Gap size : 40 (r=20)

Generated by program gapCounts : Mon Jun 27 12:41:16 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+02000.000.00
3.0000e+02000.000.00
4.0000e+02000.000.00
5.0000e+02000.000.00
6.0000e+02000.000.00
7.0000e+02000.000.00
8.0000e+02000.000.00
9.0000e+02000.000.00
1.0000e+030-0-0.00-0.00
1.1000e+030-0-0.00-0.00
1.2000e+03000.000.00
1.3000e+03000.000.00
1.4000e+03000.000.00
1.5000e+03000.000.00
1.6000e+03000.000.00
1.7000e+03000.000.00
1.8000e+03000.000.00
1.9000e+03000.000.00
2.0000e+03000.000.00
2.1000e+03000.010.00
2.2000e+03000.010.00
2.3000e+03000.010.00
2.4000e+03000.010.00
2.5000e+03000.010.00
2.6000e+03000.010.00
2.7000e+03000.020.00
2.8000e+03000.020.00
2.9000e+03000.020.00
3.0000e+03000.020.00
3.1000e+03000.030.00
3.2000e+03000.030.00
3.3000e+03000.030.00
3.4000e+03000.030.00
3.5000e+03000.040.01
3.6000e+03000.040.01
3.7000e+03000.040.01
3.8000e+03000.050.01
3.9000e+03000.050.01
4.0000e+03000.050.01
4.1000e+03000.060.01
4.2000e+03000.060.01
4.3000e+03000.070.01
4.4000e+03000.070.01
4.5000e+03000.070.01
4.6000e+03000.080.01
4.7000e+03000.080.01
4.8000e+03000.090.01
4.9000e+03000.090.01
5.0000e+03000.100.01
5.2000e+03000.110.01
5.4000e+03000.120.01
5.6000e+03000.130.02
5.8000e+03000.140.02
6.0000e+03000.150.02
6.2000e+03000.170.02
6.4000e+03000.180.02
6.6000e+03000.190.02
6.8000e+03000.210.02
7.0000e+03000.220.02
7.2000e+03000.230.02
7.4000e+03000.250.03
7.6000e+03000.260.03
7.8000e+03000.280.03
8.0000e+03000.300.03
8.2000e+03000.310.03
8.4000e+03000.330.03
8.6000e+03000.340.03
8.8000e+03000.360.04
9.0000e+03000.380.04
9.2000e+03000.400.04
9.4000e+03000.420.04
9.6000e+03000.430.04
9.8000e+03000.450.04
1.0000e+04000.470.04
1.0500e+04010.520.05
1.1000e+04010.570.05
1.1500e+04010.620.05
1.2000e+04010.680.06
1.2500e+04010.730.06
1.3000e+04010.790.07
1.3500e+04010.850.07
1.4000e+04010.910.07
1.4500e+04010.970.08
1.5000e+04011.030.08
1.5500e+04011.100.09
1.6000e+04011.160.09
1.6500e+04011.230.09
1.7000e+04011.300.10
1.7500e+04011.370.10
1.8000e+04011.440.10
1.8500e+04021.510.11
1.9000e+04021.580.11
1.9500e+04120.650.05
2.0000e+04120.730.05
2.1000e+0422-0.12-0.01
2.2000e+04220.040.00
2.3000e+0432-0.80-0.05
2.4000e+0432-0.64-0.04
2.5000e+0433-0.47-0.03
2.6000e+0443-1.30-0.08
2.7000e+0443-1.12-0.07
2.8000e+0443-0.94-0.06
2.9000e+0443-0.76-0.05
3.0000e+0443-0.58-0.03
3.1000e+0444-0.39-0.02
3.2000e+0444-0.20-0.01
3.3000e+0444-0.01-0.00
3.4000e+0454-0.82-0.05
3.5000e+0454-0.62-0.03
3.6000e+0455-0.42-0.02
3.7000e+0455-0.22-0.01
3.8000e+0455-0.01-0.00
3.9000e+0465-0.81-0.04
4.0000e+0465-0.60-0.03
4.1000e+0466-0.39-0.02
