Gap size : 82 (r=41)

Generated by program gapCounts : Mon Jun 27 12:44:29 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+020-0-0.00-0.00
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+03000.000.00
1.1000e+03000.000.00
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+03000.000.00
2.2000e+03000.000.00
2.3000e+03000.000.00
2.4000e+03000.000.00
2.5000e+03000.000.00
2.6000e+03000.000.00
2.7000e+03000.000.00
2.8000e+03000.000.00
2.9000e+03000.000.00
3.0000e+03000.000.00
3.1000e+03000.000.00
3.2000e+03000.000.00
3.3000e+030-0-0.00-0.00
3.4000e+030-0-0.00-0.00
3.5000e+030-0-0.00-0.00
3.6000e+030-0-0.00-0.00
3.7000e+030-0-0.00-0.00
3.8000e+030-0-0.00-0.00
3.9000e+030-0-0.00-0.00
4.0000e+030-0-0.00-0.00
4.1000e+030-0-0.00-0.00
4.2000e+030-0-0.00-0.00
4.3000e+030-0-0.00-0.00
4.4000e+030-0-0.00-0.00
4.5000e+030-0-0.00-0.00
4.6000e+030-0-0.00-0.00
4.7000e+030-0-0.00-0.00
4.8000e+030-0-0.00-0.00
4.9000e+030-0-0.00-0.00
5.0000e+030-0-0.00-0.00
5.2000e+03000.000.00
5.4000e+03000.000.00
5.6000e+03000.000.00
5.8000e+03000.000.00
6.0000e+03000.000.00
6.2000e+03000.000.00
6.4000e+03000.000.00
6.6000e+03000.000.00
6.8000e+03000.000.00
7.0000e+03000.000.00
7.2000e+03000.000.00
7.4000e+03000.000.00
7.6000e+03000.000.00
7.8000e+03000.000.00
8.0000e+03000.000.00
8.2000e+03000.000.00
8.4000e+03000.000.00
8.6000e+03000.000.00
8.8000e+03000.000.00
9.0000e+03000.000.00
9.2000e+03000.000.00
9.4000e+03000.000.00
9.6000e+03000.000.00
9.8000e+03000.000.00
1.0000e+04000.000.00
1.0500e+04000.000.00
1.1000e+04000.000.00
1.1500e+04000.000.00
1.2000e+04000.000.00
1.2500e+04000.000.00
1.3000e+04000.000.00
1.3500e+04000.000.00
1.4000e+04000.000.00
1.4500e+04000.000.00
1.5000e+04000.000.00
1.5500e+04000.000.00
1.6000e+04000.000.00
1.6500e+04000.000.00
1.7000e+04000.000.00
1.7500e+04000.000.00
1.8000e+04000.000.00
1.8500e+04000.000.00
1.9000e+04000.000.00
1.9500e+04000.000.00
2.0000e+04000.000.00
2.1000e+04000.000.00
2.2000e+04000.000.00
2.3000e+04000.000.00
2.4000e+04000.000.00
2.5000e+04000.000.00
2.6000e+04000.000.00
2.7000e+04000.000.00
2.8000e+04000.000.00
2.9000e+04000.000.00
3.0000e+04000.000.00
3.1000e+04000.000.00
3.2000e+04000.000.00
3.3000e+04000.000.00
3.4000e+04000.000.00
3.5000e+04000.000.00
3.6000e+04000.000.00
3.7000e+04000.000.00
3.8000e+04000.000.00
3.9000e+04000.000.00
4.0000e+04000.000.00
4.1000e+04000.000.00
4.2000e+04000.000.00
4.3000e+04000.000.00
4.4000e+04000.010.00
4.5000e+04000.010.00
4.6000e+04000.010.00
4.7000e+04000.010.00
4.8000e+04000.010.00
4.9000e+04000.010.00
5.0000e+04000.010.00
5.2000e+04000.010.00
5.4000e+04000.010.00
5.6000e+04000.010.00
5.8000e+04000.010.00
6.0000e+04000.010.00
6.2000e+04000.010.00
6.4000e+04000.010.00
6.6000e+04000.010.00
6.8000e+04000.020.00
7.0000e+04000.020.00
7.2000e+04000.020.00
7.4000e+04000.020.00
7.6000e+04000.020.00
7.8000e+04000.020.00
8.0000e+04000.020.00
8.2000e+04000.020.00
8.4000e+04000.030.00
8.6000e+04000.030.00
8.8000e+04000.030.00
9.0000e+04000.030.00
9.2000e+04000.030.00
9.4000e+04000.030.00
9.6000e+04000.040.00
9.8000e+04000.040.00
1.0000e+05000.040.00
