Gap size : 20 (r=10)

Generated by program gapCounts : Mon Jun 27 12:36:48 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+02000.020.01
2.0000e+02000.010.00
3.0000e+020-0-0.01-0.00
4.0000e+020-0-0.00-0.00
5.0000e+02000.020.01
6.0000e+02000.050.01
7.0000e+02000.100.02
8.0000e+02000.150.04
9.0000e+02000.220.05
1.0000e+0310-0.71-0.16
1.1000e+0310-0.63-0.13
1.2000e+0310-0.55-0.11
1.3000e+0311-0.46-0.09
1.4000e+0311-0.36-0.07
1.5000e+0311-0.26-0.05
1.6000e+0311-0.16-0.03
1.7000e+0321-1.05-0.19
1.8000e+0321-0.94-0.17
1.9000e+0321-0.82-0.14
2.0000e+0321-0.70-0.12
2.1000e+0321-0.58-0.10
2.2000e+0322-0.46-0.07
2.3000e+0322-0.33-0.05
2.4000e+0322-0.20-0.03
2.5000e+0322-0.07-0.01
2.6000e+03220.070.01
2.7000e+03220.200.03
2.8000e+03220.340.05
2.9000e+03220.480.07
3.0000e+03230.630.09
3.1000e+03230.770.11
3.2000e+0333-0.08-0.01
3.3000e+03330.060.01
3.4000e+03330.210.03
3.5000e+0343-0.64-0.09
3.6000e+0344-0.49-0.07
3.7000e+0344-0.33-0.04
3.8000e+0344-0.18-0.02
3.9000e+0344-0.02-0.00
4.0000e+0354-0.87-0.11
4.1000e+0354-0.71-0.09
4.2000e+0354-0.55-0.07
4.3000e+0355-0.39-0.05
4.4000e+0355-0.23-0.03
4.5000e+0355-0.06-0.01
4.6000e+03550.100.01
4.7000e+03550.270.03
4.8000e+03550.430.05
4.9000e+03560.600.07
5.0000e+03560.760.09
5.2000e+03561.100.13
5.4000e+03561.440.17
5.6000e+03571.790.21
5.8000e+03671.130.13
6.0000e+03770.480.05
6.2000e+0388-0.17-0.02
6.4000e+03880.190.02
6.6000e+03890.550.06
6.8000e+03890.900.10
7.0000e+03990.270.03
7.2000e+039100.630.07
7.4000e+039101.000.10
7.6000e+039101.360.14
7.8000e+0310110.730.07
8.0000e+0310111.100.11
8.2000e+0310111.480.15
8.4000e+0311120.850.08
8.6000e+0312120.230.02
8.8000e+0312130.610.06
9.0000e+031413-1.01-0.10
9.2000e+031413-0.63-0.06
9.4000e+031514-1.25-0.12
9.6000e+031514-0.87-0.08
9.8000e+031515-0.48-0.04
1.0000e+041515-0.09-0.01
1.0500e+041716-1.12-0.10
1.1000e+041817-1.14-0.10
1.1500e+042218-4.16-0.36
1.2000e+042519-6.17-0.53
1.2500e+042620-6.17-0.52
1.3000e+042621-5.16-0.43
1.3500e+042822-6.15-0.50
1.4000e+042923-6.14-0.50
1.4500e+043124-7.12-0.57
1.5000e+043125-6.10-0.48
1.5500e+043226-6.07-0.47
1.6000e+043227-5.04-0.39
1.6500e+043228-4.00-0.30
1.7000e+043329-3.96-0.30
1.7500e+043330-2.92-0.22
1.8000e+043531-3.87-0.28
1.8500e+043732-4.82-0.35
1.9000e+043933-5.77-0.41
1.9500e+043934-4.72-0.33
2.0000e+044035-4.66-0.33
2.1000e+044237-4.53-0.31
2.2000e+044340-3.40-0.23
2.3000e+044642-4.26-0.28
2.4000e+044644-2.10-0.14
2.5000e+045046-3.94-0.25
2.6000e+045348-4.78-0.30
2.7000e+045550-4.60-0.29
2.8000e+045753-4.42-0.27
2.9000e+046055-5.23-0.32
3.0000e+046357-6.04-0.36
3.1000e+046559-5.84-0.34
3.2000e+046961-7.63-0.44
3.3000e+047164-7.42-0.43
3.4000e+047266-6.21-0.35
3.5000e+047368-4.99-0.28
3.6000e+047570-4.77-0.26
3.7000e+047772-4.54-0.25
3.8000e+048375-8.31-0.45
3.9000e+048577-8.08-0.43
4.0000e+048779-7.84-0.42
4.1000e+049081-8.60-0.45
4.2000e+049184-7.35-0.38
4.3000e+049286-6.10-0.31
4.4000e+049488-5.85-0.30
4.5000e+049690-5.60-0.28
4.6000e+049893-5.34-0.27
4.7000e+0410195-6.08-0.30
4.8000e+0410497-6.82-0.34
4.9000e+0410699-6.56-0.32
5.0000e+04106102-4.29-0.21
5.2000e+04111106-4.75-0.23
5.4000e+04117111-6.20-0.29
5.6000e+04122115-6.64-0.31
5.8000e+04127120-7.08-0.32
6.0000e+04129124-4.51-0.20
6.2000e+04134129-4.93-0.22
6.4000e+04139134-5.35-0.23
