Gap size : 88 (r=44)

Generated by program gapCounts : Mon Jun 27 12:44:37 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+030-0-0.00-0.00
5.6000e+030-0-0.00-0.00
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+04000.000.00
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+04000.010.00
6.4000e+04000.010.00
6.6000e+04000.010.00
6.8000e+04000.010.00
7.0000e+04000.010.00
7.2000e+04000.010.00
7.4000e+04000.010.00
7.6000e+04000.010.00
7.8000e+04000.010.00
8.0000e+04000.010.00
8.2000e+04000.010.00
8.4000e+04000.010.00
8.6000e+04000.010.00
8.8000e+04000.010.00
9.0000e+04000.010.00
9.2000e+04000.020.00
9.4000e+04000.020.00
9.6000e+04000.020.00
9.8000e+04000.020.00
1.0000e+05000.020.00
1.0500e+05000.020.00
1.1000e+05000.020.00
1.1500e+05000.030.00
1.2000e+05000.030.00
1.2500e+05000.030.00
1.3000e+05000.030.00
1.3500e+05000.040.00
1.4000e+05000.040.00
1.4500e+05000.040.00
1.5000e+05000.050.00
1.5500e+05000.050.00
1.6000e+05000.050.00
1.6500e+05000.060.00
1.7000e+05000.060.00
1.7500e+05000.070.00
1.8000e+05000.070.00
1.8500e+05000.080.00
1.9000e+05000.080.00
1.9500e+05000.080.00
2.0000e+05000.090.00
2.1000e+05000.100.00
2.2000e+05000.110.00
2.3000e+05000.120.00
2.4000e+05000.130.00
2.5000e+05000.140.00
2.6000e+05000.160.00
2.7000e+05000.170.00
2.8000e+05000.180.00
2.9000e+05000.190.00
3.0000e+05000.210.00
3.1000e+05000.220.01
3.2000e+05000.240.01
3.3000e+05000.250.01
3.4000e+05000.270.01
3.5000e+05000.280.01
3.6000e+05000.300.01
3.7000e+05000.310.01
3.8000e+05000.330.01
3.9000e+05000.350.01
4.0000e+05000.370.01
4.1000e+05000.380.01
4.2000e+05000.400.01
4.3000e+05000.420.01
4.4000e+05000.440.01
4.5000e+05000.460.01
4.6000e+05000.480.01
4.7000e+05010.500.01
4.8000e+05010.520.01
4.9000e+05010.540.01
5.0000e+05010.560.01
5.2000e+05010.600.01
5.4000e+05010.650.01
5.6000e+0511-0.31-0.01
5.8000e+0511-0.26-0.00
6.0000e+0511-0.21-0.00
6.2000e+0511-0.16-0.00
6.4000e+0511-0.11-0.00
6.6000e+0511-0.06-0.00
6.8000e+0511-0.01-0.00
7.0000e+05110.040.00
7.2000e+05110.100.00
7.4000e+05110.150.00
7.6000e+05110.210.00
7.8000e+05110.270.00
8.0000e+05110.320.00
8.2000e+05110.380.01
8.4000e+05110.440.01
8.6000e+05120.500.01
8.8000e+05120.570.01
9.0000e+05120.630.01
9.2000e+05120.690.01
9.4000e+05120.760.01
9.6000e+05120.830.01
9.8000e+05120.890.01
1.0000e+06120.960.01
1.0500e+06121.130.02
1.1000e+06121.310.02
1.1500e+06121.490.02
1.2000e+06230.680.01
1.2500e+06230.880.01
1.3000e+06231.070.01
1.3500e+06231.280.02
1.4000e+06330.480.01
1.4500e+06340.690.01
1.5000e+0644-0.09-0.00
1.5500e+06440.130.00
1.6000e+06440.350.00
1.6500e+06450.580.01
1.7000e+06450.810.01
1.7500e+06451.050.01
1.8000e+06451.280.01
1.8500e+06461.530.02
1.9000e+06560.770.01
1.9500e+06561.020.01
2.0000e+06561.280.01
2.1000e+06571.790.02
2.2000e+06572.320.02
2.3000e+06582.870.03
2.4000e+06682.420.02
2.5000e+06692.990.03
2.6000e+066103.570.03
2.7000e+067103.160.03
2.8000e+067113.760.03
2.9000e+067114.380.04
3.0000e+068124.000.03
3.1000e+069133.630.03
3.2000e+069134.280.04
3.3000e+0610143.930.03
3.4000e+0612152.590.02
3.5000e+0612153.260.03
3.6000e+0615160.950.01
3.7000e+0616170.640.00
3.8000e+061817-0.67-0.01
3.9000e+061918-0.96-0.01
4.0000e+062019-1.24-0.01
4.1000e+062119-1.52-0.01
4.2000e+062120-0.78-0.01
4.3000e+062321-2.04-0.02
4.4000e+062422-2.29-0.02
4.5000e+062422-1.54-0.01
4.6000e+062423-0.77-0.01
4.7000e+062424-0.00-0.00
4.8000e+0624250.780.01
4.9000e+0624261.560.01
