Gap size : 24 (r=12)

Generated by program gapCounts : Mon Jun 27 12:36:54 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+02000.000.00
2.0000e+020-0-0.00-0.00
3.0000e+020-0-0.01-0.00
4.0000e+020-0-0.01-0.00
5.0000e+02000.000.00
6.0000e+02000.030.01
7.0000e+02000.060.01
8.0000e+02000.100.02
9.0000e+02000.160.04
1.0000e+03000.220.05
1.1000e+03000.280.06
1.2000e+03000.360.07
1.3000e+03000.430.09
1.4000e+03010.520.10
1.5000e+03010.610.11
1.6000e+03010.700.13
1.7000e+0311-0.20-0.04
1.8000e+0311-0.10-0.02
1.9000e+03110.010.00
2.0000e+03110.120.02
2.1000e+03110.230.04
2.2000e+03110.340.06
2.3000e+0321-0.54-0.09
2.4000e+0322-0.42-0.07
2.5000e+0322-0.29-0.05
2.6000e+0322-0.17-0.03
2.7000e+0322-0.04-0.01
2.8000e+03220.100.01
2.9000e+03220.230.03
3.0000e+03220.370.05
3.1000e+03230.500.07
3.2000e+03230.640.09
3.3000e+03230.780.11
3.4000e+03230.930.13
3.5000e+03231.070.15
3.6000e+03231.220.17
3.7000e+03231.370.19
3.8000e+03241.520.20
3.9000e+03241.670.22
4.0000e+03241.830.24
4.1000e+03241.980.26
4.2000e+03242.140.28
4.3000e+03341.300.17
4.4000e+03341.450.18
4.5000e+03351.620.20
4.6000e+03450.780.10
4.7000e+03450.940.12
4.8000e+03550.100.01
4.9000e+03550.270.03
5.0000e+03550.440.05
5.2000e+03560.770.09
5.4000e+03660.110.01
5.6000e+03660.460.05
5.8000e+03670.800.09
6.0000e+03671.150.13
6.2000e+03780.510.06
6.4000e+03780.870.10
6.6000e+03880.230.02
6.8000e+0399-0.41-0.04
7.0000e+0399-0.04-0.00
7.2000e+03109-0.67-0.07
7.4000e+031110-1.30-0.13
7.6000e+031110-0.92-0.09
7.8000e+031110-0.54-0.06
8.0000e+031211-1.16-0.12
8.2000e+031311-1.78-0.18
8.4000e+031412-2.39-0.24
8.6000e+031412-2.01-0.20
8.8000e+031412-1.62-0.16
9.0000e+031413-1.22-0.12
9.2000e+031513-1.83-0.17
9.4000e+031514-1.44-0.14
9.6000e+031514-1.04-0.10
9.8000e+031514-0.64-0.06
1.0000e+041515-0.24-0.02
1.0500e+0415160.770.07
1.1000e+0415171.790.16
1.1500e+0416181.830.16
1.2000e+0418190.860.07
1.2500e+042020-0.09-0.01
1.3000e+0420210.970.08
1.3500e+0422220.030.00
1.4000e+0422231.100.09
1.4500e+0422242.180.17
1.5000e+0422253.270.26
1.5500e+0422264.360.34
1.6000e+0422275.450.42
1.6500e+0425293.560.27
1.7000e+0427302.670.20
1.7500e+0428312.780.21
1.8000e+0429322.900.21
1.8500e+0430333.020.22
1.9000e+0432342.150.15
1.9500e+0433352.280.16
2.0000e+0434362.420.17
2.1000e+0435393.700.25
2.2000e+0435416.000.40
2.3000e+0437436.320.42
2.4000e+0440465.650.37
2.5000e+0441486.990.45
2.6000e+0442508.350.53
2.7000e+04425310.710.67
2.8000e+04435512.090.74
2.9000e+04435714.480.87
3.0000e+04456014.880.89
3.1000e+04466216.280.96
3.2000e+04466518.701.08
3.3000e+04496718.121.04
3.4000e+04517018.551.05
3.5000e+04517220.991.17
3.6000e+04537421.441.19
3.7000e+04547722.891.25
3.8000e+04547925.351.37
3.9000e+04558226.821.44
4.0000e+04568428.301.50
4.1000e+04608726.781.40
4.2000e+04628927.261.42
4.3000e+04679224.751.27
4.4000e+04709424.251.24
4.5000e+04709726.751.35
4.6000e+04709929.261.46
4.7000e+047210229.771.48
4.8000e+047310431.291.54
4.9000e+047910727.811.36
5.0000e+048310926.341.27
5.2000e+048711427.401.30
5.4000e+049111928.481.34
5.6000e+049912525.581.18
5.8000e+0410113028.691.31
6.0000e+0410413530.811.38
6.2000e+0410814031.951.42
6.4000e+0411214533.101.45
6.6000e+0411215038.261.65
6.8000e+0411615539.441.68
7.0000e+0411916141.621.75
7.2000e+0412716638.811.62
7.4000e+0413217139.021.61
7.6000e+0413817638.231.56
7.8000e+0414518136.451.47
8.0000e+0415018736.691.46
