Gap size : 8 (r=4)

Generated by program gapCounts : Mon Jun 27 12:28:15 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+0210-0.91-0.42
2.0000e+02110.460.17
3.0000e+02131.840.61
4.0000e+02341.190.36
5.0000e+0276-1.48-0.41
6.0000e+0277-0.17-0.05
7.0000e+02880.110.03
8.0000e+02129-2.64-0.62
9.0000e+021211-1.40-0.32
1.0000e+031512-3.17-0.69
1.1000e+031513-1.97-0.42
1.2000e+031714-2.77-0.57
1.3000e+031815-2.59-0.52
1.4000e+031917-2.42-0.47
1.5000e+032018-2.27-0.43
1.6000e+032319-4.12-0.76
1.7000e+032320-2.98-0.54
1.8000e+032421-2.85-0.50
1.9000e+032522-2.73-0.47
2.0000e+032623-2.62-0.45
2.1000e+032724-2.52-0.42
2.2000e+032826-2.42-0.40
2.3000e+033127-4.33-0.70
2.4000e+033128-3.25-0.52
2.5000e+033229-3.17-0.50
2.6000e+033330-3.10-0.48
2.7000e+033531-4.03-0.61
2.8000e+033732-4.97-0.75
2.9000e+033933-5.92-0.88
3.0000e+034034-5.87-0.86
3.1000e+034235-6.82-0.99
3.2000e+034236-5.78-0.83
3.3000e+034437-6.75-0.95
3.4000e+034438-5.72-0.80
3.5000e+034639-6.69-0.92
3.6000e+034640-5.67-0.77
3.7000e+034741-5.65-0.76
3.8000e+034942-6.64-0.89
3.9000e+035043-6.63-0.88
4.0000e+035044-5.62-0.74
4.1000e+035045-4.62-0.60
4.2000e+035046-3.62-0.47
4.3000e+035147-3.62-0.46
4.4000e+035248-3.63-0.46
4.5000e+035249-2.64-0.33
4.6000e+035350-2.65-0.33
4.7000e+035351-1.67-0.21
4.8000e+035452-1.68-0.21
4.9000e+035453-0.71-0.09
5.0000e+035554-0.73-0.09
5.2000e+035856-1.79-0.21
5.4000e+0358580.140.02
5.6000e+0360600.060.01
5.8000e+036262-0.03-0.00
6.0000e+0363640.880.10
6.2000e+036666-0.23-0.03
6.4000e+037068-2.35-0.26
6.6000e+037270-2.47-0.27
6.8000e+037371-1.60-0.17
7.0000e+037673-2.74-0.29
7.2000e+037875-2.89-0.30
7.4000e+037977-2.04-0.21
7.6000e+038179-2.20-0.23
7.8000e+038381-2.37-0.24
8.0000e+038482-1.55-0.16
8.2000e+038684-1.73-0.17
8.4000e+038786-0.92-0.09
8.6000e+038988-1.11-0.11
8.8000e+039390-3.31-0.32
9.0000e+039491-2.52-0.24
9.2000e+039693-2.73-0.26
9.4000e+039795-1.95-0.18
9.6000e+039897-1.17-0.11
9.8000e+039999-0.40-0.04
1.0000e+04101100-0.63-0.06
1.0500e+04107105-2.23-0.20
1.1000e+04113109-3.86-0.34
1.1500e+04116113-2.52-0.22
1.2000e+04120118-2.21-0.19
1.2500e+04127122-4.92-0.42
1.3000e+04134126-7.66-0.64
1.3500e+04139131-8.42-0.69
1.4000e+04143135-8.20-0.66
1.4500e+04145139-6.00-0.48
1.5000e+04152143-8.82-0.69
1.5500e+04158147-10.67-0.83
1.6000e+04161151-9.53-0.73
1.6500e+04162156-6.40-0.48
1.7000e+04164160-4.30-0.32
1.7500e+04171164-7.21-0.53
1.8000e+04172168-4.14-0.30
1.8500e+04176172-4.09-0.30
1.9000e+04178176-2.05-0.15
1.9500e+04182180-2.02-0.14
2.0000e+04186184-2.01-0.14
2.1000e+04194192-2.03-0.14
2.2000e+04203200-3.10-0.21
2.3000e+04208208-0.22-0.01
2.4000e+04216216-0.39-0.03
2.5000e+04226223-2.60-0.17
2.6000e+04233231-1.86-0.12
2.7000e+04243239-4.16-0.26
2.8000e+04248247-1.49-0.09
2.9000e+04257254-2.87-0.17
3.0000e+04264262-2.27-0.14
3.1000e+04271269-1.72-0.10
3.2000e+04280277-3.19-0.19
3.3000e+042842840.300.02
3.4000e+04296292-4.24-0.24
3.5000e+04301299-1.81-0.10
3.6000e+043053071.590.09
3.7000e+04315314-1.04-0.06
3.8000e+04324321-2.69-0.15
3.9000e+04330329-1.37-0.07
4.0000e+04345336-9.07-0.48
4.1000e+04351343-7.80-0.41
4.2000e+04359350-8.55-0.44
4.3000e+04370358-12.33-0.63
4.4000e+04376365-11.13-0.57
4.5000e+04387372-14.95-0.76