5.0000e+0624262.350.02
5.2000e+0624283.960.03
5.4000e+0629300.590.00
5.6000e+0630311.260.01
5.8000e+0632330.940.01
6.0000e+0634350.650.00
6.2000e+063736-0.61-0.00
6.4000e+063938-0.85-0.01
6.6000e+064040-0.07-0.00
6.8000e+064242-0.27-0.00
7.0000e+0642441.560.01
7.2000e+0645450.410.00
7.4000e+064847-0.72-0.00
7.6000e+0648491.170.01
7.8000e+065251-0.93-0.01
8.0000e+0653530.000.00
8.2000e+065655-1.05-0.01
8.4000e+065757-0.08-0.00
8.6000e+0658590.910.00
8.8000e+0658612.910.02
9.0000e+0659633.930.02
9.2000e+0660654.970.03
9.4000e+0664673.030.02
9.6000e+0666693.100.02
9.8000e+0669712.200.01
1.0000e+0771732.300.01
1.0500e+0775793.640.02
1.1000e+0779845.070.02
1.1500e+0783906.600.03
1.2000e+07839512.220.06
1.2500e+078610114.920.07
1.3000e+079010716.710.08
1.3500e+079611316.580.07
1.4000e+079711921.530.09
1.4500e+0710212522.550.10
1.5000e+0710913121.650.09
1.5500e+0711813718.820.08
1.6000e+0712214321.060.09
1.6500e+0713514914.360.06
1.7000e+0713915616.740.07
1.7500e+0714716215.170.06
1.8000e+0715116917.670.07
1.8500e+0715617519.240.07
1.9000e+0716318218.860.07
1.9500e+0716818920.540.08
2.0000e+0717019525.280.10
2.1000e+0718220926.930.10
2.2000e+0720122321.790.08
2.3000e+0722123715.860.06
2.4000e+072422519.130.03
2.5000e+0725526610.590.04
2.6000e+0727028010.230.03
2.7000e+0728129514.060.05
2.8000e+0729431016.060.05
2.9000e+0730832517.230.05
3.0000e+0732334117.560.06
3.1000e+0734135615.050.05
3.2000e+0735737214.690.04
3.3000e+0737438713.480.04
3.4000e+0739140312.420.04
3.5000e+0739641923.500.07
3.6000e+0741443621.710.06
3.7000e+0743545217.070.05
3.8000e+0745246916.550.05
3.9000e+0746348522.160.06
4.0000e+0748650215.900.04
4.1000e+0750051918.760.05
4.2000e+0751553620.740.06
4.3000e+0753355319.840.05
4.4000e+0754757023.050.06
4.5000e+075825875.370.01
4.6000e+076006054.810.01
4.7000e+076216221.350.00
4.8000e+076406400.000.00
4.9000e+07664658-6.24-0.02
5.0000e+07676676-0.39-0.00
5.2000e+077087123.620.01
5.4000e+077397489.020.02
5.6000e+077757859.800.02
5.8000e+078138228.940.02
6.0000e+078508599.430.02
6.2000e+078888979.260.02
6.4000e+0792493511.420.03
6.6000e+079719742.900.01
6.8000e+0710151013-2.31-0.01
7.0000e+0710601052-8.21-0.02
7.2000e+0711031091-11.82-0.03
7.4000e+0711351131-4.13-0.01
7.6000e+071158117112.830.03
7.8000e+07120312118.070.02
8.0000e+071241125210.580.02
8.2000e+07128312929.350.02
8.4000e+07132913334.370.01
8.6000e+07136913755.650.01
8.8000e+0714191416-2.83-0.01
9.0000e+07145314584.930.01
9.2000e+071478150021.930.04
9.4000e+071528154214.150.03
9.6000e+071565158519.600.04
9.8000e+071607162720.280.04
1.0000e+081637167033.170.06
1.0500e+081752177826.320.05
1.1000e+081850188837.750.07
1.1500e+081935199863.390.11
1.2000e+082039211071.210.12
1.2500e+082142222381.150.14
1.3000e+082257233780.180.13
1.3500e+082393245259.250.10
1.4000e+082512256856.330.09
1.4500e+082641268544.380.07
1.5000e+082748280355.380.09
1.5500e+082871292251.290.08
1.6000e+083006304236.080.05
1.6500e+083126316336.740.05
1.7000e+083236328448.230.07
1.7500e+083352340754.530.08
1.8000e+083464353065.620.09
1.8500e+083600365353.480.07
1.9000e+083730377848.080.07
1.9500e+083861390342.420.06
2.0000e+084003402926.480.04
2.1000e+084273428410.650.01
2.2000e+084509454031.490.04
2.3000e+08479448005.870.01
2.4000e+085044506217.680.02
2.5000e+0853345326-8.16-0.01
2.6000e+0856035592-10.75-0.01
2.7000e+08585458616.830.01
2.8000e+0861416132-9.50-0.01
2.9000e+086371640433.200.04