4.2000e+0466-0.17-0.01
4.3000e+04660.040.00
4.4000e+04660.260.01
4.5000e+04660.480.02
4.6000e+0477-0.30-0.01
4.7000e+0477-0.08-0.00
4.8000e+04770.150.01
4.9000e+0487-0.62-0.03
5.0000e+0488-0.39-0.02
5.2000e+04880.070.00
5.4000e+0499-0.46-0.02
5.6000e+04990.010.00
5.8000e+04990.500.02
6.0000e+049100.980.04
6.2000e+041110-0.52-0.02
6.4000e+041311-2.02-0.09
6.6000e+041511-3.52-0.15
6.8000e+041512-3.01-0.13
7.0000e+041613-3.49-0.15
7.2000e+041613-2.97-0.12
7.4000e+041714-3.45-0.14
7.6000e+041714-2.92-0.12
7.8000e+041815-3.38-0.14
8.0000e+041815-2.84-0.11
8.2000e+041816-2.30-0.09
8.4000e+042016-3.75-0.15
8.6000e+042117-4.20-0.16
8.8000e+042217-4.65-0.18
9.0000e+042518-7.09-0.27
9.2000e+042618-7.53-0.28
9.4000e+042619-6.96-0.26
9.6000e+042620-6.39-0.24
9.8000e+042820-7.81-0.29
1.0000e+052821-7.24-0.26
1.0500e+052822-5.78-0.21
1.1000e+052824-4.30-0.15
1.1500e+053025-4.80-0.17
1.2000e+053127-4.29-0.14
1.2500e+053328-4.76-0.16
1.3000e+053430-4.21-0.14
1.3500e+053631-4.64-0.15
1.4000e+053933-6.06-0.19
1.4500e+054135-6.46-0.20
1.5000e+054236-5.85-0.18
1.5500e+054638-8.23-0.25
1.6000e+055039-10.59-0.32
1.6500e+055041-8.94-0.26
1.7000e+055643-13.28-0.39
1.7500e+055644-11.61-0.33
1.8000e+055646-9.92-0.28
1.8500e+056048-12.22-0.34
1.9000e+056049-10.52-0.29
1.9500e+056451-12.80-0.35
2.0000e+056653-13.07-0.36
2.1000e+057056-13.58-0.36
2.2000e+057660-16.06-0.42
2.3000e+057864-14.50-0.37
2.4000e+058467-16.90-0.43
2.5000e+058871-17.28-0.43
2.6000e+059574-20.62-0.50
2.7000e+0510078-21.93-0.53
2.8000e+0510382-21.21-0.50
2.9000e+0510886-22.47-0.52
3.0000e+0511189-21.70-0.50
3.1000e+0511393-19.91-0.45
3.2000e+0511997-22.09-0.49
3.3000e+05124101-23.24-0.51
3.4000e+05129105-24.38-0.53
3.5000e+05135109-26.49-0.57
3.6000e+05135112-22.58-0.48
3.7000e+05141116-24.65-0.52
3.8000e+05145120-24.70-0.51
3.9000e+05149124-24.74-0.51
4.0000e+05150128-21.75-0.44
4.1000e+05154132-21.74-0.44
4.2000e+05158136-21.72-0.43
4.3000e+05168140-27.68-0.55
4.4000e+05170144-25.62-0.50
4.5000e+05176148-27.55-0.53
4.6000e+05180153-27.46-0.53
4.7000e+05184157-27.36-0.52
4.8000e+05189161-28.24-0.53
4.9000e+05190165-25.10-0.47
5.0000e+05195169-25.95-0.48
5.2000e+05203177-25.61-0.47
5.4000e+05213186-27.22-0.49
5.6000e+05218194-23.77-0.42
5.8000e+05234203-31.28-0.55
6.0000e+05245211-33.74-0.58
6.2000e+05258220-38.15-0.65
6.4000e+05267228-38.52-0.64
6.6000e+05274237-36.85-0.61
6.8000e+05286246-40.13-0.65
7.0000e+05289255-34.38-0.55
7.2000e+05294263-30.59-0.49
7.4000e+05306272-33.76-0.53
7.6000e+05318281-36.90-0.57
7.8000e+05322290-32.00-0.49
8.0000e+05332299-33.07-0.50
