Gap size : 12 (r=6)

Generated by program gapCounts : Mon Jun 27 12:32:55 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+020-1-0.56-0.26
2.0000e+020-0-0.02-0.01
3.0000e+0221-1.18-0.39
4.0000e+0222-0.21-0.06
5.0000e+0233-0.17-0.05
6.0000e+0244-0.09-0.02
7.0000e+0265-0.98-0.24
8.0000e+02660.160.04
9.0000e+02770.300.07
1.0000e+03781.450.32
1.1000e+038101.620.34
1.2000e+038112.780.57
1.3000e+0310121.950.39
1.4000e+0311132.130.41
1.5000e+0312142.300.43
1.6000e+0315150.480.09
1.7000e+0315171.660.30
1.8000e+0316181.840.32
1.9000e+0318191.010.18
2.0000e+0319201.190.20
2.1000e+0320211.370.23
2.2000e+0321231.550.25
2.3000e+0321242.730.44
2.4000e+0322252.900.46
2.5000e+0324262.080.33
2.6000e+0325272.250.35
2.7000e+0326282.430.37
2.8000e+0327302.600.39
2.9000e+0327313.770.56
3.0000e+0328323.940.58
3.1000e+0330333.110.45
3.2000e+0331343.280.47
3.3000e+0333352.440.34
3.4000e+0335371.610.22
3.5000e+0335382.770.38
3.6000e+0337391.940.26
3.7000e+0338402.100.28
3.8000e+0338413.260.44
3.9000e+0338424.420.58
4.0000e+0339444.580.60
4.1000e+0341453.730.48
4.2000e+0342463.890.50
4.3000e+0342475.040.64
4.4000e+0342486.200.78
4.5000e+0344495.350.67
4.6000e+0345505.500.68
4.7000e+0346525.650.70
4.8000e+0347535.800.71
4.9000e+0349544.940.60
5.0000e+0350555.090.61
5.2000e+0352575.380.64
5.4000e+0354605.660.66
5.6000e+0356625.940.69
5.8000e+0356648.220.94
6.0000e+0358668.490.95
6.2000e+0360698.760.97
6.4000e+03617110.021.10
6.6000e+03617312.281.33
6.8000e+03637612.531.34
7.0000e+03647813.781.46
7.2000e+03688012.031.26
7.4000e+03698213.271.37
7.6000e+03708514.511.49
7.8000e+03728714.741.50
8.0000e+03778911.971.20
8.2000e+03799112.201.21
8.4000e+03809313.431.32
8.6000e+03829613.651.33
8.8000e+03849813.871.34
9.0000e+038710013.081.26
9.2000e+039110211.291.07
9.4000e+039310411.501.08
9.6000e+039510711.701.10
9.8000e+031001098.900.83
1.0000e+041051116.100.56
1.0500e+041111175.580.50
1.1000e+041151227.050.63
1.1500e+041231274.500.39
1.2000e+041281334.930.42
1.2500e+041321386.340.53
1.3000e+041391444.740.39
1.3500e+041441495.120.42
1.4000e+041451549.490.77
1.4500e+0414816011.840.94
1.5000e+0415116514.181.11
1.5500e+0415717113.501.05
1.6000e+0416417611.820.90
1.6500e+0416718114.121.07
1.7000e+0417518611.400.85
1.7500e+0417819213.681.01
1.8000e+0418619710.940.80
1.8500e+041952027.190.52
1.9000e+042022075.440.39
1.9500e+042062136.660.47
2.0000e+042142183.880.27
2.1000e+04230228-1.71-0.12
2.2000e+042382390.660.04
2.3000e+04251249-2.01-0.13
2.4000e+04264259-4.72-0.31
2.5000e+04276270-6.46-0.41
2.6000e+04285280-5.24-0.33
2.7000e+04297290-7.04-0.44
2.8000e+04305300-4.88-0.30
2.9000e+04317310-6.75-0.41
3.0000e+04327320-6.65-0.40
3.1000e+04339330-8.58-0.50
3.2000e+04344340-3.54-0.21
3.3000e+04354350-3.52-0.20
3.4000e+04363360-2.52-0.14
3.5000e+04374370-3.56-0.20
3.6000e+04390380-9.61-0.53
3.7000e+04404390-13.69-0.75
3.8000e+04410400-9.79-0.53
3.9000e+04419410-8.92-0.48
4.0000e+04426420-6.07-0.32
4.1000e+04441430-11.23-0.59
4.2000e+04450440-10.42-0.54
4.3000e+04461449-11.63-0.60
4.4000e+04468459-8.86-0.45
4.5000e+04485469-16.11-0.81
4.6000e+04492479-13.38-0.67
4.7000e+04502488-13.66-0.68
4.8000e+04510498-11.97-0.59
4.9000e+04522508-14.29-0.70
5.0000e+04534517-16.63-0.80
5.2000e+04553537-16.35-0.78
5.4000e+04574556-18.14-0.85
5.6000e+04587575-12.00-0.55
5.8000e+04603594-8.91-0.41
6.0000e+04615613-1.89-0.08
6.2000e+046296323.080.14