1.0500e+05000.040.00
1.1000e+05000.050.00
1.1500e+05000.050.00
1.2000e+05000.060.00
1.2500e+05000.060.00
1.3000e+05000.070.00
1.3500e+05000.080.00
1.4000e+05000.080.00
1.4500e+05000.090.00
1.5000e+05000.100.00
1.5500e+05000.100.00
1.6000e+05000.110.00
1.6500e+05000.120.00
1.7000e+05000.130.00
1.7500e+05000.130.00
1.8000e+05000.140.00
1.8500e+05000.150.00
1.9000e+05000.160.00
1.9500e+05000.170.00
2.0000e+05000.180.00
2.1000e+05000.190.01
2.2000e+05000.210.01
2.3000e+05000.230.01
2.4000e+05000.250.01
2.5000e+05000.270.01
2.6000e+05000.300.01
2.7000e+0510-0.68-0.02
2.8000e+0510-0.66-0.02
2.9000e+0510-0.63-0.01
3.0000e+0510-0.61-0.01
3.1000e+0510-0.58-0.01
3.2000e+0510-0.56-0.01
3.3000e+0510-0.53-0.01
3.4000e+0511-0.50-0.01
3.5000e+0511-0.48-0.01
3.6000e+0511-0.45-0.01
3.7000e+0511-0.42-0.01
3.8000e+0511-0.39-0.01
3.9000e+0511-0.36-0.01
4.0000e+0511-0.33-0.01
4.1000e+0511-0.30-0.01
4.2000e+0511-0.26-0.01
4.3000e+0511-0.23-0.00
4.4000e+0511-0.20-0.00
4.5000e+0511-0.17-0.00
4.6000e+0511-0.13-0.00
4.7000e+0511-0.10-0.00
4.8000e+0511-0.06-0.00
4.9000e+0511-0.03-0.00
5.0000e+05110.010.00
5.2000e+05110.080.00
5.4000e+0521-0.84-0.02
5.6000e+0521-0.76-0.01
5.8000e+0521-0.68-0.01
6.0000e+0521-0.60-0.01
6.2000e+0521-0.52-0.01
6.4000e+0522-0.43-0.01
6.6000e+0522-0.35-0.01
6.8000e+0522-0.26-0.00
7.0000e+0532-1.17-0.02
7.2000e+0532-1.08-0.02
7.4000e+0532-0.99-0.02
7.6000e+0532-0.89-0.01
7.8000e+0532-0.79-0.01
8.0000e+0532-0.70-0.01
8.2000e+0532-0.60-0.01
8.4000e+0533-0.50-0.01
8.6000e+0543-1.40-0.02
8.8000e+0543-1.29-0.02
9.0000e+0543-1.19-0.02
9.2000e+0543-1.08-0.02
9.4000e+0543-0.97-0.01
9.6000e+0543-0.86-0.01
9.8000e+0543-0.75-0.01
1.0000e+0653-1.64-0.02
1.0500e+0654-1.36-0.02
1.1000e+0664-2.07-0.03
1.1500e+0684-3.77-0.05
1.2000e+0685-3.46-0.04
1.2500e+0695-4.15-0.05
1.3000e+0695-3.83-0.05
1.3500e+0696-3.50-0.04
1.4000e+06106-4.17-0.05
1.4500e+06116-4.83-0.06
1.5000e+06127-5.48-0.06
1.5500e+06137-6.13-0.07
1.6000e+06137-5.77-0.07
1.6500e+06138-5.40-0.06
1.7000e+06138-5.04-0.06
1.7500e+06138-4.66-0.05
1.8000e+06139-4.28-0.05
1.8500e+06149-4.89-0.05
1.9000e+06159-5.50-0.06
1.9500e+061510-5.11-0.05
2.0000e+061610-5.71-0.06
2.1000e+061711-5.89-0.06
2.2000e+061712-5.06-0.05
2.3000e+061713-4.20-0.04
2.4000e+061814-4.33-0.04
2.5000e+062015-5.44-0.05
2.6000e+062215-6.54-0.06
2.7000e+062216-5.62-0.05
2.8000e+062317-5.68-0.05
2.9000e+062318-4.73-0.04
3.0000e+062419-4.77-0.04
3.1000e+062620-5.79-0.05
3.2000e+062721-5.79-0.05
3.3000e+062722-4.78-0.04
3.4000e+062723-3.76-0.03
3.5000e+062724-2.73-0.02
3.6000e+062825-2.68-0.02
3.7000e+062826-1.62-0.01
3.8000e+063027-2.55-0.02
3.9000e+063129-2.47-0.02
4.0000e+063230-2.38-0.02
4.1000e+063431-3.27-0.02
4.2000e+063432-2.15-0.02
4.3000e+063533-2.03-0.01
4.4000e+063534-0.89-0.01
4.5000e+0635350.260.00
4.6000e+063736-0.58-0.00
4.7000e+063938-1.41-0.01
4.8000e+064039-1.23-0.01
4.9000e+064040-0.04-0.00
5.0000e+0640411.160.01
5.2000e+0640443.590.02
5.4000e+0643463.050.02
5.6000e+0644494.550.03
5.8000e+0650511.080.01
6.0000e+0652541.650.01
6.2000e+0654562.250.01
6.4000e+0655593.880.02