8.2000e+05341308-33.10-0.50
8.4000e+05347317-30.11-0.45
8.6000e+05354326-28.08-0.41
8.8000e+05366335-31.03-0.45
9.0000e+05373344-28.94-0.42
9.2000e+05383353-29.83-0.43
9.4000e+05394362-31.69-0.45
9.6000e+05402371-30.52-0.43
9.8000e+05413381-32.32-0.45
1.0000e+06424390-34.10-0.47
1.0500e+06447413-33.95-0.46
1.1000e+06468436-31.64-0.42
1.1500e+06487460-27.20-0.35
1.2000e+06517483-33.63-0.43
1.2500e+06536507-28.92-0.36
1.3000e+06563531-32.10-0.40
1.3500e+06584555-29.17-0.35
1.4000e+06613579-34.13-0.41
1.4500e+06633603-29.98-0.35
1.5000e+06652627-24.73-0.29
1.5500e+06675652-23.39-0.27
1.6000e+06703676-26.95-0.30
1.6500e+06735701-34.43-0.38
1.7000e+06755725-29.81-0.33
1.7500e+06778750-28.12-0.31
1.8000e+06801775-26.35-0.28
1.8500e+06832800-32.50-0.34
1.9000e+06853824-28.57-0.30
1.9500e+06879849-29.58-0.31
2.0000e+06905874-30.51-0.31
2.1000e+06953925-28.17-0.28
2.2000e+061018975-42.58-0.42
2.3000e+0610821026-55.75-0.54
2.4000e+0611351077-57.69-0.55
2.5000e+0611921129-63.41-0.59
2.6000e+0612471180-66.92-0.61
2.7000e+0613081232-76.24-0.69
2.8000e+0613601284-76.37-0.68
2.9000e+0614201336-84.32-0.74
3.0000e+0614791388-91.09-0.78
3.1000e+0615331440-92.70-0.79
3.2000e+0615791493-86.15-0.72
3.3000e+0616301546-84.45-0.70
3.4000e+0616781598-79.60-0.65
3.5000e+0617351651-83.61-0.67
3.6000e+0617981705-93.49-0.74
3.7000e+0618481758-90.23-0.71
3.8000e+0618981811-86.84-0.67
3.9000e+0619461865-81.33-0.62
4.0000e+0619971918-78.70-0.60
4.1000e+0620671972-94.95-0.71
4.2000e+0621222026-96.09-0.72
4.3000e+0621622080-82.12-0.60
4.4000e+0622262134-92.05-0.67
4.5000e+0622802188-91.87-0.66
4.6000e+0623272242-84.59-0.61
4.7000e+0623822297-85.22-0.60
4.8000e+0624392351-87.75-0.62
4.9000e+0624882406-82.19-0.57
5.0000e+0625472460-86.53-0.60
5.2000e+0626712570-100.96-0.68
5.4000e+0627712680-91.06-0.61
5.6000e+0628842790-93.84-0.62
5.8000e+0629892901-88.31-0.57
6.0000e+0630913012-79.49-0.51
6.2000e+0631943123-71.39-0.45
6.4000e+0632873234-53.02-0.33
6.6000e+0633913346-45.40-0.28
6.8000e+0634973457-39.52-0.24
7.0000e+0636053570-35.41-0.21
7.2000e+0637193682-37.06-0.22
7.4000e+0638373795-42.49-0.25
7.6000e+0639473907-39.71-0.23
7.8000e+0640614020-40.72-0.23
8.0000e+0641704133-36.53-0.21
8.2000e+0642864247-39.14-0.22
8.4000e+0644004360-39.56-0.22
8.6000e+0645024474-27.80-0.15
8.8000e+0646064588-17.87-0.10
9.0000e+0647224702-19.76-0.11
9.2000e+0648534817-36.48-0.19
9.4000e+0649764931-45.04-0.24
9.6000e+0650785046-32.43-0.17
9.8000e+0651955160-34.68-0.18
1.0000e+0753185275-42.77-0.22
1.0500e+0756225563-58.87-0.29
1.1000e+0759205852-68.11-0.33
1.1500e+0762276141-85.54-0.41