6.4000e+0464165110.000.44
6.6000e+0465167018.860.81
6.8000e+0467868910.680.46
7.0000e+0469270715.440.65
7.2000e+047207266.150.26
7.4000e+047437451.820.08
7.6000e+04766763-2.55-0.10
7.8000e+047827820.030.00
8.0000e+047988012.570.10
8.2000e+048198190.060.00
8.4000e+04840838-2.48-0.10
8.6000e+04859856-3.07-0.12
8.8000e+04876874-1.69-0.06
9.0000e+048908932.650.10
9.2000e+049039117.950.30
9.4000e+0491792912.220.46
9.6000e+0493694711.450.42
9.8000e+0495096615.650.57
1.0000e+0596498419.810.72
1.0500e+051013102916.080.57
1.1000e+051049107425.150.88
1.1500e+051091111928.040.96
1.2000e+051131116432.751.11
1.2500e+051172120836.291.20
1.3000e+051223125329.670.97
1.3500e+051270129726.890.86
1.4000e+051316134124.970.79
1.4500e+051356138528.900.90
1.5000e+051399142929.690.91
1.5500e+051435147237.351.13
1.6000e+051480151635.881.07
1.6500e+051528155931.280.93
1.7000e+051561160341.571.21
1.7500e+051615164630.730.89
1.8000e+051657168931.790.91
1.8500e+051698173233.740.95
1.9000e+051740177534.570.96
1.9500e+051777181740.311.11
2.0000e+051821186038.951.06
2.1000e+051907194537.931.01
2.2000e+051991203038.541.01
2.3000e+052079211434.790.90
2.4000e+052157219840.711.03
2.5000e+052251228130.310.75
2.6000e+052316236548.601.19
2.7000e+052392244855.601.34
2.8000e+052472253058.311.38
2.9000e+052555261357.761.35
3.0000e+052631269563.941.47
3.1000e+052727277749.871.13
3.2000e+052820285938.550.86
3.3000e+052898294042.010.93
3.4000e+052991302130.230.66
3.5000e+053069310233.240.72
3.6000e+053160318323.030.49
3.7000e+053248326415.610.33
3.8000e+053329334415.000.31
3.9000e+053401342423.190.48
4.0000e+053487350417.190.35
4.1000e+053565358419.010.38
4.2000e+053637366426.650.53
4.3000e+053710374333.120.66
4.4000e+053782382240.410.79
4.5000e+053842390259.541.16
4.6000e+053909398171.511.37
4.7000e+053989405970.321.34
4.8000e+054078413859.971.13
4.9000e+054147421669.481.30
5.0000e+054237429557.841.07
5.2000e+054401445150.120.91
5.4000e+054551460755.861.00
5.6000e+054699476263.061.12
5.8000e+054852491764.761.13
6.0000e+055018507152.970.91
6.2000e+055183522541.710.71
6.4000e+055335537842.990.72
6.6000e+055487553143.830.72
6.8000e+055646568337.250.61
7.0000e+055775583560.260.97
7.2000e+055922598764.871.03
7.4000e+056111613827.090.43
7.6000e+056261628927.940.43
7.8000e+056394643945.430.70
8.0000e+056532659057.560.87
8.2000e+056670673969.351.04
8.4000e+056822688966.810.99
8.6000e+056973703864.940.96
8.8000e+057122718764.760.94
9.0000e+057276733559.260.86
9.2000e+057427748356.470.81
9.4000e+057567763164.380.91
9.6000e+057709777970.000.98
9.8000e+057863792663.340.88
1.0000e+068005807368.410.95
1.0500e+068373844066.920.91
1.1000e+068714880590.841.20
1.1500e+069081916887.251.14
1.2000e+069435953095.231.22
1.2500e+0697899891101.831.28
1.3000e+06101621025088.131.09
1.3500e+061050610608102.171.24
1.4000e+061086210965103.001.23
1.4500e+061120411321116.691.37
1.5000e+061153911675136.261.58
1.5500e+061189912029129.761.49
1.6000e+061222812381153.221.73
1.6500e+061258312733149.701.67
1.7000e+061293413083149.201.64
1.7500e+061328913433143.781.56
1.8000e+061368113781100.461.08
1.8500e+06140401412989.260.95
1.9000e+06144251447651.210.54
1.9500e+06147961482226.340.27
2.0000e+06151411516826.670.27
2.1000e+06158351585621.020.21
2.2000e+06165151654126.420.26
2.3000e+06172111722413.020.13
2.4000e+061792217904-18.04-0.17
2.5000e+061860418581-22.64-0.21