3.0000e+086664667914.840.02
3.1000e+086923695532.380.04
3.2000e+087189723444.750.05
3.3000e+087470751443.900.05
3.4000e+087734779661.770.07
3.5000e+088006807973.320.08
3.6000e+088279836585.500.09
3.7000e+0885458651106.270.11
3.8000e+0888078940132.590.13
3.9000e+0890839229146.410.15
4.0000e+0893789521142.690.14
4.1000e+089723981390.420.09
4.2000e+08100251010882.540.08
4.3000e+08103141040389.030.09
4.4000e+081058710700112.850.11
4.5000e+081088610998111.990.11
4.6000e+081119211297105.400.10
4.7000e+08115131159885.060.08
4.8000e+081178811900111.950.10
4.9000e+081208812203115.040.10
5.0000e+081239112507116.310.10
5.2000e+08130271311992.290.08
5.4000e+08136831373652.710.05
5.6000e+08143161435640.420.03
5.8000e+08149651498116.270.01
6.0000e+08155911561019.110.02
6.2000e+08162081624334.820.03
6.4000e+0816872168797.280.01
6.6000e+081753417519-14.64-0.01
6.8000e+081824818163-85.03-0.07
7.0000e+081891218810-102.00-0.08
7.2000e+081951719460-56.65-0.04
7.4000e+082020920114-95.06-0.07
7.6000e+082086720771-96.32-0.07
7.8000e+082155221430-121.52-0.09
8.0000e+082219622093-102.72-0.07
8.2000e+082284322759-84.01-0.06
8.4000e+082345723428-29.45-0.02
8.6000e+082412524099-26.12-0.02
8.8000e+082478124773-8.06-0.01
9.0000e+082545925450-9.35-0.01
9.2000e+08261162612912.960.01
9.4000e+0826805268115.800.00
9.6000e+08274812749514.140.01
9.8000e+082819528182-13.08-0.01
1.0000e+092887828871-6.92-0.00
1.0500e+093067830604-73.87-0.05
1.1000e+093244832351-96.88-0.06
1.1500e+093420134111-89.57-0.06
1.2000e+0935877358847.490.00
1.2500e+09376273767042.760.03
1.3000e+0939466394670.770.00
1.3500e+094132741275-51.94-0.03
1.4000e+094313143094-36.78-0.02
1.4500e+094503044924-106.14-0.06
1.5000e+094689346764-129.38-0.07
1.5500e+094873948613-125.83-0.07
1.6000e+095059550472-122.81-0.07
1.6500e+095235152340-10.61-0.01
1.7000e+095425454217-36.51-0.02
1.7500e+09560935610310.220.01
1.8000e+095801357997-15.65-0.01
1.8500e+09598855990014.630.01
1.9000e+096182361810-13.15-0.01
1.9500e+09636926372835.810.02
2.0000e+09656126565341.290.02
2.1000e+09694296952697.100.05
2.2000e+097330873427118.880.05
2.3000e+097719577354159.370.07
2.4000e+098111381307194.390.09
2.5000e+098503385285251.870.11
2.6000e+098910989286176.830.08
2.7000e+099313493309175.370.07
2.8000e+099717097355184.630.08
2.9000e+09101307101421113.850.05
3.0000e+0910545510550752.280.02
3.1000e+0910954410961369.260.03
3.2000e+09113744113738-5.86-0.00
3.3000e+09117934117881-52.67-0.02
3.4000e+09122166122042-123.74-0.05
3.5000e+09126294126220-73.58-0.03
3.6000e+09130496130415-80.70-0.03
3.7000e+09134662134626-35.56-0.01
3.8000e+09138903138853-49.62-0.02
3.9000e+09143097143096-1.29-0.00
4.0000e+09147403147353-49.97-0.02
4.1000e+09151757151625-132.04-0.05
4.2000e+09156033155911-121.86-0.04
4.3000e+09160391160211-179.78-0.06
4.4000e+09164642164525-117.13-0.04
4.5000e+09168890168852-38.21-0.01
4.6000e+0917316417319227.670.01
4.7000e+0917748717754457.230.02
4.8000e+0918185618190953.190.02
4.9000e+09186118186286168.290.05
5.0000e+09190431190675244.290.08
5.2000e+09199379199488108.980.03
5.4000e+09208159208345186.450.06
5.6000e+09217087217246159.010.05
5.8000e+09225990226188198.080.06
6.0000e+09235023235170147.220.04
6.2000e+09243916244191275.060.08
6.4000e+09252872253249377.330.11
6.6000e+09261949262344394.830.11
6.8000e+09270887271473586.450.16
7.0000e+09280297280637340.120.09
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