Gap size : 10 (r=5)

Generated by program gapCounts : Mon Jun 27 12:28:17 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+02000.120.05
2.0000e+0222-0.39-0.14
3.0000e+0243-0.82-0.27
4.0000e+0255-0.25-0.07
5.0000e+0276-0.69-0.19
6.0000e+0298-1.16-0.30
7.0000e+02109-0.65-0.16
8.0000e+021311-2.16-0.51
9.0000e+021512-2.68-0.61
1.0000e+031614-2.22-0.48
1.1000e+031915-3.77-0.80
1.2000e+032117-4.34-0.89
1.3000e+032218-3.92-0.78
1.4000e+032219-2.52-0.49
1.5000e+032421-3.12-0.59
1.6000e+032422-1.74-0.32
1.7000e+032524-1.36-0.25
1.8000e+032725-2.00-0.35
1.9000e+032926-2.64-0.46
2.0000e+032928-1.30-0.22
2.1000e+033329-3.96-0.66
2.2000e+033430-3.63-0.59
2.3000e+033432-2.30-0.37
2.4000e+033433-0.98-0.16
2.5000e+0334340.330.05
2.6000e+0335360.630.10
2.7000e+0336370.930.14
2.8000e+033938-0.78-0.12
2.9000e+034040-0.50-0.07
3.0000e+034141-0.22-0.03
3.1000e+0342420.060.01
3.2000e+0343430.330.05
3.3000e+0343451.590.22
3.4000e+0344461.850.26
3.5000e+0344473.110.43
3.6000e+0348480.360.05
3.7000e+0348501.610.22
3.8000e+0350510.850.11
3.9000e+0352520.090.01
4.0000e+0352531.320.17
4.1000e+0352552.550.33
4.2000e+0352563.770.49
4.3000e+035857-1.00-0.13
4.4000e+036158-2.78-0.35
4.5000e+036259-2.57-0.32
4.6000e+036261-1.36-0.17
4.7000e+036362-1.15-0.14
4.8000e+0363630.050.01
4.9000e+0364640.260.03
5.0000e+036665-0.55-0.07
5.2000e+036868-0.16-0.02
5.4000e+0369701.220.14
5.6000e+0370732.580.30
5.8000e+0372752.930.33
6.0000e+0374773.280.37
6.2000e+0379800.610.07
6.4000e+038482-2.07-0.23
6.6000e+038684-1.76-0.19
6.8000e+039087-3.45-0.37
7.0000e+039289-3.16-0.33
7.2000e+039491-2.87-0.30
7.4000e+039793-3.59-0.37
7.6000e+0310096-4.32-0.44
7.8000e+0310098-2.06-0.21
8.0000e+031001000.200.02
8.2000e+031021020.440.04
8.4000e+03106105-1.32-0.13
8.6000e+03108107-1.08-0.11
8.8000e+031091090.140.01
9.0000e+03112111-0.64-0.06
9.2000e+031131140.580.05
9.4000e+031141161.780.17
9.6000e+031171180.990.09
9.8000e+031181202.180.20
1.0000e+041191223.370.31
1.0500e+041241283.820.34
1.1000e+041281335.230.46
1.1500e+041341394.610.40
1.2000e+041381445.970.51
1.2500e+041411498.290.70
1.3000e+041461558.580.71
1.3500e+041501609.850.81
1.4000e+041571658.090.65
1.4500e+041631707.310.58
1.5000e+0416517610.500.82
1.5500e+041751815.680.44
1.6000e+041791866.830.52
1.6500e+041811919.960.75
1.7000e+0418219614.061.05
1.7500e+0418520116.151.19
1.8000e+0419320613.220.97
1.8500e+0419621115.281.10
1.9000e+0420021616.311.17
1.9500e+0420322118.331.30
2.0000e+0421122615.331.07
2.1000e+0421923617.281.19
2.2000e+0423024616.171.09
2.3000e+0423925617.001.13
2.4000e+0424726618.781.22
2.5000e+0425627619.511.25
2.6000e+0426328522.181.40
2.7000e+0427429520.811.29
2.8000e+0427830426.391.61
2.9000e+0428731426.921.62
3.0000e+0429532328.421.69
3.1000e+0430433328.871.70
3.2000e+0431434228.291.64
3.3000e+0432035231.661.81
3.4000e+0433136130.001.70
3.5000e+0434237028.311.58
3.6000e+0435138028.581.58
3.7000e+0436338925.811.41
3.8000e+0437639822.021.19
3.9000e+0438340724.191.30
4.0000e+0439741619.341.02
4.1000e+0440242523.451.23
4.2000e+0441243522.541.17
4.3000e+0442444419.601.01
4.4000e+0443345319.631.00
4.5000e+0444046221.641.09
4.6000e+0445147119.620.98
4.7000e+0446148018.580.92
4.8000e+0447348915.510.76
4.9000e+0448149716.420.80
5.0000e+0448950617.300.84
5.2000e+0450552419.010.91
5.4000e+0451754224.621.15