2.6000e+061928319256-26.67-0.24
2.7000e+061993319929-4.03-0.04
2.8000e+062060220599-2.61-0.02
2.9000e+062128321268-15.34-0.13
3.0000e+062193421934-0.13-0.00
3.1000e+062260622598-7.89-0.07
3.2000e+062327223260-11.57-0.10
3.3000e+06239062392114.900.12
3.4000e+06245572458022.600.18
3.5000e+06252052523731.560.25
3.6000e+06258652589226.860.21
3.7000e+06265032654642.540.33
3.8000e+06271312719866.650.52
3.9000e+06277892784859.230.46
4.0000e+06284562849741.340.31
4.1000e+06290772914568.000.51
4.2000e+06297462979145.270.34
4.3000e+06303743043662.170.46
4.4000e+06310413108038.740.28
4.5000e+06316793172243.020.31
4.6000e+06323213236342.030.30
4.7000e+06329643300338.820.28
4.8000e+06336113364130.400.21
4.9000e+06342383427940.800.28
5.0000e+06348883491527.060.19
5.2000e+06361513618433.230.23
5.4000e+0637446374493.100.02
5.6000e+0638702387107.850.05
5.8000e+06399453996721.630.14
6.0000e+06412084122011.610.07
6.2000e+06424514246917.930.11
6.4000e+0643705437159.700.06
6.6000e+064498044957-22.93-0.14
6.8000e+064623846196-41.86-0.25
7.0000e+064748847432-55.98-0.33
7.2000e+064873148665-66.19-0.39
7.4000e+064996049895-65.40-0.38
7.6000e+06510965112125.500.15
7.8000e+06523315234614.580.08
8.0000e+065358353567-16.08-0.09
8.2000e+0654778547867.600.04
8.4000e+065603256002-30.31-0.17
8.6000e+065723157215-15.74-0.09
8.8000e+065844258426-15.63-0.08
9.0000e+065966059635-24.90-0.13
9.2000e+06608176084124.490.13
9.4000e+06620036204642.600.22
9.6000e+06632076324740.490.21
9.8000e+06643756444772.200.37
1.0000e+076551365645131.800.67
1.0500e+076851168630118.800.59
1.1000e+07715507160352.510.26
1.1500e+07744827456481.560.39
1.2000e+07774777751436.510.17
1.2500e+078049580453-42.14-0.19
1.3000e+078342983382-46.90-0.21
1.3500e+078639486302-92.35-0.41
1.4000e+078922689212-14.08-0.06
1.4500e+079214992113-35.72-0.15
1.5000e+079502695006-19.95-0.09
1.5500e+079792097891-29.43-0.12
1.6000e+07100801100767-33.87-0.14
1.6500e+0710362110363615.010.06
1.7000e+07106529106497-31.54-0.13
1.7500e+0710933110935220.740.08
1.8000e+0711215011219949.050.19
1.8500e+0711500711504032.630.13
1.9000e+0711777511787498.680.38
1.9500e+07120591120701110.380.42
2.0000e+07123410123523112.920.42
2.1000e+07129031129148117.180.43
2.2000e+0713466913475181.740.29
2.3000e+07140222140332109.740.39
2.4000e+07145748145892144.220.50
2.5000e+07151327151433106.140.36
2.6000e+0715690015695555.370.19
2.7000e+071624561624603.700.01
2.8000e+07167969167947-22.13-0.07
2.9000e+07173425173418-7.43-0.02
3.0000e+07178927178872-54.58-0.17
3.1000e+07184427184312-114.99-0.36
3.2000e+07189827189737-90.10-0.28
3.3000e+07195220195148-72.41-0.22
3.4000e+07200651200545-106.45-0.32
3.5000e+07206051205928-122.75-0.36
3.6000e+07211411211299-111.90-0.32
3.7000e+07216821216657-163.50-0.47
3.8000e+07222156222004-152.19-0.43
3.9000e+07227538227338-199.59-0.56
4.0000e+07232763232662-101.39-0.28
4.1000e+07238121237974-147.26-0.40
4.2000e+07243347243275-71.90-0.19
4.3000e+07248618248566-52.03-0.14
4.4000e+072538432538473.630.01
4.5000e+07259138259117-20.67-0.05
4.6000e+07264545264378-166.69-0.43
4.7000e+07269812269630-182.18-0.47
4.8000e+07275076274872-203.92-0.52
4.9000e+07280368280105-262.71-0.66
5.0000e+07285617285330-287.32-0.72
5.2000e+07296045295753-292.27-0.72
5.4000e+07306340306143-197.30-0.48
5.6000e+07316776316501-275.05-0.66
5.8000e+07326963326829-134.25-0.32
