Gap size : 4 (r=2)

Generated by program gapCounts : Mon Jun 27 12:23:39 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+027114.001.84
2.0000e+0213163.321.24
3.0000e+0216214.671.54
4.0000e+0220254.521.36
5.0000e+0225283.060.85
6.0000e+0226315.381.41
7.0000e+0229355.531.37
8.0000e+0232385.551.31
9.0000e+0237403.450.78
1.0000e+0340433.260.71
1.1000e+0343462.990.63
1.2000e+0343495.641.16
1.3000e+0345516.241.24
1.4000e+0347546.781.31
1.5000e+0352564.270.81
1.6000e+0355593.720.69
1.7000e+0359612.130.38
1.8000e+0360633.500.62
1.9000e+0362663.830.66
2.0000e+0363685.130.87
2.1000e+0365705.400.90
2.2000e+0366736.641.09
2.3000e+0370754.860.78
2.4000e+0373774.050.64
2.5000e+0375794.220.66
2.6000e+0376815.360.83
2.7000e+0380833.490.53
2.8000e+0382863.590.54
2.9000e+0385882.680.40
3.0000e+0386903.750.55
3.1000e+0389922.800.40
3.2000e+0391942.840.40
3.3000e+0393962.850.40
3.4000e+0395982.860.40
3.5000e+03971002.850.39
3.6000e+03981023.820.52
3.7000e+031001043.790.51
3.8000e+031021063.740.50
3.9000e+031041083.670.49
4.0000e+031071102.600.34
4.1000e+031081123.510.46
4.2000e+031101133.410.44
4.3000e+031101155.310.68
4.4000e+031101177.190.91
4.5000e+031111198.061.01
4.6000e+031131217.920.98
4.7000e+031141238.771.08
4.8000e+031171257.610.93
4.9000e+031181268.451.03
5.0000e+031201288.271.00
5.2000e+031231328.891.06
5.4000e+031261359.481.11
5.6000e+031321397.040.81
5.8000e+031371435.580.63
6.0000e+031401466.080.68
6.2000e+031421507.550.84
6.4000e+031441539.000.99
6.6000e+031471569.431.02
6.8000e+0314816011.831.27
7.0000e+0315216311.211.19
7.2000e+0315416712.571.32
7.4000e+0315617013.911.44
7.6000e+0315917314.221.46
7.8000e+031671779.520.97
8.0000e+031701809.800.98
8.2000e+0317218311.061.10
8.4000e+0317618610.301.02
8.6000e+0317919010.531.03
8.8000e+031841938.740.85
9.0000e+031871968.930.86
9.2000e+031901999.110.87
9.4000e+031942028.270.78
9.6000e+031972058.420.79
9.8000e+032002098.550.79
1.0000e+042022129.670.89
1.0500e+042112198.410.76
1.1000e+0421622711.080.98
1.1500e+0422423510.660.93
1.2000e+0423124211.180.96
1.2500e+042422507.630.64
1.3000e+042482579.020.75
1.3500e+042572647.340.60
1.4000e+042642727.620.61
1.4500e+042712797.830.62
1.5000e+042822864.000.31
1.5500e+042882935.110.40
1.6000e+042963004.180.32
1.6500e+043063071.200.09
1.7000e+043123142.180.16
1.7500e+043183213.120.23
1.8000e+043213287.010.51
1.8500e+043303354.870.35
1.9000e+043343427.690.55
1.9500e+043413487.470.53
2.0000e+0434335512.220.86
2.1000e+0435636912.620.87
2.2000e+043723829.880.67
2.3000e+0438539510.030.66
2.4000e+043994089.070.59
2.5000e+044114219.990.64
2.6000e+0442243411.820.75
2.7000e+0443344713.550.84
2.8000e+0444545914.180.87
2.9000e+0445747214.730.89
3.0000e+0446748417.201.02
3.1000e+0447549721.581.27
3.2000e+0448950919.891.15
3.3000e+0450452117.120.98
3.4000e+0451853315.280.86
3.5000e+0452654519.381.08
3.6000e+0453655721.401.18
3.7000e+0454856921.371.17
3.8000e+0455858123.271.26
3.9000e+0456759326.111.40
4.0000e+0458060524.901.32
4.1000e+0459361723.631.24
4.2000e+0460562823.311.21
4.3000e+0461764022.931.18
4.4000e+0462765224.511.25
4.5000e+0464266321.031.06
4.6000e+0465267522.511.13
4.7000e+0466268623.941.19
4.8000e+0467169726.331.30
4.9000e+0468170927.671.35
5.0000e+0469272027.971.35
5.2000e+0471574227.441.31
5.4000e+0474276522.761.07
5.6000e+0476578721.921.01
5.8000e+0478680922.951.04
6.0000e+0480783123.831.07
6.2000e+0482585327.581.22
6.4000e+0484487430.201.32
6.6000e+0486589630.701.33
6.8000e+0488891729.091.24
7.0000e+0490593833.361.41
7.2000e+0492296037.521.56