5.6000e+0453255927.161.25
5.8000e+0455757719.610.89
6.0000e+0457559418.990.85
6.2000e+0459061121.300.94
6.4000e+0461062918.540.81
6.6000e+0462964616.710.72
6.8000e+0465066312.810.55
7.0000e+0466468015.850.67
7.2000e+0468169715.830.66
7.4000e+0469771416.750.69
7.6000e+0471073120.610.84
7.8000e+0472574722.420.90
8.0000e+0474376421.180.85
8.2000e+0476178119.880.79
8.4000e+0477979818.530.72
8.6000e+0479481420.130.78
8.8000e+0481183119.680.76
9.0000e+0482784720.190.77
9.2000e+0484186422.650.85
9.4000e+0486088020.070.75
9.6000e+0487989617.440.65
9.8000e+0489991313.780.51
1.0000e+0591692913.070.48
1.0500e+0595597014.620.52
1.1000e+05999101010.930.38
1.1500e+051034105016.020.55
1.2000e+05108410905.890.20
1.2500e+0511311130-1.44-0.05
1.3000e+0511721169-2.96-0.10
1.3500e+05120412084.330.14
1.4000e+05124312474.440.14
1.4500e+05128612860.380.01
1.5000e+0513281325-2.84-0.09
1.5500e+0513651364-1.22-0.04
1.6000e+0514071402-4.75-0.14
1.6500e+0514481441-7.42-0.22
1.7000e+05147414794.760.14
1.7500e+05151115175.810.17
1.8000e+05155015554.730.13
1.8500e+0515931593-0.49-0.01
1.9000e+0516371630-6.82-0.19
1.9500e+0516721668-4.27-0.12
2.0000e+05170517050.160.00
2.1000e+0517911780-11.31-0.30
2.2000e+0518691854-15.21-0.40
2.3000e+0519471927-19.51-0.50
2.4000e+0520332001-32.20-0.81
2.5000e+0521092074-35.24-0.88
2.6000e+0521762146-29.64-0.72
2.7000e+0522602219-41.36-1.00
2.8000e+0523352291-44.41-1.05
2.9000e+0524062362-43.76-1.02
3.0000e+0524792434-45.40-1.05
3.1000e+0525512505-46.32-1.05
3.2000e+0526142575-38.51-0.86
3.3000e+0526872646-40.96-0.91
3.4000e+0527452716-28.67-0.63
3.5000e+0528102786-23.61-0.51
3.6000e+0528742856-17.79-0.38
3.7000e+0529402926-14.20-0.30
3.8000e+0530142995-18.83-0.39
3.9000e+0530843064-19.67-0.41
4.0000e+0531393133-5.72-0.12
4.1000e+0532033202-0.97-0.02
4.2000e+05326832712.580.05
4.3000e+05333733391.940.04
4.4000e+0534123407-4.88-0.10
4.5000e+0534823475-6.88-0.13
4.6000e+0535623543-19.05-0.37
4.7000e+0536363611-25.40-0.48
4.8000e+0537053678-26.91-0.51
4.9000e+0537823745-36.59-0.68
5.0000e+0538423813-29.43-0.55
5.2000e+0539883946-41.56-0.76
5.4000e+0541184080-38.29-0.69
5.6000e+0542474212-34.58-0.61
5.8000e+0543764345-31.42-0.55
6.0000e+0544904476-13.78-0.24
6.2000e+0546254607-17.65-0.30
6.4000e+0547544738-15.99-0.27
6.6000e+0548894868-20.81-0.34
6.8000e+0550144998-16.07-0.26
7.0000e+0551635127-35.77-0.58
7.2000e+0552995256-42.89-0.68
7.4000e+0554195385-34.42-0.54
7.6000e+0555395513-26.34-0.41
7.8000e+0556935640-52.64-0.81
8.0000e+0558165768-48.31-0.73
8.2000e+0559595895-64.35-0.97
8.4000e+0560896021-67.73-1.01
8.6000e+0562046148-56.45-0.83
8.8000e+0563406273-66.51-0.97
9.0000e+0564666399-66.88-0.97
9.2000e+0565886524-63.57-0.91
9.4000e+0567116649-61.57-0.87
9.6000e+0568266774-51.87-0.73
9.8000e+0569596899-60.45-0.84
1.0000e+0670797023-56.33-0.78
1.0500e+0673817332-49.21-0.67
1.1000e+0676867639-46.73-0.62
1.1500e+0679717945-25.82-0.34
1.2000e+0682698250-19.38-0.25
1.2500e+0685868553-33.35-0.42
1.3000e+0688758854-20.66-0.26
1.3500e+0691659155-10.26-0.12
1.4000e+06945194542.920.03
1.4500e+0697599752-7.08-0.08
1.5000e+061007810049-29.21-0.34
1.5500e+061038910345-44.43-0.51
1.6000e+061066410639-24.70-0.28
1.6500e+061095110933-17.98-0.20
1.7000e+061123411226-8.23-0.09
1.7500e+061152211518-4.42-0.05
1.8000e+061181411808-5.52-0.06
1.8500e+06120831209815.500.16
