.00
4.2000e+05000.010.00
4.3000e+05000.010.00
4.4000e+05000.010.00
4.5000e+05000.010.00
4.6000e+05000.010.00
4.7000e+05000.010.00
4.8000e+05000.010.00
4.9000e+05000.010.00
5.0000e+05000.010.00
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+05000.020.00
6.8000e+05000.020.00
7.0000e+05000.020.00
7.2000e+05000.020.00
7.4000e+05000.020.00
7.6000e+05000.020.00
7.8000e+05000.020.00
8.0000e+05000.020.00
8.2000e+05000.030.00
8.4000e+05000.030.00
8.6000e+05000.030.00
8.8000e+05000.030.00
9.0000e+05000.030.00
9.2000e+05000.030.00
9.4000e+05000.030.00
9.6000e+05000.040.00
9.8000e+05000.040.00
1.0000e+06000.040.00
1.0500e+06000.040.00
1.1000e+06000.050.00
1.1500e+06000.050.00
1.2000e+06000.060.00
1.2500e+06000.060.00
1.3000e+06000.070.00
1.3500e+06000.070.00
1.4000e+06000.080.00
1.4500e+06000.090.00
1.5000e+06000.090.00
1.5500e+06000.100.00
1.6000e+06000.110.00
1.6500e+06000.110.00
1.7000e+06000.120.00
1.7500e+06000.130.00
1.8000e+06000.130.00
1.8500e+06000.140.00
1.9000e+06000.150.00
1.9500e+06000.160.00
2.0000e+06000.170.00
2.1000e+06000.180.00
2.2000e+06000.200.00
2.3000e+06000.220.00
2.4000e+06000.240.00
2.5000e+06000.260.00
2.6000e+06000.280.00
2.7000e+06000.300.00
2.8000e+06000.320.00
2.9000e+06000.340.00
3.0000e+06000.370.00
3.1000e+06000.390.00
3.2000e+0610-0.59-0.00
3.3000e+0610-0.56-0.00
3.4000e+0610-0.54-0.00
3.5000e+0610-0.51-0.00
3.6000e+0611-0.48-0.00
3.7000e+0611-0.46-0.00
3.8000e+0611-0.43-0.00
3.9000e+0611-0.40-0.00
4.0000e+0611-0.37-0.00
4.1000e+0611-0.34-0.00
4.2000e+0611-0.31-0.00
4.3000e+0611-0.28-0.00
4.4000e+0611-0.25-0.00
4.5000e+0611-0.22-0.00
4.6000e+0611-0.19-0.00
4.7000e+0611-0.16-0.00
4.8000e+0611-0.12-0.00
4.9000e+0611-0.09-0.00
5.0000e+0611-0.05-0.00
5.2000e+06110.010.00
5.4000e+06110.090.00
5.6000e+06110.160.00
5.8000e+06110.230.00
6.0000e+06110.310.00
6.2000e+06110.390.00
6.4000e+06110.470.00
6.6000e+06120.550.00
6.8000e+0622-0.36-0.00
7.0000e+0622-0.28-0.00
7.2000e+0622-0.19-0.00
7.4000e+0622-0.10-0.00
7.6000e+0622-0.01-0.00
7.8000e+06220.080.00
8.0000e+06220.180.00
8.2000e+06220.270.00
8.4000e+06220.370.00
8.6000e+06220.470.00
8.8000e+06230.570.00
9.0000e+0633-0.33-0.00
9.2000e+0633-0.23-0.00
9.4000e+0633-0.12-0.00
9.6000e+0633-0.02-0.00
9.8000e+06330.090.00
1.0000e+07330.200.00
1.0500e+0743-0.52-0.00
1.1000e+0744-0.24-0.00
1.1500e+07440.060.00
1.2000e+07440.360.00
1.2500e+07450.670.00
1.3000e+07450.980.00
1.3500e+07550.310.00
1.4000e+07560.640.00
1.4500e+07560.980.00
1.5000e+07561.320.01
1.5500e+07670.680.00
1.6000e+07770.040.00
1.6500e+07770.400.00
1.7000e+07780.770.00
1.7500e+07781.150.00
1.8000e+07791.530.01
1.8500e+07791.930.01
1.9000e+07792.320.01
1.9500e+077102.720.01
2.0000e+077103.130.01
2.1000e+077113.960.01
2.2000e+0710121.820.01
2.3000e+0711131.690.01
2.4000e+0711142.590.01
2.5000e+0713151.510.01
2.6000e+0715150.450.00