8.2000e+0415219239.921.58
8.4000e+0415619741.171.61
8.6000e+0415820244.431.72
8.8000e+0416520842.691.64
9.0000e+0417321339.961.52
9.2000e+0417621842.241.59
9.4000e+0418322440.521.51
9.6000e+0419022938.811.44
9.8000e+0420023434.101.25
1.0000e+0520623933.401.22
1.0500e+0522325329.681.06
1.1000e+0523026636.001.26
1.1500e+0524627933.341.15
1.2000e+0525729335.711.21
1.2500e+0526930637.111.23
1.3000e+0527932040.531.32
1.3500e+0529133341.981.35
1.4000e+0530534641.441.31
1.4500e+0531436045.931.43
1.5000e+0533437339.441.21
1.5500e+0534738739.961.21
1.6000e+0535540145.511.36
1.6500e+0537041444.061.30
1.7000e+0537842849.641.45
1.7500e+0538944152.231.51
1.8000e+0539945555.831.59
1.8500e+0541846850.441.42
1.9000e+0543548247.071.31
1.9500e+0544649649.711.37
2.0000e+0545750952.361.43
2.1000e+0548253754.691.46
2.2000e+0550856456.061.47
2.3000e+0553259159.471.53
2.4000e+0555861960.911.54
2.5000e+0558764659.381.48
2.6000e+0562067453.881.32
2.7000e+0565370148.401.17
2.8000e+0568772941.950.99
2.9000e+0570875748.521.13
3.0000e+0575078434.110.79
3.1000e+0577281239.720.90
3.2000e+0580183938.350.86
3.3000e+0582386743.990.97
3.4000e+0585389541.650.91
3.5000e+0587392249.331.06
3.6000e+0589895052.011.11
3.7000e+0592497853.711.13
3.8000e+05952100553.421.11
3.9000e+05984103349.151.01
4.0000e+051013106147.880.98
4.1000e+051039108949.621.00
4.2000e+051061111655.371.11
4.3000e+051080114464.141.27
4.4000e+051110117261.901.21
4.5000e+051130120069.681.35
4.6000e+051156122771.461.37
4.7000e+051193125562.261.19
4.8000e+051214128369.051.30
4.9000e+051247131163.861.20
5.0000e+051278133960.661.13
5.2000e+051331139463.301.16
5.4000e+051396145053.950.97
5.6000e+051457150648.620.86
5.8000e+051510156151.300.89
6.0000e+051559161757.991.00
6.2000e+051609167363.701.08
6.4000e+051672172856.410.94
6.6000e+051728178456.140.93
6.8000e+051796184043.870.71
7.0000e+051860189635.610.57
7.2000e+051917195134.350.55
7.4000e+051976200731.100.49
7.6000e+052042206320.850.32
7.8000e+052106211912.600.19
8.0000e+052160217414.360.22
8.2000e+052217223013.110.20
8.4000e+052261228624.870.37
8.6000e+052322234219.630.29
8.8000e+052379239718.390.27
9.0000e+052440245313.140.19
9.2000e+052491250917.900.26
9.4000e+052542256522.650.32
9.6000e+052588262032.400.46
9.8000e+052633267643.150.60
1.0000e+062682273249.900.69
1.0500e+062825287146.260.63
1.1000e+062971301139.590.53
1.1500e+063108315041.900.55
1.2000e+063257328932.170.41
1.2500e+063400342828.420.36
1.3000e+063538356829.640.37
1.3500e+063671370735.820.44
1.4000e+063811384634.960.42
1.4500e+063951398534.070.40
1.5000e+064088412436.140.42
1.5500e+064231426332.180.37
1.6000e+06439644026.170.07
1.6500e+064525454116.120.18
1.7000e+064653468027.030.30
1.7500e+064797481921.910.24
1.8000e+064934495823.740.25
1.8500e+065073509723.530.25
1.9000e+065216523519.280.20
1.9500e+065361537412.980.13
2.0000e+0655225513-9.35-0.10
2.1000e+0657905790-0.14-0.00
2.2000e+066056606710.900.11
2.3000e+066332634411.770.11
2.4000e+066602662018.490.18
2.5000e+066887689710.040.09
2.6000e+067161717312.430.11
2.7000e+067409745040.670.37
2.8000e+067698772627.740.25
2.9000e+067960800241.670.36
3.0000e+068227827750.430.43
3.1000e+068517855336.050.31
3.2000e+068793882935.520.30
3.3000e+069067910436.840.30
3.4000e+069323937956.020.46
3.5000e+069605965449.050.40
3.6000e+069856992972.940.58
3.7000e+06101391020464.700.51
3.8000e+06104291047849.310.38