1.9000e+0612386123881.660.02
1.9500e+0612671126765.000.05
2.0000e+061296712964-3.47-0.04
2.1000e+061354513536-8.72-0.09
2.2000e+061410814106-1.92-0.02
2.3000e+061469114673-17.92-0.17
2.4000e+061525015237-12.57-0.12
2.5000e+06157781579921.240.20
2.6000e+06163471635911.650.11
2.7000e+06168981691617.740.16
2.8000e+06174161747154.630.48
2.9000e+06179861802337.410.33
3.0000e+06185371857437.150.32
3.1000e+06190831912339.930.34
3.2000e+06196431967026.840.22
3.3000e+0620214202150.920.01
3.4000e+062078720758-28.74-0.23
3.5000e+0621295213004.900.04
3.6000e+06218292184010.910.09
3.7000e+0622374223784.330.03
3.8000e+0622909229156.220.05
3.9000e+0623444234516.610.05
4.0000e+062399523985-10.43-0.08
4.1000e+0624511245176.110.05
4.2000e+06250262504822.300.17
4.3000e+06255382557840.150.30
4.4000e+06260822610724.720.18
4.5000e+0626626266348.020.06
4.6000e+062718027160-19.90-0.14
4.7000e+062769927685-14.01-0.10
4.8000e+062823528209-26.29-0.18
4.9000e+062875228731-20.71-0.14
5.0000e+062927529253-22.24-0.15
5.2000e+063031930292-26.54-0.18
5.4000e+063137231328-43.99-0.29
5.6000e+063239032360-30.41-0.20
5.8000e+063338833387-0.65-0.00
6.0000e+063444434411-32.56-0.21
6.2000e+063545035432-17.99-0.11
6.4000e+063645036449-0.81-0.01
6.6000e+0637457374636.100.04
6.8000e+063847638474-2.15-0.01
7.0000e+063951439482-32.46-0.19
7.2000e+064051840486-31.71-0.19
7.4000e+064155141488-62.83-0.37
7.6000e+064256642487-78.71-0.45
7.8000e+064353143484-47.28-0.27
8.0000e+064453744478-59.46-0.33
8.2000e+064554345469-74.17-0.41
8.4000e+064650746458-49.34-0.27
8.6000e+064750747444-62.91-0.34
8.8000e+064850048428-71.80-0.39
9.0000e+064955949410-148.97-0.80
9.2000e+065050550390-115.35-0.61
9.4000e+065152551367-157.89-0.83
9.6000e+065246252342-119.54-0.62
9.8000e+065348353316-167.23-0.86
1.0000e+075443154287-143.94-0.73
1.0500e+075684456707-137.19-0.68
1.1000e+075925459115-139.03-0.68
1.1500e+076170761512-194.86-0.93
1.2000e+076414763899-248.15-1.17
1.2500e+076650666276-230.38-1.06
1.3000e+076893668643-293.10-1.33
1.3500e+077122471001-222.91-1.00
1.4000e+077354573351-194.41-0.85
1.4500e+077581675692-124.25-0.54
1.5000e+077818378025-158.10-0.67
1.5500e+078046280350-111.66-0.47
1.6000e+078277882668-109.64-0.45
1.6500e+078512884979-148.78-0.61
1.7000e+078745087283-166.83-0.67
1.7500e+078974589580-164.56-0.66
1.8000e+079205691871-184.75-0.73
1.8500e+079431694156-160.20-0.62
1.9000e+079668696434-251.71-0.97
1.9500e+079894098707-233.10-0.89
2.0000e+07101198100974-224.21-0.84
2.1000e+07105717105491-225.90-0.83
2.2000e+07110225109987-237.59-0.86
2.3000e+07114707114464-243.19-0.86
2.4000e+07119135118921-213.71-0.74
2.5000e+07123561123361-200.25-0.68
2.6000e+07128088127783-304.99-1.02
2.7000e+07132499132189-310.19-1.02
2.8000e+07136850136579-271.14-0.88
2.9000e+07141151140954-197.21-0.63
3.0000e+07145526145314-211.81-0.67
3.1000e+07149989149661-328.37-1.02
3.2000e+07154375153994-381.40-1.17
3.3000e+07158690158314-376.41-1.13
3.4000e+07162996162621-374.95-1.12
3.5000e+07167284166916-367.61-1.08
3.6000e+07171515171200-314.99-0.91
3.7000e+07175731175472-258.72-0.74
3.8000e+07180045179734-311.46-0.88
3.9000e+07184283183984-298.86-0.84
4.0000e+07188509188224-284.63-0.79
4.1000e+07192801192455-346.47-0.95
4.2000e+07197020196675-345.10-0.93
4.3000e+07201090200886-204.25-0.55