6.6000e+0658623.550.02
6.8000e+0660644.240.03
7.0000e+0663673.960.02
7.2000e+0666703.710.02
7.4000e+0667725.490.03
7.6000e+0668757.300.04
7.8000e+0670788.130.05
8.0000e+0671819.990.06
8.2000e+06728411.880.07
8.4000e+06748712.790.07
8.6000e+06779012.730.07
8.8000e+06819311.690.06
9.0000e+0686969.670.05
9.2000e+06889910.680.06
9.4000e+069110210.700.06
9.6000e+069410510.760.06
9.8000e+06981089.830.05
1.0000e+0710011110.920.06
1.0500e+0710611912.760.06
1.1000e+0711412712.710.06
1.1500e+0712013514.790.07
1.2000e+071371435.990.03
1.2500e+071421519.300.04
1.3000e+0714916010.720.05
1.3500e+071591689.240.04
1.4000e+071691777.870.03
1.4500e+071801865.600.02
1.5000e+071921942.420.01
1.5500e+071972036.330.03
1.6000e+072042128.340.03
1.6500e+072122219.430.04
1.7000e+072282312.610.01
1.7500e+072382401.880.01
1.8000e+072492490.220.00
1.8500e+072572591.640.01
1.9000e+072642684.140.02
1.9500e+072742783.720.01
2.0000e+072852872.370.01
2.1000e+073043072.880.01
2.2000e+073243272.670.01
2.3000e+07351347-4.28-0.02
2.4000e+07370367-2.97-0.01
2.5000e+07389388-1.41-0.00
2.6000e+074034085.380.02
2.7000e+07431429-1.61-0.01
2.8000e+07451451-0.37-0.00
2.9000e+07473472-0.92-0.00
3.0000e+07494494-0.27-0.00
3.1000e+07520516-4.41-0.01
3.2000e+07546538-8.37-0.03
3.3000e+07576560-16.13-0.05
3.4000e+07593582-10.71-0.03
3.5000e+07611605-6.11-0.02
3.6000e+07638628-10.34-0.03
3.7000e+07659651-8.40-0.02
3.8000e+07674674-0.29-0.00
3.9000e+07701697-4.03-0.01
4.0000e+07722720-1.61-0.00
4.1000e+07754744-10.03-0.03
4.2000e+07776768-8.31-0.02
4.3000e+07799792-7.43-0.02
4.4000e+07826816-10.42-0.03
4.5000e+07855840-15.26-0.04
4.6000e+07882864-17.97-0.05
4.7000e+07908888-19.54-0.05
4.8000e+07929913-15.98-0.04
4.9000e+07964938-26.29-0.07
5.0000e+07991963-28.48-0.07
5.2000e+0710381013-25.47-0.06
5.4000e+0710871063-23.99-0.06
5.6000e+0711371114-23.04-0.05
5.8000e+0711871165-21.65-0.05
6.0000e+0712281217-10.82-0.03
6.2000e+0712761269-6.57-0.01
6.4000e+07131813224.090.01
6.6000e+07137013755.140.01
6.8000e+07142414294.570.01
7.0000e+0714921482-9.62-0.02
7.2000e+0715411537-4.45-0.01
7.4000e+0716031591-11.92-0.03
7.6000e+0716571646-11.05-0.02
7.8000e+0717271701-25.85-0.05
8.0000e+0717861757-29.32-0.06
8.2000e+0718281813-15.46-0.03
8.4000e+0718921869-23.30-0.05
8.6000e+0719511925-25.83-0.05
8.8000e+0720141982-32.06-0.06
9.0000e+0720502039-10.99-0.02
9.2000e+0721092096-12.65-0.02
9.4000e+0721762154-22.02-0.04
9.6000e+0722392212-27.11-0.05
9.8000e+0723092270-38.94-0.07
1.0000e+0823622328-33.51-0.06
1.0500e+0825202476-44.30-0.08
1.1000e+0826722624-47.55-0.08
1.1500e+0828282775-53.32-0.09
1.2000e+0829662926-39.68-0.07
1.2500e+0830993079-19.68-0.03
1.3000e+0832563234-22.38-0.04
1.3500e+0834083389-18.82-0.03
1.4000e+0835613546-15.04-0.02
1.4500e+0837303704-26.10-0.04
1.5000e+0838773863-14.03-0.02
1.5500e+0840364023-12.87-0.02
1.6000e+0842084184-23.64-0.04
1.6500e+0843564347-9.39-0.01
1.7000e+084494451015.860.02
1.7500e+084650467424.080.03
1.8000e+084811483928.240.04
1.8500e+084990500515.320.02
1.9000e+085146517226.290.04
1.9500e+085318534022.130.03
2.0000e+085495550913.810.02