6.6000e+04144138-5.76-0.25
6.8000e+04150143-7.16-0.31
7.0000e+04154147-6.56-0.28
7.2000e+04161152-8.96-0.37
7.4000e+04169157-12.35-0.51
7.6000e+04175161-13.73-0.56
7.8000e+04182166-16.11-0.65
8.0000e+04188171-17.49-0.70
8.2000e+04194175-18.87-0.75
8.4000e+04200180-20.24-0.79
8.6000e+04203184-18.61-0.72
8.8000e+04207189-17.97-0.69
9.0000e+04212194-18.33-0.70
9.2000e+04216198-17.69-0.67
9.4000e+04222203-19.05-0.71
9.6000e+04227208-19.40-0.72
9.8000e+04231212-18.75-0.69
1.0000e+05238217-21.10-0.77
1.0500e+05250229-21.46-0.77
1.1000e+05260240-19.81-0.69
1.1500e+05269252-17.15-0.59
1.2000e+05282264-18.47-0.62
1.2500e+05299275-23.79-0.79
1.3000e+05315287-28.10-0.92
1.3500e+05328299-29.40-0.95
1.4000e+05333310-22.70-0.72
1.4500e+05349322-26.99-0.84
1.5000e+05361334-27.27-0.84
1.5500e+05370345-24.55-0.75
1.6000e+05382357-24.82-0.74
1.6500e+05394369-25.09-0.74
1.7000e+05405381-24.36-0.71
1.7500e+05416392-23.62-0.68
1.8000e+05424404-19.88-0.57
1.8500e+05436416-20.14-0.57
1.9000e+05449428-21.39-0.60
1.9500e+05460439-20.65-0.57
2.0000e+05471451-19.90-0.54
2.1000e+05496475-21.40-0.57
2.2000e+05517498-18.89-0.50
2.3000e+05540522-18.38-0.47
2.4000e+05567545-21.86-0.55
2.5000e+05598569-29.35-0.73
2.6000e+05624592-31.83-0.78
2.7000e+05651616-35.32-0.85
2.8000e+05673639-33.80-0.80
2.9000e+05693663-30.29-0.71
3.0000e+05715686-28.78-0.66
3.1000e+05746710-36.27-0.82
3.2000e+05770733-36.76-0.82
3.3000e+05793757-36.26-0.80
3.4000e+05818780-37.76-0.82
3.5000e+05846804-42.26-0.91
3.6000e+05867827-39.77-0.85
3.7000e+05888851-37.28-0.79
3.8000e+05906874-31.80-0.66
3.9000e+05938898-40.32-0.83
4.0000e+05958921-36.85-0.75
4.1000e+05979945-34.38-0.69
4.2000e+051010968-41.92-0.84
4.3000e+051036992-44.46-0.88
4.4000e+0510621015-47.00-0.92
4.5000e+0510821038-43.55-0.85
4.6000e+0511111062-49.11-0.94
4.7000e+0511411085-55.67-1.06
4.8000e+0511631109-54.24-1.02
4.9000e+0511881132-55.81-1.04
5.0000e+0512141156-58.39-1.08
5.2000e+0512701202-67.57-1.23
5.4000e+0513061249-56.77-1.02
5.6000e+0513501296-53.99-0.95
5.8000e+0513901343-47.23-0.82
6.0000e+0514301390-40.50-0.70
6.2000e+0514781436-41.79-0.71
6.4000e+0515241483-41.10-0.69
6.6000e+0515551530-25.44-0.42
6.8000e+0516021576-25.80-0.42
7.0000e+0516551623-32.18-0.52
7.2000e+0517021669-32.58-0.52
7.4000e+0517471716-31.01-0.49
7.6000e+0518071763-44.46-0.69
7.8000e+0518721809-62.93-0.97
8.0000e+0519311856-75.42-1.15
8.2000e+0519771902-74.94-1.13
8.4000e+0520281949-79.47-1.18
8.6000e+0520781995-83.03-1.22
8.8000e+0521242041-82.61-1.21
9.0000e+0521812088-93.21-1.35
9.2000e+0522202134-85.83-1.23
9.4000e+0522742181-93.47-1.33
9.6000e+0523192227-92.14-1.30
9.8000e+0523672273-93.82-1.31
1.0000e+0624012319-81.52-1.13
1.0500e+0625092435-73.87-1.00
1.1000e+0626072551-56.34-0.75
1.1500e+0627292666-62.92-0.82
1.2000e+0628282781-46.62-0.60
1.2500e+0629362897-39.44-0.50
1.3000e+0630453012-33.37-0.41
1.3500e+0631713127-44.40-0.54
1.4000e+0632683241-26.55-0.32
1.4500e+0633863356-29.79-0.35
1.5000e+0634963471-25.14-0.29
1.5500e+0636023585-16.59-0.19
1.6000e+0637023700-2.13-0.02
1.6500e+06381138143.230.04
1.7000e+06392839280.500.01
1.7500e+064028404314.670.16
1.8000e+064145415711.750.13
1.8500e+06426642714.750.05
1.9000e+064370438514.660.15
1.9500e+064468449830.490.32
2.0000e+064581461231.230.32
2.1000e+064812483927.470.28