2.7000e+0715161.400.00
2.8000e+0716171.380.00
2.9000e+0716182.370.01
3.0000e+0719190.380.00
3.1000e+0720200.410.00
3.2000e+0720211.450.00
3.3000e+0720232.510.01
3.4000e+0721242.590.01
3.5000e+0722252.680.01
3.6000e+072626-0.21-0.00
3.7000e+072727-0.08-0.00
3.8000e+073128-2.94-0.01
3.9000e+073329-3.79-0.01
4.0000e+073830-7.62-0.02
4.1000e+073832-6.43-0.02
4.2000e+074033-7.23-0.02
4.3000e+074234-8.02-0.02
4.4000e+074335-7.80-0.02
4.5000e+074436-7.56-0.02
4.6000e+074738-9.30-0.02
4.7000e+074939-10.04-0.03
4.8000e+074940-8.76-0.02
4.9000e+075242-10.47-0.03
5.0000e+075343-10.17-0.03
5.2000e+075745-11.52-0.03
5.4000e+075848-9.83-0.02
5.6000e+076151-10.09-0.02
5.8000e+076354-9.31-0.02
6.0000e+076657-9.48-0.02
6.2000e+076859-8.61-0.02
6.4000e+077362-10.70-0.02
6.6000e+077765-11.75-0.03
6.8000e+077968-10.75-0.02
7.0000e+078571-13.72-0.03
7.2000e+078874-13.64-0.03
7.4000e+079177-13.53-0.03
7.6000e+079581-14.39-0.03
7.8000e+079784-13.20-0.03
8.0000e+079987-11.98-0.02
8.2000e+0710290-11.73-0.02
8.4000e+0710394-9.44-0.02
8.6000e+0710797-10.11-0.02
8.8000e+07110100-9.76-0.02
9.0000e+07111104-7.37-0.01
9.2000e+07116107-8.95-0.02
9.4000e+07117111-6.49-0.01
9.6000e+07122114-8.01-0.02
9.8000e+07125118-7.49-0.01
1.0000e+08131121-9.95-0.02
1.0500e+08140130-9.95-0.02
1.1000e+08146139-6.78-0.01
1.1500e+08157149-8.44-0.01
1.2000e+08169158-10.92-0.02
1.2500e+08175168-7.25-0.01
1.3000e+08181178-3.41-0.01
1.3500e+08188188-0.43-0.00
1.4000e+08198198-0.29-0.00
1.4500e+082062081.980.00
1.5000e+082172181.400.00
1.5500e+082282290.960.00
1.6000e+08240240-0.35-0.00
1.6500e+08252250-1.53-0.00
1.7000e+08264261-2.58-0.00
1.7500e+08273272-0.51-0.00
1.8000e+08287284-3.32-0.00
1.8500e+08300295-5.00-0.01
1.9000e+08313306-6.58-0.01
1.9500e+08329318-11.03-0.02
2.0000e+08340330-10.38-0.01
2.1000e+08360353-6.74-0.01
2.2000e+08386377-8.68-0.01
2.3000e+08414402-12.22-0.02
2.4000e+08445427-18.36-0.02
2.5000e+08477452-25.12-0.03
2.6000e+08499477-21.51-0.03
2.7000e+08530503-26.55-0.03
2.8000e+08555530-25.24-0.03
2.9000e+08583556-26.60-0.03
3.0000e+08605583-21.63-0.02
3.1000e+08630611-19.34-0.02
3.2000e+08657638-18.74-0.02
3.3000e+08690666-23.83-0.03
3.4000e+08719694-24.64-0.03
3.5000e+08744723-21.15-0.02
3.6000e+08763752-11.39-0.01
3.7000e+08792781-11.35-0.01
3.8000e+08817810-7.04-0.01
3.9000e+08846840-6.47-0.01
4.0000e+08887869-17.64-0.02
4.1000e+08923899-23.56-0.02
4.2000e+08948930-18.23-0.02
4.3000e+08984960-23.66-0.02
4.4000e+081014991-22.85-0.02
4.5000e+0810391022-16.81-0.02
4.6000e+0810731053-19.54-0.02
4.7000e+0811091085-24.05-0.02
4.8000e+0811391117-22.33-0.02
4.9000e+0811781149-29.40-0.03
5.0000e+0812081181-27.25-0.02
5.2000e+0812751246-29.33-0.03
5.4000e+0813371311-25.59-0.02
5.6000e+0814101378-32.07-0.03
5.8000e+0814871445-41.78-0.04
6.0000e+0815581513-44.74-0.04
6.2000e+0816271582-44.99-0.04
6.4000e+0816981651-46.53-0.04