6.0000e+07337223337127-95.74-0.22
6.2000e+07347640347398-242.44-0.55
6.4000e+07357814357641-173.33-0.39
6.6000e+07368119367858-261.46-0.58
6.8000e+07378223378049-173.97-0.38
7.0000e+07388370388216-154.01-0.33
7.2000e+07398559398359-199.80-0.43
7.4000e+07408650408479-170.62-0.36
7.6000e+07418849418577-271.77-0.57
7.8000e+07428806428653-152.60-0.31
8.0000e+07438908438709-199.49-0.41
8.2000e+07449088448743-344.85-0.69
8.4000e+07459143458758-385.14-0.77
8.6000e+07469106468753-352.82-0.70
8.8000e+07479124478730-394.39-0.77
9.0000e+07488902488688-214.38-0.41
9.2000e+07498850498628-222.33-0.43
9.4000e+07508749508550-198.80-0.38
9.6000e+07518574518456-118.39-0.22
9.8000e+07528573528344-228.69-0.43
1.0000e+08538382538217-165.33-0.30
1.0500e+08563096562828-267.56-0.48
1.1000e+08587488587346-142.39-0.25
1.1500e+08611876611773-103.05-0.18
1.2000e+08636195636115-80.20-0.14
1.2500e+08660210660375165.120.28
1.3000e+08684582684558-24.48-0.04
1.3500e+08708915708665-249.68-0.40
1.4000e+08732940732702-238.39-0.38
1.4500e+08756912756669-242.80-0.38
1.5000e+08780824780571-253.27-0.39
1.5500e+08804630804409-221.35-0.34
1.6000e+08828602828185-416.78-0.62
1.6500e+08852430851903-527.41-0.78
1.7000e+08876109875563-546.27-0.79
1.7500e+08899921899168-753.48-1.08
1.8000e+08923402922719-683.29-0.97
1.8500e+08946935946218-717.04-1.00
1.9000e+08970282969667-615.18-0.85
1.9500e+08993762993067-695.24-0.95
2.0000e+0810170471016419-627.82-0.85
2.1000e+0810639401062987-953.36-1.26
2.2000e+0811103101109379-931.03-1.21
2.3000e+0811566301155605-1025.01-1.30
2.4000e+0812027451201673-1072.28-1.34
2.5000e+0812485251247589-935.53-1.14
2.6000e+0812940861293362-724.06-0.87
2.7000e+0813400571338996-1060.72-1.25
2.8000e+0813857871384498-1288.85-1.50
2.9000e+0814308761429873-1003.20-1.15
3.0000e+0814761291475125-1003.90-1.13
3.1000e+0815213061520260-1046.43-1.16
3.2000e+0815664441565280-1163.59-1.27
3.3000e+0816113851610192-1193.44-1.29
3.4000e+0816558511654997-854.29-0.91
3.5000e+0817006441699699-944.68-0.99
3.6000e+0817454141744303-1111.38-1.15
3.7000e+0817900731788810-1263.32-1.30
3.8000e+0818346431833223-1419.63-1.44
3.9000e+0818785141877546-967.57-0.97
4.0000e+0819226861921781-904.58-0.90
4.1000e+0819668211965931-890.21-0.87
4.2000e+0820105622009997-565.15-0.55
4.3000e+0820547972053982-815.21-0.78
4.4000e+0820987092097888-821.29-0.78
4.5000e+0821425242141717-807.40-0.76
4.6000e+0821863502185470-879.65-0.82
4.7000e+0822298732229151-722.23-0.67
4.8000e+0822733572272760-597.40-0.55
4.9000e+0823169872316298-688.52-0.62
5.0000e+0823607042359769-935.01-0.84
5.2000e+0824471582446511-647.08-0.57
5.4000e+0825334912532997-494.23-0.43
5.6000e+0826193812619237-143.96-0.12
5.8000e+0827053862705241-144.56-0.12
6.0000e+0827917082791019-689.03-0.57
6.2000e+0828775562876578-978.00-0.80
6.4000e+0829626452961926-718.67-0.58
6.6000e+0830479153047071-843.74-0.67
6.8000e+0831330683132020-1048.41-0.82
7.0000e+0832175213216778-743.27-0.57
7.2000e+0833021083301352-756.31-0.57
7.4000e+0833864663385747-718.86-0.54
7.6000e+0834705423469969-572.60-0.42
7.8000e+0835549393554024-915.47-0.67
8.0000e+0836386583637914-743.71-0.54
8.2000e+0837224193721646-772.79-0.55
8.4000e+0838055833805224-359.44-0.25
8.6000e+0838890183888650-367.57-0.26
8.8000e+0839720253971931-94.33-0.07
9.0000e+084055032405506835.990.02
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