4.6000e+04394379-14.79-0.74
4.7000e+04399386-12.65-0.63
4.8000e+04408393-14.54-0.72
4.9000e+04413401-12.44-0.61
5.0000e+04417408-9.36-0.45
5.2000e+04429422-7.26-0.35
5.4000e+04443436-7.24-0.34
5.6000e+04461450-11.28-0.52
5.8000e+04478464-14.39-0.66
6.0000e+04499477-21.56-0.97
6.2000e+04516491-24.79-1.10
6.4000e+04530505-25.09-1.10
6.6000e+04543519-24.43-1.06
6.8000e+04561532-28.84-1.23
7.0000e+04573546-27.29-1.15
7.2000e+04588559-28.80-1.20
7.4000e+04600573-27.35-1.13
7.6000e+04612586-25.96-1.06
7.8000e+04624599-24.61-0.99
8.0000e+04640613-27.30-1.09
8.2000e+04652626-26.04-1.03
8.4000e+04662639-22.82-0.89
8.6000e+04672652-19.64-0.76
8.8000e+04691665-25.50-0.98
9.0000e+04702679-23.40-0.89
9.2000e+04717692-25.34-0.95
9.4000e+04734705-29.32-1.09
9.6000e+04749718-31.33-1.16
9.8000e+04761731-30.37-1.12
1.0000e+05773744-29.45-1.07
1.0500e+05801776-25.30-0.90
1.1000e+05837808-29.34-1.03
1.1500e+05867839-27.57-0.95
1.2000e+05897871-25.98-0.88
1.2500e+05928902-25.56-0.85
1.3000e+05962934-28.30-0.92
1.3500e+05991965-26.19-0.84
1.4000e+051025996-29.22-0.93
1.4500e+0510521027-25.40-0.79
1.5000e+0510801057-22.72-0.70
1.5500e+0511091088-21.16-0.64
1.6000e+0511441118-25.73-0.77
1.6500e+0511771149-28.42-0.84
1.7000e+0512151179-36.22-1.06
1.7500e+0512541209-45.14-1.30
1.8000e+0512781239-39.17-1.12
1.8500e+0512981269-29.30-0.83
1.9000e+0513321298-33.53-0.93
1.9500e+0513691328-40.86-1.13
2.0000e+0513911358-33.28-0.91
2.1000e+0514531417-36.41-0.97
2.2000e+0515131475-37.89-0.99
2.3000e+0515701533-36.69-0.94
2.4000e+0516221591-30.82-0.78
2.5000e+0516811649-32.24-0.80
2.6000e+0517431706-36.94-0.90
2.7000e+0517981763-34.92-0.84
2.8000e+0518631820-43.16-1.02
2.9000e+0519211876-44.65-1.04
3.0000e+0519811933-48.38-1.11
3.1000e+0520411989-52.34-1.19
3.2000e+0520982044-53.52-1.20
3.3000e+0521452100-44.91-0.99
3.4000e+0522012155-45.51-0.99
3.5000e+0522582211-47.31-1.02
3.6000e+0523142266-48.30-1.03
3.7000e+0523722321-51.48-1.09
3.8000e+0524342375-58.84-1.23
3.9000e+0524722430-42.37-0.87
4.0000e+0525212484-37.07-0.76
4.1000e+0525782538-39.93-0.81
4.2000e+0526262592-33.96-0.68
4.3000e+0526702646-24.14-0.48
4.4000e+0527382700-38.47-0.75
4.5000e+0528112753-57.95-1.12
4.6000e+0528592806-52.57-1.01
4.7000e+0529092860-49.33-0.94
4.8000e+0529792913-66.22-1.25
4.9000e+0530362966-70.25-1.31
5.0000e+0530813019-62.41-1.16
5.2000e+0531783124-54.11-0.99
5.4000e+0532803229-51.29-0.92
5.6000e+0533873333-53.93-0.95
5.8000e+0534903437-53.02-0.92
6.0000e+0535793540-38.53-0.66
6.2000e+0536933644-49.45-0.84
6.4000e+0537873746-40.76-0.68
6.6000e+0538903849-41.46-0.68
6.8000e+0539893950-38.52-0.63
7.0000e+0540794052-26.93-0.43
7.2000e+0541874153-33.69-0.54
7.4000e+0542924254-37.77-0.59
7.6000e+0543824355-27.18-0.42
7.8000e+0544784455-22.90-0.35
8.0000e+0545884555-32.92-0.50
8.2000e+0547074655-52.23-0.79
8.4000e+0548064754-51.82-0.77
8.6000e+0548984853-44.69-0.66
8.8000e+0550034952-50.83-0.74
9.0000e+0551015051-50.24-0.73
9.2000e+0551965149-46.89-0.67
9.4000e+0552905247-42.80-0.61
9.6000e+0553795345-33.95-0.48
9.8000e+0554695443-26.33-0.37
1.0000e+0655695540-28.95-0.40
1.0500e+0658205783-37.46-0.51
1.1000e+0660706024-46.31-0.61
1.1500e+0663086264-44.41-0.58
1.2000e+0665626502-59.72-0.76