3.9000e+06106981075354.790.42
4.0000e+06109671102760.140.46
4.1000e+06112651130136.350.27
4.2000e+06115481157527.430.20
4.3000e+0611841118498.390.06
4.4000e+0612115121238.220.06
4.5000e+0612394123972.920.02
4.6000e+06126491267021.500.15
4.7000e+061294412944-0.04-0.00
4.8000e+06132071321710.290.07
4.9000e+06134411349149.510.34
5.0000e+06136981376465.610.45
5.2000e+06142181430991.460.62
5.4000e+06147671485587.860.59
5.6000e+061528215400117.820.77
5.8000e+06158621594482.350.53
6.0000e+06164141648874.450.47
6.2000e+06169521703280.140.50
6.4000e+06175061757569.430.43
6.6000e+06180641811854.320.33
6.8000e+061855818661102.830.62
7.0000e+061907219203130.950.78
7.2000e+061963619745108.710.64
7.4000e+062015020286136.100.79
7.6000e+062069520827132.130.76
7.8000e+062118721368180.821.03
8.0000e+062174021908168.150.94
8.2000e+062228722448161.160.90
8.4000e+062284522988142.830.79
8.6000e+062341223527115.170.63
8.8000e+06239882406678.200.42
9.0000e+062450424605100.910.54
9.2000e+062500925143134.310.71
9.4000e+06255862568195.400.50
9.6000e+062610526219114.200.59
9.8000e+062659726757159.710.82
1.0000e+072717027294123.920.63
1.0500e+072849928636136.720.68
1.1000e+072983529976140.790.69
1.1500e+073117831314136.220.65
1.2000e+073250532651146.040.69
1.2500e+073383233986154.320.71
1.3000e+073521435320106.100.48
1.3500e+073652136652131.430.59
1.4000e+073785337983130.360.57
1.4500e+073914139313171.920.74
1.5000e+074050540641136.150.58
1.5500e+074176841968200.100.84
1.6000e+074314843294145.790.60
1.6500e+074442544618193.260.79
1.7000e+074576545942176.540.71
1.7500e+074710447264159.660.64
1.8000e+074841748585167.640.66
1.8500e+074973049905174.520.68
1.9000e+075105451223169.310.65
1.9500e+075236052541181.050.69
2.0000e+075367553858182.750.69
2.1000e+075629156488197.150.73
2.2000e+075896459115150.660.54
2.3000e+076149861737239.440.85
2.4000e+076406964357287.631.00
2.5000e+076673866972234.360.80
2.6000e+076933569585249.760.84
2.7000e+077205772194136.930.45
2.8000e+07747007480099.990.32
2.9000e+07773737740330.020.10
3.0000e+07799678000336.130.11
3.1000e+07825858260015.400.05
3.2000e+078524985195-54.09-0.17
3.3000e+078786987787-82.26-0.25
3.4000e+079045590376-79.04-0.24
3.5000e+079306992963-106.36-0.31
3.6000e+079563395547-86.15-0.25
3.7000e+079816798129-38.35-0.11
3.8000e+07100818100708-109.91-0.31
3.9000e+07103390103285-104.76-0.29
4.0000e+07105919105860-58.85-0.16
4.1000e+0710841310843319.860.05
4.2000e+07111036111003-32.57-0.09
4.3000e+07113601113572-29.10-0.08
4.4000e+07116232116138-93.67-0.25
4.5000e+07118819118703-116.26-0.31
4.6000e+07121412121265-146.82-0.38
4.7000e+07123980123826-154.30-0.40
4.8000e+07126650126384-265.68-0.68
4.9000e+07129106128941-164.91-0.42
5.0000e+07131723131496-226.96-0.57
5.2000e+07136747136601-146.39-0.36
5.4000e+07141908141698-209.72-0.51
5.6000e+07147026146789-236.69-0.56
5.8000e+07152158151874-284.11-0.67
6.0000e+07157208156952-255.75-0.59
6.2000e+07162288162025-263.42-0.60
6.4000e+07167412167091-320.95-0.72
6.6000e+07172491172152-339.16-0.75
6.8000e+07177586177207-378.89-0.83
7.0000e+07182594182257-336.99-0.73
7.2000e+07187622187302-320.31-0.68
7.4000e+07192682192341-340.72-0.72
7.6000e+07197723197376-347.09-0.72
7.8000e+07202806202406-400.29-0.82
8.0000e+07207737207431-306.21-0.62
8.2000e+07212748212451-296.73-0.60
8.4000e+07217781217467-313.75-0.62