4.4000e+07205321205087-233.67-0.62
4.5000e+07209479209280-199.13-0.52
4.6000e+07213711213464-247.39-0.64
4.7000e+07217914217639-275.23-0.71
4.8000e+07221935221806-129.46-0.33
4.9000e+07226149225964-184.87-0.47
5.0000e+07230276230115-161.27-0.40
5.2000e+07238547238393-154.33-0.38
5.4000e+07246654246641-13.28-0.03
5.6000e+0725480025486060.150.14
5.8000e+07262943263052109.110.26
6.0000e+0727116927121848.670.11
6.2000e+07279412279358-54.17-0.12
6.4000e+0728745028747423.530.05
6.6000e+07295420295566145.620.32
6.8000e+0730353830363596.920.21
7.0000e+07311582311682100.190.22
7.2000e+0731961331970895.150.20
7.4000e+07327512327713201.460.42
7.6000e+07335542335699156.750.33
7.8000e+07343492343665172.630.36
8.0000e+07351464351612147.650.30
8.2000e+07359347359540193.360.39
8.4000e+0736736236745189.250.18
8.6000e+07375168375345176.810.35
8.8000e+07383041383222180.500.35
9.0000e+0739100239108279.750.15
9.2000e+07398940398926-14.04-0.03
9.4000e+07406654406755100.550.19
9.6000e+0741447641456891.880.17
9.8000e+0742227942236687.310.16
1.0000e+08430016430150134.190.25
1.0500e+08449368449548180.360.33
1.1000e+0846883146886231.390.06
1.1500e+0848806648809730.600.05
1.2000e+08507116507255138.920.24
1.2500e+0852631052634130.920.05
1.3000e+0854526954535888.880.15
1.3500e+08564111564309197.780.32
1.4000e+08582956583196240.400.38
1.4500e+08601848602023175.290.27
1.5000e+0862070962079282.810.13
1.5500e+08639382639504122.170.19
1.6000e+08658009658162153.400.23
1.6500e+08676595676768173.420.26
1.7000e+08695044695324280.020.41
1.7500e+08713638713831192.870.28
1.8000e+08731988732291302.540.43
1.8500e+08750373750705331.510.46
1.9000e+08768740769074334.180.46
1.9500e+08787163787401237.860.33
2.0000e+08805277805686408.790.55
2.1000e+08841865842135270.080.36
2.2000e+08878005878431425.760.55
2.3000e+08914055914581525.690.67
2.4000e+08950130950592462.020.58
2.5000e+08985957986471514.260.63
2.6000e+0810217581022224466.370.56
2.7000e+0810573781057857478.800.57
2.8000e+0810929061093374467.590.54
2.9000e+0811283501128779429.390.49
3.0000e+0811635331164079545.530.61
3.1000e+0811989131199275361.990.40
3.2000e+0812341601234373212.510.23
3.3000e+0812692001269375174.570.19
3.4000e+081304212130428472.430.08
3.5000e+0813392081339105-102.86-0.11
3.6000e+081373769137384070.570.07
3.7000e+0814086231408490-132.59-0.14
3.8000e+0814431771443060-116.79-0.12
3.9000e+0814779671477551-415.63-0.42
4.0000e+0815123711511966-404.84-0.40
4.1000e+0815466881546307-381.28-0.37
4.2000e+0815809571580575-381.90-0.37
4.3000e+0816153511614773-577.77-0.55
4.4000e+0816492861648903-383.07-0.36
4.5000e+0816834591682966-493.02-0.46
4.6000e+0817173541716964-389.98-0.36
4.7000e+0817515421750899-643.35-0.59
4.8000e+0817851351784771-363.61-0.33
4.9000e+0818190261818584-442.31-0.40
5.0000e+0818523441852337-7.07-0.01
5.2000e+081919609191967262.510.06
5.4000e+0819869581986785-172.90-0.15
5.6000e+082053601205368785.900.07
5.8000e+0821202422120385143.400.12
6.0000e+0821864302186888458.480.38
6.2000e+082253150225320353.450.04
6.4000e+0823196592319337-321.86-0.26
6.6000e+0823856882385296-392.11-0.31
6.8000e+0824514772451086-391.34-0.31
7.0000e+0825172122516712-499.97-0.38
7.2000e+0825828552582180-674.76-0.51
7.4000e+0826484362647495-940.78-0.71
7.6000e+0827133712712662-709.38-0.53
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