1.2500e+0668226740-82.16-1.03
1.3000e+0670696976-92.69-1.14
1.3500e+0673027212-90.27-1.10
1.4000e+0675477446-100.83-1.21
1.4500e+0677887680-108.35-1.28
1.5000e+0680227912-109.78-1.27
1.5500e+0682538144-109.09-1.25
1.6000e+0684838375-108.25-1.22
1.6500e+0687068605-101.22-1.13
1.7000e+0689358834-100.98-1.11
1.7500e+0691579063-94.50-1.03
1.8000e+0693679290-76.75-0.82
1.8500e+0695859517-67.72-0.72
1.9000e+0698209744-76.38-0.80
1.9500e+06100419969-71.70-0.74
2.0000e+061028010194-85.67-0.88
2.1000e+061071110643-68.48-0.69
2.2000e+061117311088-84.68-0.83
2.3000e+061159611532-64.12-0.62
2.4000e+061203911973-65.71-0.62
2.5000e+061249512413-82.34-0.77
2.6000e+061294312850-92.91-0.85
2.7000e+061337313286-87.33-0.79
2.8000e+061381713719-97.54-0.87
2.9000e+061423914152-87.45-0.76
3.0000e+061468714582-104.99-0.90
3.1000e+061510215011-91.11-0.77
3.2000e+061552415438-85.75-0.72
3.3000e+061597915864-114.84-0.95
3.4000e+061639416289-105.34-0.86
3.5000e+061678616712-74.21-0.60
3.6000e+061719417134-60.38-0.48
3.7000e+061758617554-31.84-0.25
3.8000e+06179621797311.470.09
3.9000e+06183741839217.590.14
4.0000e+0618804188094.550.03
4.1000e+0619222192242.370.02
4.2000e+0619637196392.100.02
4.3000e+06200422005310.770.08
4.4000e+06204432046522.400.16
4.5000e+06208602087717.020.12
4.6000e+06212632128824.650.18
4.7000e+06216612169736.330.26
4.8000e+06220772210629.070.20
4.9000e+06224962251417.890.12
5.0000e+06229082292112.830.09
5.2000e+062375723732-24.90-0.17
5.4000e+062457724540-36.96-0.25
5.6000e+062535025345-5.20-0.03
5.8000e+06261032614643.490.28
6.0000e+06269152694530.250.19
6.2000e+06277082774133.190.21
6.4000e+06285042853430.400.19
6.6000e+06292762932549.000.30
6.8000e+06300943011319.060.12
7.0000e+06308713089927.680.16
7.2000e+06316403168241.940.25
7.4000e+06324323246330.910.18
7.6000e+06331993324242.660.25
7.8000e+06339953401823.260.13
8.0000e+06347513479341.780.23
8.2000e+06355543556511.260.06
8.4000e+06363163633619.780.11
8.6000e+06370873710417.390.09
8.8000e+0637865378716.120.03
9.0000e+06385913863645.050.24
9.2000e+06393773939922.200.12
9.4000e+06401064016154.630.29
9.6000e+06408724092048.370.25
9.8000e+06415974167881.480.42
1.0000e+07423524243582.980.42
1.0500e+0744315443194.440.02
1.1000e+074621746195-22.36-0.11
1.1500e+074811348061-51.94-0.25
1.2000e+074997849919-58.86-0.28
1.2500e+075179551769-25.73-0.12
1.3000e+075367553612-63.18-0.29
1.3500e+075548055447-32.87-0.15
1.4000e+075735957275-83.51-0.37
1.4500e+075917159097-73.79-0.32
1.5000e+076099660913-83.47-0.36
1.5500e+076279362722-71.30-0.30
1.6000e+076454864525-23.04-0.10
1.6500e+076638366323-60.50-0.25
1.7000e+076816068115-45.46-0.18
1.7500e+076998769901-85.75-0.34
1.8000e+077177171683-88.19-0.35
1.8500e+077346773459-7.61-0.03
1.9000e+077526075231-28.87-0.11
1.9500e+077705976998-60.81-0.23
2.0000e+077879278761-31.31-0.12
2.1000e+078232382273-50.42-0.19
2.2000e+078587085768-102.26-0.37
2.3000e+078937389247-125.94-0.45
2.4000e+079285092711-138.69-0.48
2.5000e+079637496161-212.79-0.72
2.6000e+079976799597-169.57-0.57
2.7000e+07103188103021-167.44-0.55
2.8000e+07106593106431-161.85-0.52
2.9000e+07109944109830-114.28-0.36
3.0000e+07113368113217-151.26-0.48
3.1000e+07116741116593-148.35-0.46