2.2000e+06506150665.390.05
2.3000e+0653145293-21.00-0.20
2.4000e+0655455519-25.68-0.24
2.5000e+0657695745-23.64-0.22
2.6000e+0659885971-16.89-0.15
2.7000e+0662236197-26.40-0.24
2.8000e+06641864223.820.03
2.9000e+066634664712.790.11
3.0000e+066843687228.510.25
3.1000e+067043709652.990.45
3.2000e+067258732062.230.52
3.3000e+067502754442.250.35
3.4000e+067732776836.040.29
3.5000e+067961799230.610.25
3.6000e+068173821541.970.33
3.7000e+068414843824.120.19
3.8000e+06865586616.070.05
3.9000e+068869888414.820.11
4.0000e+069082910624.370.19
4.1000e+069312932916.730.13
4.2000e+069527955123.910.18
4.3000e+069754977318.900.14
4.4000e+069977999517.710.13
4.5000e+061022110216-4.65-0.03
4.6000e+061044810438-10.19-0.07
4.7000e+061068910659-29.90-0.21
4.8000e+061091210880-31.78-0.22
4.9000e+061113111101-29.81-0.21
5.0000e+061134011322-18.01-0.12
5.2000e+061176511763-1.89-0.01
5.4000e+06121851220418.630.12
5.6000e+06126121264431.560.21
5.8000e+06130431308339.910.26
6.0000e+06134651352256.700.36
6.2000e+06138771396082.950.52
6.4000e+061427414398123.680.77
6.6000e+061470014835134.900.82
6.8000e+061514515272126.620.76
7.0000e+061559415708113.860.68
7.2000e+061602516144118.620.70
7.4000e+061644616579132.930.77
7.6000e+061690717014106.790.61
7.8000e+061732817448120.200.68
8.0000e+061777317882109.190.61
8.2000e+061819718316118.770.66
8.4000e+06186561874992.930.51
8.6000e+061905419182127.690.70
8.8000e+061945419614160.060.86
9.0000e+061991120046135.050.72
9.2000e+062034520478132.660.70
9.4000e+062078920909119.900.63
9.6000e+062121821340121.780.63
9.8000e+062165421770116.310.60
1.0000e+072208422200116.490.59
1.0500e+07232042327470.450.35
1.1000e+07242812434665.370.32
1.1500e+07253782541638.330.18
1.2000e+07264662648418.420.09
1.2500e+07275052755145.700.21
1.3000e+07285982861517.250.08
1.3500e+07296232967855.120.25
1.4000e+07306623073977.370.34
1.4500e+07317123179987.060.38
1.5000e+07327943285763.240.27
1.5500e+073381033914103.950.44
1.6000e+073483534969134.250.56
1.6500e+073591036023113.160.46
1.7000e+07370033707672.740.29
1.7500e+07380463812781.010.32
1.8000e+073904539177132.020.52
1.8500e+074005540226170.800.66
1.9000e+07411924127381.370.31
1.9500e+07422264232093.770.36
2.0000e+07432844336581.040.30
2.1000e+07453654545287.240.32
2.2000e+074742347535112.190.40
2.3000e+074949449614120.070.42
2.4000e+07516065168983.050.29
2.5000e+075364553760115.280.39
2.6000e+075564755828180.910.61
2.7000e+075772757892165.080.54
2.8000e+075977659953176.910.57
2.9000e+076182662011184.510.59
3.0000e+07639666406598.990.31
3.1000e+076598666116130.460.40
3.2000e+076796768165198.000.60
3.3000e+077006170211149.720.45
3.4000e+07721547225499.680.30
3.5000e+077418274294111.970.33
3.6000e+077620076332131.670.38
3.7000e+077824878367118.850.34
3.8000e+07803288040071.560.20
3.9000e+0782424824305.880.02
4.0000e+0784449844588.870.02
4.1000e+0786475864848.580.02
4.2000e+078852888507-20.93-0.06
4.3000e+079058990528-60.61-0.16
4.4000e+079261092548-62.41-0.17
4.5000e+079466694565-101.29-0.27
4.6000e+079665696580-76.19-0.20
4.7000e+079865498593-61.07-0.16
4.8000e+07100696100604-91.90-0.23
4.9000e+07102732102613-118.63-0.30
5.0000e+07104739104621-118.23-0.30
5.2000e+07108746108630-115.86-0.29
5.4000e+07112710112632-77.53-0.19
5.6000e+07116701116628-72.97-0.17