1.2000e+0765166432-84.19-0.40
1.2500e+0767916723-68.12-0.31
1.3000e+0770797015-64.36-0.29
1.3500e+0773957307-87.94-0.39
1.4000e+0776767600-75.90-0.33
1.4500e+0780017894-107.26-0.46
1.5000e+0782998188-111.05-0.47
1.5500e+0786118483-128.29-0.54
1.6000e+0788918778-113.01-0.47
1.6500e+0791969074-122.23-0.50
1.7000e+0795179370-146.97-0.59
1.7500e+0798389667-171.24-0.68
1.8000e+07101339964-169.06-0.67
1.8500e+071042310262-161.46-0.63
1.9000e+071071710560-157.44-0.61
1.9500e+071098910858-131.01-0.50
2.0000e+071127111157-114.20-0.43
2.1000e+071191311756-157.46-0.58
2.2000e+071250412356-148.31-0.53
2.3000e+071310412957-146.83-0.52
2.4000e+071366713560-107.10-0.37
2.5000e+071430014164-136.18-0.46
2.6000e+071486514769-96.14-0.32
2.7000e+071546515375-90.04-0.30
2.8000e+071607815982-95.92-0.31
2.9000e+071668316590-92.84-0.30
3.0000e+071725017199-50.83-0.16
3.1000e+071786017809-50.94-0.16
3.2000e+071848518420-65.21-0.20
3.3000e+071907919031-47.66-0.14
3.4000e+071968719644-43.34-0.13
3.5000e+072026320257-6.28-0.02
3.6000e+072087820871-7.49-0.02
3.7000e+072148921485-4.01-0.01
3.8000e+072210322100-2.87-0.01
3.9000e+072273422716-18.08-0.05
4.0000e+0723323233329.330.03
4.1000e+07239222394927.340.07
4.2000e+07245362456730.940.08
4.3000e+07251632518522.090.06
4.4000e+07257202580483.790.22
4.5000e+072631926423104.020.27
4.6000e+072691727043125.760.33
4.7000e+072753127663132.000.34
4.8000e+072816828284115.730.30
4.9000e+072873528905169.920.43
5.0000e+072932029527206.570.52
5.2000e+073055730771214.190.53
5.4000e+073178432018233.500.57
5.6000e+073303633265229.410.55
5.8000e+073427634515238.850.56
6.0000e+073551235766253.740.59
6.2000e+073676537018253.010.58
6.4000e+073802038272251.610.57
6.6000e+073928439526242.490.54
6.8000e+074053840783244.570.53
7.0000e+074181742040222.830.48
7.2000e+074308043298218.210.47
7.4000e+074434244558215.670.45
7.6000e+074557345818245.160.51
7.8000e+074681747080262.660.54
8.0000e+074809448342248.120.50
8.2000e+074936149606244.520.49
8.4000e+075060350870266.810.53
8.6000e+075187052135264.980.52
8.8000e+075317353401227.980.44
9.0000e+075437754668290.810.56
9.2000e+075565855935277.420.53
9.4000e+075695657204247.800.47
9.6000e+075822758473245.930.46
9.8000e+075948159743261.780.49
1.0000e+086076161013252.320.46
1.0500e+086391564193277.630.50
1.1000e+086713067376245.920.43
1.1500e+087031170563251.920.44
1.2000e+087353573753218.430.37
1.2500e+087671576947232.210.39
1.3000e+087990980144235.100.39
1.3500e+088316383344180.910.29
1.4000e+088640286547144.500.23
1.4500e+088955389752198.720.31
1.5000e+089270192959258.440.40
1.5500e+089589396170276.540.42