6.6000e+0817661722-44.38-0.04
6.8000e+0818311792-38.57-0.03
7.0000e+0819081864-44.11-0.03
7.2000e+0819701936-34.01-0.03
7.4000e+0820332009-24.29-0.02
7.6000e+0821042082-21.96-0.02
7.8000e+0821772156-21.04-0.02
8.0000e+0822432230-12.54-0.01
8.2000e+0823212306-15.47-0.01
8.4000e+0823822381-0.84-0.00
8.6000e+082445245712.330.01
8.8000e+082518253416.040.01
9.0000e+082596261115.270.01
9.2000e+082673268916.020.01
9.4000e+082756276711.270.01
9.6000e+082816284630.020.02
9.8000e+082881292544.250.03
1.0000e+092975300529.970.02
1.0500e+093153320653.300.03
1.1000e+093338341072.450.05
1.1500e+093550361767.310.04
1.2000e+093763382763.790.04
1.2500e+093997403941.790.02
1.3000e+094215425338.220.02
1.3500e+094427447043.010.02
1.4000e+094620468969.070.04
1.4500e+094832491078.330.04
1.5000e+095036513497.750.05
1.5500e+095285535974.240.04
1.6000e+095492558794.750.05
1.6500e+0957065816110.230.06
1.7000e+095950604897.620.05
1.7500e+096198628182.880.04
1.8000e+096425651690.970.05
1.8500e+096676675376.830.04
1.9000e+096926699165.420.03
1.9500e+097173723258.710.03
2.0000e+097408747465.650.03
2.1000e+097872796290.370.04
2.2000e+0983498457108.300.05
2.3000e+098882895876.200.03
2.4000e+099423946541.840.02
2.5000e+099911997766.010.03
2.6000e+09104681049526.510.01
2.7000e+09109741101743.170.02
2.8000e+09115181154526.810.01
2.9000e+09120041207773.280.03
3.0000e+091251412614100.430.04
3.1000e+09130581315698.120.04
3.2000e+091360113702101.230.04
3.3000e+091414714253105.620.04
3.4000e+091469214807115.200.04
3.5000e+09152791536686.830.03
3.6000e+09158531592875.440.03
3.7000e+09164421649552.900.02
3.8000e+09170261706539.140.01
3.9000e+0917630176399.060.00
4.0000e+091822918217-12.41-0.00
4.1000e+091885818798-60.37-0.02
4.2000e+091941219382-29.89-0.01
4.3000e+092000119970-31.04-0.01
4.4000e+092058620561-24.88-0.01
4.5000e+09211412115614.500.00
4.6000e+09217322175321.050.01
4.7000e+09223102235443.710.01
4.8000e+09229422295715.420.00
4.9000e+09235332356431.110.01
5.0000e+09241562417417.750.01
5.2000e+09253812540220.600.01
5.4000e+09266062664134.600.01
5.6000e+0927887278903.350.00
5.8000e+0929145291515.520.00
6.0000e+09303753042145.780.01
6.2000e+09316643170136.830.01
6.4000e+09329373299053.380.02
6.6000e+09342533428936.170.01
6.8000e+09355003559796.930.03
7.0000e+093676036913153.440.04
7.2000e+093810438238134.460.04
7.4000e+093937639572195.780.05
7.6000e+094071740913196.190.05
7.8000e+094197542263287.510.07
8.0000e+094335643620263.550.07
8.2000e+094471344984271.140.07
8.4000e+094607746356279.090.07
8.6000e+094745247735283.270.07
8.8000e+094880449122317.500.08
9.0000e+095023450515280.660.07
9.2000e+095158251915332.590.08
9.4000e+095295853321363.160.09
9.6000e+095437054734364.250.09
9.8000e+095576956154384.720.09
1.0000e+105711757579462.460.11
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