5.8000e+07120645120617-27.94-0.07
6.0000e+07124619124600-19.22-0.04
6.2000e+07128451128576125.400.29
6.4000e+07132382132547165.120.37
6.6000e+07136293136512219.110.49
6.8000e+07140231140472240.560.53
7.0000e+07144159144426266.630.58
7.2000e+07148115148374259.460.55
7.4000e+07152067152318251.210.53
7.6000e+07155987156257270.010.56
7.8000e+07159984160191206.990.43
8.0000e+0716402916412091.270.19
8.2000e+07167878168045166.980.34
8.4000e+07171784171965181.230.36
8.6000e+07175584175881297.120.59
8.8000e+07179515179793277.750.54
9.0000e+07183487183700213.220.41
9.2000e+07187347187604256.620.49
9.4000e+07191236191503267.050.51
9.6000e+07195089195399309.580.58
9.8000e+07198990199290300.300.56
1.0000e+08202922203178256.290.47
1.0500e+08212539212882343.420.62
1.1000e+08222096222565468.780.83
1.1500e+08231702232226524.370.91
1.2000e+08241242241868626.091.06
1.2500e+08250810251491680.791.14
1.3000e+08260392261095703.241.15
1.3500e+08269857270682825.141.33
1.4000e+08279375280252877.161.39
1.4500e+08289096289806709.901.11
1.5000e+08298675299344668.941.03
1.5500e+08308168308867698.801.06
1.6000e+08317570318375804.991.20
1.6500e+08327010327869858.961.27
1.7000e+08336442337349907.161.32
1.7500e+08346019346816797.001.14
1.8000e+08355370356270899.861.27
1.8500e+083646613657111050.121.47
1.9000e+083741073751401033.121.43
1.9500e+083835283845571029.191.41
2.0000e+083928763939631086.641.47
2.1000e+08411812412740927.861.23
2.2000e+084303734314741100.971.43
2.3000e+084490724501671094.981.39
2.4000e+084677784688211042.711.30
2.5000e+08486515487437921.851.13
2.6000e+08505086506017930.911.12
2.7000e+085235305245621032.341.22
2.8000e+085420105430741064.431.24
2.9000e+085605385615541016.421.16
3.0000e+085788835800031120.431.26
3.1000e+085971985984231224.521.36
3.2000e+086156126168131200.691.31
3.3000e+086340456351751129.871.22
3.4000e+086521246535101385.911.48
3.5000e+086706066718191212.661.28
3.6000e+086886936901021408.861.46
3.7000e+087070647083601296.271.33
3.8000e+087252887265951306.561.32
3.9000e+087436217448051184.381.19
4.0000e+087616857629931308.371.30
4.1000e+08780169781159990.100.97
4.2000e+087982777993031026.130.99
4.3000e+088163938174261033.000.99
4.4000e+08834579835528949.210.90
4.5000e+088525538536101057.250.99
4.6000e+088705768716731096.581.02
4.7000e+088886698897161046.640.96
4.8000e+08906763907740976.850.89
4.9000e+089247419257461004.630.91
5.0000e+08942829943733904.350.81
5.2000e+08978707979656949.100.84
5.4000e+0810145921015511918.940.80
5.6000e+0810504161051300884.450.75
5.8000e+0810860551087027972.040.81
6.0000e+0811219141122693778.960.64
6.2000e+0811573941158300906.290.74
6.4000e+08119279111938511060.000.85
6.6000e+08122833512293471011.920.80
6.8000e+08126374512647901044.750.81
7.0000e+08129911813001811063.130.82
7.2000e+08133427813355231244.570.95
7.4000e+08136945513708161360.511.02
7.6000e+08140472314060611338.310.99
7.8000e+08143990514412611356.250.99
8.0000e+08147511614764171300.550.94
8.2000e+08151019215115281336.370.96
8.4000e+08154547515465981122.810.80
8.6000e+08158041415816261211.920.85
8.8000e+08161521016166141403.690.97
9.0000e+08165030616515621256.080.86
9.2000e+08168497616864721495.991.02
9.4000e+08171973317213441611.301.09
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