2.1000e+08584058498.650.01
2.2000e+086179619212.640.02
2.3000e+08653365384.640.01
2.4000e+086862688724.520.03
2.5000e+087204723834.180.04
2.6000e+087546759246.490.06
2.7000e+087898794951.360.06
2.8000e+088259830949.700.06
2.9000e+088653867017.410.02
3.0000e+08903090344.420.00
3.1000e+089378940122.650.03
3.2000e+089742976927.030.03
3.3000e+08101081014031.500.03
3.4000e+081051810512-6.01-0.01
3.5000e+081089610886-9.56-0.01
3.6000e+081127511263-12.20-0.01
3.7000e+081167011641-28.99-0.03
3.8000e+081204512021-23.97-0.02
3.9000e+081243112403-28.20-0.03
4.0000e+081282512786-38.71-0.04
4.1000e+081318513171-13.55-0.01
4.2000e+081357213558-13.76-0.01
4.3000e+081398013947-33.38-0.03
4.4000e+081436414337-27.44-0.03
4.5000e+081475814728-29.99-0.03
4.6000e+081514615121-25.05-0.02
4.7000e+081553215515-16.65-0.02
4.8000e+081596715911-55.83-0.05
4.9000e+081636616308-57.62-0.05
5.0000e+081676316707-56.05-0.05
5.2000e+081753717508-28.91-0.03
5.4000e+081837718314-62.63-0.05
5.6000e+081920519126-79.39-0.07
5.8000e+082003019942-88.37-0.07
6.0000e+082085620762-93.75-0.08
6.2000e+082172721587-139.66-0.11
6.4000e+082255422417-137.26-0.11
6.6000e+082337823250-127.68-0.10
6.8000e+082421524088-127.04-0.10
7.0000e+082507124930-141.48-0.11
7.2000e+082592625775-151.09-0.11
7.4000e+082675726624-133.00-0.10
7.6000e+082759027477-113.29-0.08
7.8000e+082844228333-109.07-0.08
8.0000e+082928329193-90.42-0.07
8.2000e+083012830056-72.43-0.05
8.4000e+083095830922-36.19-0.03
8.6000e+083183531791-43.76-0.03
8.8000e+083272532664-61.24-0.04
9.0000e+083359433539-54.68-0.04
9.2000e+083442434418-6.16-0.00
9.4000e+083534535299-45.74-0.03
9.6000e+083618936184-5.48-0.00
9.8000e+083707637071-5.44-0.00
1.0000e+093798237960-21.69-0.01
1.0500e+09401584019638.240.02
1.1000e+094246842448-19.97-0.01
1.1500e+09446904471524.930.02
1.2000e+09469414699655.300.03
1.2500e+094914949292142.510.08
1.3000e+095146251600138.000.08
1.3500e+095376953921152.260.09
1.4000e+09562365625518.800.01
1.4500e+09585425860058.170.03
1.5000e+09609146095742.960.02
1.5500e+096332563325-0.22-0.00
1.6000e+09656216570382.270.04
1.6500e+096798368092109.080.06
1.7000e+09704237049167.910.04
1.7500e+09728247289975.440.04
1.8000e+09752827531735.390.02
1.8500e+09776777774467.500.03
1.9000e+098006780181113.510.06
1.9500e+09825518262574.180.04
2.0000e+09850308507848.290.02
2.1000e+09899319000977.960.04
2.2000e+099500894971-37.09-0.02
2.3000e+099998199963-18.31-0.01
2.4000e+0910489910498383.950.04
2.5000e+09109848110030182.480.08
2.6000e+09114835115104269.170.11
2.7000e+09120054120203148.970.06
2.8000e+09125136125326189.920.08
2.9000e+09130302130472170.150.07
3.0000e+09135330135641310.810.12
3.1000e+09140569140831262.150.10
3.2000e+09145838146042204.440.08
3.3000e+09151068151274206.000.08
3.4000e+09156279156525246.200.09
3.5000e+09161506161795289.450.11
3.6000e+09166836167084248.170.09
3.7000e+09172034172391356.850.13
3.8000e+09177314177715400.980.14
3.9000e+09182670183056386.070.14
4.0000e+09188055188414358.700.13
4.1000e+09193508193787279.420.10
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