7.4000e+0494498136.581.51
7.6000e+04969100232.541.33
7.8000e+04992102230.391.23
8.0000e+041013104330.161.20
8.2000e+041033106430.831.22
8.4000e+041053108431.411.23
8.6000e+041066110538.911.51
8.8000e+041091112534.321.32
9.0000e+041112114633.661.28
9.2000e+041135116630.911.16
9.4000e+041156118630.081.12
9.6000e+041177120629.191.08
9.8000e+041197122629.211.07
1.0000e+051215124631.171.13
1.0500e+051264129631.761.13
1.1000e+051317134527.950.98
1.1500e+051368139425.750.88
1.2000e+051412144230.191.02
1.2500e+051462149028.290.94
1.3000e+051508153830.060.98
1.3500e+051557158628.520.92
1.4000e+051604163328.680.91
1.4500e+051650168029.560.92
1.5000e+051686172640.161.24
1.5500e+051731177341.511.26
1.6000e+051779181939.611.19
1.6500e+051817186447.461.40
1.7000e+051863191047.091.38
1.7500e+051909195546.491.34
1.8000e+051957200143.681.25
1.8500e+051990204655.661.57
1.9000e+052035209055.451.55
1.9500e+052084213551.031.41
2.0000e+052134217945.441.24
2.1000e+052224226843.701.17
2.2000e+052315235540.281.06
2.3000e+052402244240.211.04
2.4000e+052485252943.541.10
2.5000e+052578261436.280.90
2.6000e+052661269938.480.94
2.7000e+052737278447.151.13
2.8000e+052810286858.321.38
2.9000e+052891295261.021.43
3.0000e+052974303561.251.41
3.1000e+053055311863.051.43
3.2000e+053144320056.421.26
3.3000e+053220328262.391.38
3.4000e+053306336457.971.27
3.5000e+053392344553.171.15
3.6000e+053474352652.011.11
3.7000e+053562360744.500.94
3.8000e+053641368745.660.95
3.9000e+053720376646.480.96
4.0000e+053812384633.990.69
4.1000e+053877392548.190.97
4.2000e+053958400446.090.92
4.3000e+054043408339.700.79
4.4000e+054121416140.030.78
4.5000e+054194423945.080.87
4.6000e+054265431751.871.00
4.7000e+054340439454.401.04
4.8000e+054417447254.681.03
4.9000e+054483454965.721.23
5.0000e+054558462667.511.25
5.2000e+054709477869.401.27
5.4000e+054866493064.401.16
5.6000e+055018508263.551.12
5.8000e+055182523249.880.87
6.0000e+055333538148.440.83
6.2000e+055481553049.250.83
6.4000e+055630567848.340.81
6.6000e+055774582651.740.85
6.8000e+055936597236.470.59
7.0000e+056084611934.560.56
7.2000e+056215626449.030.78
7.4000e+056364640944.910.71
7.6000e+056495655358.210.90
7.8000e+056644669752.940.81
8.0000e+056797684043.140.66
8.2000e+056924698358.810.88
8.4000e+057067712557.970.86
8.6000e+057202726764.630.95
8.8000e+057342740865.810.96
9.0000e+057470754978.521.13
9.2000e+057610768978.781.13
9.4000e+057750782978.601.11
9.6000e+057885796882.981.17
9.8000e+058019810787.941.23
1.0000e+0681438245102.491.42
1.0500e+068511859079.141.07
1.1000e+068843893289.421.19
1.1500e+069196927276.481.00
1.2000e+069548961062.420.80
1.2500e+069873994673.350.92
1.3000e+06102141028066.380.82
1.3500e+06105481061364.590.78
1.4000e+06108911094352.050.62
1.4500e+06112021127269.850.82
1.5000e+06115311159968.060.79
1.5500e+06118481192576.740.88
1.6000e+06121881224960.940.69
1.6500e+06125281257243.730.49
1.7000e+06128791289314.160.16
1.7500e+06132001321313.270.14
1.8000e+06134971353235.110.38
1.8500e+06138281385021.720.23
1.9000e+06141331416633.140.35
1.9500e+06144441448137.420.39
2.0000e+06147411479654.580.56
2.1000e+06153341542186.690.87
2.2000e+061594016042101.721.00
2.3000e+061654916659109.891.06
2.4000e+061714117272131.421.25
2.5000e+06177951788287.470.81
2.6000e+06183991848990.210.83
2.7000e+06190181909374.810.67
2.8000e+06196361969357.390.51
2.9000e+06202282029163.080.55
3.0000e+06208252088661.020.53
3.1000e+06213982147880.290.68
3.2000e+06219982206870.020.59
3.3000e+06225672265588.290.73