8.6000e+07222887222479-408.17-0.80
8.8000e+07227867227486-380.89-0.74
9.0000e+07232799232489-309.82-0.60
9.2000e+07237779237488-290.87-0.56
9.4000e+07242788242483-304.95-0.58
9.6000e+07247695247474-220.98-0.41
9.8000e+07252605252461-143.88-0.27
1.0000e+08257548257444-103.59-0.19
1.0500e+08270089269887-202.49-0.36
1.1000e+08282437282306-130.62-0.23
1.1500e+08294956294705-251.02-0.43
1.2000e+08307399307083-315.78-0.54
1.2500e+08319781319442-339.10-0.57
1.3000e+08331961331782-179.23-0.29
1.3500e+08344264344104-160.45-0.26
1.4000e+08356557356408-149.13-0.24
1.4500e+08368843368695-147.67-0.23
1.5000e+08381028380967-61.49-0.09
1.5500e+08393319393222-97.08-0.15
1.6000e+08405552405462-89.94-0.13
1.6500e+08417756417687-68.61-0.10
1.7000e+08430088429898-189.65-0.28
1.7500e+08442346442095-250.64-0.36
1.8000e+08454618454279-339.21-0.48
1.8500e+08466762466449-312.98-0.44
1.9000e+08478900478606-293.60-0.41
1.9500e+08491155490751-403.75-0.55
2.0000e+08503402502884-518.12-0.70
2.1000e+08527499527114-385.29-0.51
2.2000e+08551828551298-529.90-0.69
2.3000e+08576123575439-683.93-0.87
2.4000e+08600101599538-562.52-0.70
2.5000e+08624093623598-494.96-0.61
2.6000e+08647971647619-351.70-0.42
2.7000e+08671968671604-364.27-0.43
2.8000e+08695915695553-362.34-0.42
2.9000e+08720013719467-545.64-0.62
3.0000e+08743753743349-404.02-0.46
3.1000e+08767574767199-375.39-0.42
3.2000e+08791268791017-250.72-0.27
3.3000e+08815081814806-275.06-0.30
3.4000e+08838826838565-260.51-0.28
3.5000e+08862489862297-192.21-0.20
3.6000e+08886256886001-255.37-0.27
3.7000e+08909711909678-33.23-0.03
3.8000e+08933479933329-150.07-0.15
3.9000e+08957026956955-71.21-0.07
4.0000e+08980691980556-135.02-0.13
4.1000e+0810044191004133-285.86-0.28
4.2000e+0810279211027687-234.17-0.23
4.3000e+0810515261051218-308.39-0.30
4.4000e+0810748561074726-129.97-0.12
4.5000e+081098163109821349.570.05
4.6000e+0811214841121678193.730.18
4.7000e+0811449721145122149.980.14
4.8000e+0811683741168546171.750.16
4.9000e+081191874119194975.470.07
5.0000e+0812154501215334-116.45-0.10
5.2000e+0812621861262044-141.66-0.12
5.4000e+0813088111308681-129.90-0.11
5.6000e+0813555241355247-277.45-0.24
5.8000e+0814022921401743-548.74-0.46
6.0000e+0814489581448174-784.40-0.65
6.2000e+0814951171494540-577.21-0.47
6.4000e+0815414691540844-625.10-0.50
6.6000e+0815872701587088-182.12-0.14
6.8000e+0816333981633274-124.44-0.10
7.0000e+0816796821679403-279.33-0.22
7.2000e+0817259551725477-478.17-0.36
7.4000e+0817719971771498-499.42-0.37
7.6000e+0818181091817466-642.64-0.48
7.8000e+0818643071863385-922.44-0.68
8.0000e+0819103451909253-1091.52-0.79
8.2000e+0819563661955074-1291.63-0.93
8.4000e+0820020982000848-1249.60-0.89
8.6000e+0820478132046577-1236.30-0.87
8.8000e+0820937602092260-1499.65-1.04
9.0000e+0821395302137900-1629.64-1.12
9.2000e+0821850872183498-1589.29-1.08
9.4000e+0822309652229053-1911.65-1.29
9.6000e+0822764322274568-1863.83-1.24
9.8000e+0823222032320043-2159.97-1.43
1.0000e+0923674742365479-1995.25-1.31
1.0500e+0924810092478902-2107.06-1.35
1.1000e+0925944472592097-2350.06-1.48
1.1500e+0927073502705074-2275.74-1.40
1.2000e+0928200682817843-2224.52-1.34
1.2500e+0929326622930413-2248.59-1.33
1.3000e+0930448543042792-2061.89-1.20
1.3500e+0931566543154987-1666.93-0.95
1.4000e+0932688773267005-1871.81-1.05
1.4500e+0933805073378853-1654.11-0.92
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