1.6000e+089920299382179.910.27
1.6500e+08102315102596281.440.41
1.7000e+08105488105813325.040.47
1.7500e+08108725109032306.630.44
1.8000e+08111944112252308.110.44
1.8500e+08115089115474385.410.54
1.9000e+08118267118698431.450.60
1.9500e+08121450121924474.180.65
2.0000e+08124701125152450.520.61
2.1000e+08131095131611515.800.68
2.2000e+08137579138076496.870.64
2.3000e+08144120144546426.330.54
2.4000e+08150560151022461.830.58
2.5000e+08157063157502439.040.54
2.6000e+08163515163987471.690.57
2.7000e+08170129170476346.510.41
2.8000e+08176520176968448.260.52
2.9000e+08182957183465507.730.58
3.0000e+08189376189965588.730.66
3.1000e+08195926196468542.060.60
3.2000e+08202342202975632.560.69
3.3000e+08208853209484631.070.68
3.4000e+08215381215996615.450.66
3.5000e+08221920222512591.560.62
3.6000e+08228373229029656.290.68
3.7000e+08234919235550630.500.65
3.8000e+08241361242072711.110.72
3.9000e+08247938248597659.000.66
4.0000e+08254439255124685.070.68
4.1000e+08260976261653677.250.66
4.2000e+08267494268184690.440.67
4.3000e+08274026274718691.570.66
4.4000e+08280687281253565.560.54
4.5000e+08287276287789513.340.48
4.6000e+08293780294328547.840.51
4.7000e+08300212300868656.010.60
4.8000e+08306770307410639.780.58
4.9000e+08313432313953521.100.47
5.0000e+08319951320498546.910.49
5.2000e+08332928333592663.800.58
5.4000e+08346004346691687.080.59
5.6000e+08359181359795614.410.52
5.8000e+08372292372904612.470.51
6.0000e+08385336386018681.980.56
6.2000e+08398477399136658.660.54
6.4000e+08411625412257632.300.51
6.6000e+08424784425383598.650.47
6.8000e+08437995438512516.510.40
7.0000e+08451256451644387.710.30
7.2000e+08464416464779363.050.28
7.4000e+08477524477917393.370.30
7.6000e+08490774491059284.530.21
7.8000e+08503914504202288.380.21
8.0000e+08517156517349192.790.14
8.2000e+08530134530498363.630.26
8.4000e+08543322543649326.790.23
8.6000e+08556352556802450.160.32
8.8000e+08569470569958487.640.34
9.0000e+08582830583115285.120.20
9.2000e+08596037596275237.520.16
9.4000e+08609182609436253.760.17
9.6000e+08622339622599259.740.17
9.8000e+0863570963576354.400.04
1.0000e+09648780648930149.660.10
1.0500e+09681394681852457.880.29
1.1000e+09714576714783206.700.13
1.1500e+09747230747721491.270.30
1.2000e+09780222780667444.820.27
1.2500e+09813104813619514.670.30
1.3000e+09846014846576562.210.33
1.3500e+09878870879539668.900.38
1.4000e+09911664912506842.240.47
1.4500e+09944537945478940.800.52
1.5000e+099772699784531184.180.65
1.5500e+0910106851011432747.000.40
1.6000e+0910436631044414750.940.40
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