3.4000e+062313423240106.200.87
3.5000e+062372023823102.820.83
3.6000e+062430024403103.230.82
3.7000e+06248852498296.510.76
3.8000e+06254782555879.730.62
3.9000e+06260962613235.950.28
4.0000e+06266282670476.240.58
4.1000e+06272132727561.640.46
4.2000e+06277922784351.220.38
4.3000e+06283622841048.020.35
4.4000e+06289312897544.110.32
4.5000e+06295012953937.510.27
4.6000e+06300743010026.290.19
4.7000e+06306383066022.470.16
4.8000e+06311863121933.100.23
4.9000e+06317393177637.230.26
5.0000e+06323073233224.880.17
5.2000e+0633430334398.890.06
5.4000e+06345253454015.410.10
5.6000e+06356213563715.670.10
5.8000e+06367063672821.910.14
6.0000e+06377863781428.330.18
6.2000e+06388703889626.110.16
6.4000e+06399303997343.440.27
6.6000e+06409844104662.480.38
6.8000e+06420554211560.380.36
7.0000e+06431244318056.300.34
7.2000e+06441744424167.360.40
7.4000e+06451994529999.690.58
7.6000e+06462654635287.420.50
7.8000e+064726347403139.650.79
8.0000e+064828748449162.490.91
8.2000e+064936049493133.050.74
8.4000e+065039150533142.410.78
8.6000e+065143751571133.670.73
8.8000e+065248952605115.910.62
9.0000e+065346853636168.210.90
9.2000e+065447154665193.661.02
9.4000e+065551255690178.320.93
9.6000e+065657656713137.270.71
9.8000e+065757157734162.560.84
1.0000e+075862158751130.280.66
1.0500e+076115961285125.650.63
1.1000e+076365763803146.140.71
1.1500e+076619366308114.550.55
1.2000e+07687266879972.580.34
1.2500e+07712357127741.910.19
1.3000e+07736557374388.140.40
1.3500e+077608776198110.800.50
1.4000e+07785837864158.420.26
1.4500e+07810448107430.440.13
1.5000e+07834718349726.310.11
1.5500e+07858998591011.430.05
1.6000e+07882818831433.150.14
1.6500e+07906839070925.830.11
1.7000e+079309893095-3.20-0.01
1.7500e+079548395472-10.65-0.04
1.8000e+07978009784241.760.16
1.8500e+0710015810020345.310.18
1.9000e+0710247610255781.240.31
1.9500e+07104773104904130.790.50
2.0000e+07107081107243162.180.61
2.1000e+07111741111901160.310.59
2.2000e+07116324116533209.190.75
2.3000e+07120898121140242.230.86
2.4000e+07125574125724149.680.52
2.5000e+07130175130285109.700.37
2.6000e+07134691134824133.350.45
2.7000e+07139175139344168.590.56
2.8000e+07143724143843119.290.39
2.9000e+07148189148324135.290.43
3.0000e+07152576152787211.340.66
3.1000e+07157011157233222.130.69
3.2000e+07161420161662242.330.74
3.3000e+07165868166076207.530.63
3.4000e+07170206170473267.300.79
3.5000e+07174590174856266.180.78
3.6000e+07178923179225301.670.87
3.7000e+07183189183579390.221.12
3.8000e+07187536187920384.291.09
3.9000e+07191927192248321.290.90
4.0000e+07196233196564330.600.91
4.1000e+07200426200867440.601.21
4.2000e+07204693205158464.651.26
4.3000e+07209028209437409.071.10
4.4000e+07213258213705447.171.19
4.5000e+07217485217962477.271.25
4.6000e+07221689222209519.641.35
4.7000e+07225956226445488.561.26
4.8000e+07230168230670502.291.28
4.9000e+07234317234886569.081.44
5.0000e+07238610239092482.161.21
5.2000e+07247051247476425.091.05
5.4000e+07255353255824470.791.14
5.6000e+07263724264137412.820.98
5.8000e+07272020272417396.630.93
6.0000e+07280205280665459.551.06
6.2000e+07288362288882519.821.18
6.4000e+07296601297070468.591.05
6.6000e+07304730305229498.931.11
6.8000e+07312964313361396.850.87
7.0000e+07321199321466267.290.58
7.2000e+07329310329546236.120.50
7.4000e+07337319337601282.180.59
7.6000e+07345291345632341.240.71
7.8000e+07353283353640357.030.73
8.0000e+07361346361625279.260.57
8.2000e+07369341369589247.570.50
8.4000e+07377295377531235.600.47
8.6000e+07385152385452299.920.59