3.2000e+07120125119958-167.14-0.51
3.3000e+07123486123313-173.25-0.52
3.4000e+07126777126658-119.32-0.35
3.5000e+0712998012999312.980.04
3.6000e+0713330813331910.970.03
3.7000e+07136500136636135.940.39
3.8000e+07139791139944153.160.43
3.9000e+07143135143244108.910.30
4.0000e+071465291465356.430.02
4.1000e+07149821149819-2.05-0.01
4.2000e+07153105153095-10.30-0.03
4.3000e+07156438156363-75.11-0.20
4.4000e+07159704159624-80.29-0.21
4.5000e+07162969162877-91.63-0.24
4.6000e+07166251166124-126.96-0.33
4.7000e+07169422169364-58.11-0.15
4.8000e+07172618172597-20.91-0.05
4.9000e+0717579217582431.790.08
5.0000e+07179048179044-3.84-0.01
5.2000e+07185619185466-152.56-0.38
5.4000e+07192007191865-141.99-0.34
5.6000e+07198390198241-149.13-0.36
5.8000e+07204807204595-212.06-0.50
6.0000e+07211185210928-256.91-0.59
6.2000e+07217550217241-308.91-0.70
6.4000e+07223879223535-344.30-0.77
6.6000e+07230159229810-349.40-0.77
6.8000e+07236439236066-372.56-0.81
7.0000e+07242713242306-407.18-0.88
7.2000e+07248875248528-346.70-0.74
7.4000e+07255006254734-271.57-0.57
7.6000e+07261241260925-316.30-0.66
7.8000e+07267244267100-144.41-0.30
8.0000e+07273384273260-124.45-0.25
8.2000e+07279724279405-319.00-0.64
8.4000e+07285916285536-379.66-0.76
8.6000e+07291930291654-276.04-0.54
8.8000e+07298036297758-277.79-0.54
9.0000e+07304078303849-228.55-0.44
9.2000e+07310030309928-102.00-0.19
9.4000e+07316011315994-16.82-0.03
9.6000e+07322196322048-147.72-0.28
9.8000e+07328208328091-117.41-0.22
1.0000e+08334180334121-58.62-0.11
1.0500e+0834911834915031.670.06
1.1000e+0836408936411122.390.04
1.1500e+08378883379010126.970.22
1.2000e+08393615393849233.520.40
1.2500e+08408423408630206.870.34
1.3000e+08423163423357193.630.32
1.3500e+08437875438031156.170.25
1.4000e+08452429452656226.680.36
1.4500e+08466983467232249.180.39
1.5000e+08481421481763341.560.53
1.5500e+08496004496249244.560.37
1.6000e+08510489510692202.790.30
1.6500e+08524957525094136.770.20
1.7000e+08539127539456328.920.48
1.7500e+08553464553780315.550.45
1.8000e+08567812568066253.930.36
1.8500e+0858224158231675.220.11
1.9000e+08596417596532114.520.16
1.9500e+0861063561071377.880.11
2.0000e+08624743624861118.270.16
2.1000e+08652818653063244.880.32
2.2000e+08680887681143256.230.33
2.3000e+08708896709109212.560.27
2.4000e+0873687873696586.520.11
2.5000e+0876463376471683.260.10
2.6000e+08792166792368202.490.24
2.7000e+08819689819926236.530.28
2.8000e+08847027847391364.370.42
2.9000e+08874196874770573.680.66
3.0000e+08901672902064391.880.44
3.1000e+08928846929277431.120.48
3.2000e+08956011956412401.370.44
3.3000e+08983133983472339.370.37
3.4000e+0810101801010460279.690.30
3.5000e+0810370601037377316.760.33
3.6000e+0810639861064226239.820.25
3.7000e+0810906101091009399.030.41
3.8000e+0811173451117728383.370.39
3.9000e+0811441881144386197.760.20
4.0000e+0811709881170983-5.02-0.00
4.1000e+0811976071197522-85.27-0.08
4.2000e+0812241341224004-130.37-0.13
4.3000e+0812506831250430-252.82-0.24
4.4000e+0812768711276803-68.14-0.06
4.5000e+0813031951303123-71.96-0.07
4.6000e+081329368132939224.030.02
4.7000e+0813557111355611-99.91-0.09
4.8000e+0813816681381781113.410.10
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