8.8000e+07393083393353270.090.53
9.0000e+07401024401235210.660.41
9.2000e+07408906409097191.120.37
9.4000e+07416745416941195.960.37
9.6000e+07424659424767107.640.20
9.8000e+0743249343257581.600.15
1.0000e+08440257440365108.260.20
1.0500e+08459820459769-51.21-0.09
1.1000e+08479234479072-161.51-0.29
1.1500e+08498394498282-112.39-0.19
1.2000e+08517473517401-72.09-0.12
1.2500e+08536534536435-99.27-0.17
1.3000e+08555608555387-220.98-0.36
1.3500e+08574474574261-212.58-0.34
1.4000e+08593197593061-135.73-0.22
1.4500e+0861175361179036.640.06
1.5000e+08630330630449119.390.18
1.5500e+08648820649043223.170.34
1.6000e+08667181667573392.440.59
1.6500e+08685715686042327.490.48
1.7000e+08704197704452255.470.37
1.7500e+08722414722805391.380.56
1.8000e+08740833741103270.110.38
1.8500e+08759208759347139.430.20
1.9000e+08777391777540149.020.21
1.9500e+08795573795682109.440.15
2.0000e+0881371481377662.170.08
2.1000e+08849710849823113.150.15
2.2000e+08885590885691101.350.13
2.3000e+08921401921390-10.87-0.01
2.4000e+0895687295692855.980.07
2.5000e+08992478992313-165.36-0.20
2.6000e+0810277201027551-168.83-0.20
2.7000e+08106264310626507.040.01
2.8000e+0810976851097615-69.79-0.08
2.9000e+0811325021132452-49.82-0.06
3.0000e+0811672131167166-46.96-0.05
3.1000e+081201676120176285.520.09
3.2000e+0812359851236243258.000.28
3.3000e+0812704611270615153.600.17
3.4000e+0813047211304880159.140.17
3.5000e+081338978133904365.210.07
3.6000e+081373082137310725.180.03
3.7000e+0814069271407075148.220.15
3.8000e+0814407921440950158.300.16
3.9000e+0814747591474735-23.75-0.02
4.0000e+0815083041508433128.710.13
4.1000e+0815420981542045-52.79-0.05
4.2000e+081575559157557516.120.02
4.3000e+08160901916090255.710.01
4.4000e+081642348164239648.120.05
4.5000e+08167568316756918.390.01
4.6000e+0817087891708912123.470.11
4.7000e+0817418691742061192.200.18
4.8000e+0817752551775139-115.63-0.11
4.9000e+0818082051808149-56.35-0.05
5.0000e+0818412651841091-174.34-0.16
5.2000e+0819069501906779-171.00-0.15
5.4000e+0819723071972216-91.03-0.08
5.6000e+0820375382037412-125.75-0.11
5.8000e+0821026312102378-253.30-0.21
6.0000e+0821672722167121-150.55-0.12
6.2000e+0822318462231652-194.04-0.16
6.4000e+082295925229597752.110.04
6.6000e+0823602162360104-111.74-0.09
6.8000e+082423999242404041.280.03
7.0000e+0824879472487792-155.38-0.12
7.2000e+0825511972551364167.310.13
7.4000e+0826144542614764310.040.23
7.6000e+0826778092677996187.160.14
7.8000e+0827409652741066100.720.07
8.0000e+0828040432803977-65.51-0.05
8.2000e+0828669472866736-211.01-0.15
8.4000e+0829295242929345-178.51-0.13
8.6000e+0829920372991810-226.94-0.16
8.8000e+0830544453054134-311.45-0.22
9.0000e+0831163203116320-0.38-0.00
9.2000e+083178298317837273.780.05
9.4000e+08324029332402930.360.00
9.6000e+0833017593302088328.520.22
9.8000e+0833632383363757519.300.34
1.0000e+0934246793425306626.620.41
1.0500e+0935779343578663728.900.47
1.1000e+0937305143731318804.370.50
1.1500e+09388185538833081453.430.89
1.2000e+09403341640346661250.090.75
1.2500e+09418433141854211090.420.65
1.3000e+0943346924335602909.900.53
1.3500e+09448379844852331434.750.82
1.4000e+09463247846343371859.181.05
1.4500e+09478080847829372128.621.18
1.5000e+09492891549310512135.941.17
1.5500e+09507668250786992016.551.08
1.6000e+09522411952258971777.620.94
1.6500e+09537084353726611818.160.95
1.7000e+09551749255190071515.130.78
1.7500e+09566355856649491390.560.71
1.8000e+09580937158104991127.620.57
1.8500e+09595436159556701308.680.65
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