Gap size : 32 (r=16)

Generated by program gapCounts : Mon Jun 27 12:41:06 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+020-0-0.00-0.00
6.0000e+020-0-0.00-0.00
7.0000e+020-0-0.00-0.00
8.0000e+020-0-0.00-0.00
9.0000e+020-0-0.00-0.00
1.0000e+030-0-0.00-0.00
1.1000e+03000.000.00
1.2000e+03000.000.00
1.3000e+03000.000.00
1.4000e+03000.000.00
1.5000e+03000.010.00
1.6000e+03000.010.00
1.7000e+03000.010.00
1.8000e+03000.020.00
1.9000e+03000.020.00
2.0000e+03000.020.00
2.1000e+03000.030.00
2.2000e+03000.030.01
2.3000e+03000.040.01
2.4000e+03000.040.01
2.5000e+03000.050.01
2.6000e+03000.060.01
2.7000e+03000.060.01
2.8000e+03000.070.01
2.9000e+03000.080.01
3.0000e+03000.080.01
3.1000e+03000.090.01
3.2000e+03000.100.01
3.3000e+03000.110.02
3.4000e+03000.120.02
3.5000e+03000.130.02
3.6000e+03000.140.02
3.7000e+03000.150.02
3.8000e+03000.150.02
3.9000e+03000.160.02
4.0000e+03000.180.02
4.1000e+03000.190.02
4.2000e+03000.200.03
4.3000e+03000.210.03
4.4000e+03000.220.03
4.5000e+03000.230.03
4.6000e+03000.240.03
4.7000e+03000.250.03
4.8000e+03000.270.03
4.9000e+03000.280.03
5.0000e+03000.290.03
5.2000e+03000.320.04
5.4000e+03000.340.04
5.6000e+03000.370.04
5.8000e+0310-0.60-0.07
6.0000e+0310-0.57-0.06
6.2000e+0310-0.55-0.06
6.4000e+0310-0.52-0.06
6.6000e+0311-0.48-0.05
6.8000e+0311-0.45-0.05
7.0000e+0311-0.42-0.04
7.2000e+0311-0.39-0.04
7.4000e+0311-0.36-0.04
7.6000e+0311-0.32-0.03
7.8000e+0311-0.29-0.03
8.0000e+0311-0.25-0.03
8.2000e+0311-0.22-0.02
8.4000e+0311-0.18-0.02
8.6000e+0311-0.14-0.01
8.8000e+0311-0.11-0.01
9.0000e+0311-0.07-0.01
9.2000e+0311-0.03-0.00
9.4000e+03110.010.00
9.6000e+03110.040.00
9.8000e+03110.080.01
1.0000e+04110.120.01
1.0500e+04110.230.02
1.1000e+0421-0.67-0.06
1.1500e+0421-0.56-0.05
1.2000e+0422-0.45-0.04
1.2500e+0422-0.34-0.03
1.3000e+0422-0.23-0.02
1.3500e+0422-0.11-0.01
1.4000e+04220.000.00
1.4500e+04220.120.01
1.5000e+04220.240.02
1.5500e+04220.370.03
1.6000e+04220.490.04
1.6500e+04230.620.05
1.7000e+04230.750.06
1.7500e+04230.880.06
1.8000e+04231.010.07
1.8500e+04231.140.08
1.9000e+04231.280.09
1.9500e+04231.420.10
2.0000e+04241.550.11
2.1000e+04241.830.13
2.2000e+04242.120.14
2.3000e+04242.410.16
2.4000e+04252.700.18
2.5000e+04253.000.19
2.6000e+04253.300.21
2.7000e+04263.610.22
2.8000e+04461.920.12
2.9000e+04462.230.13
3.0000e+04472.550.15
3.1000e+04472.870.17
3.2000e+04473.200.19
3.3000e+04483.530.20
3.4000e+04582.860.16
3.5000e+04583.190.18
3.6000e+04593.530.20
3.7000e+04593.870.21
3.8000e+04594.220.23
3.9000e+045104.560.24
4.0000e+046103.910.21
4.1000e+046104.260.22
4.2000e+048112.620.14
4.3000e+048112.970.15
4.4000e+049112.330.12
4.5000e+0410121.690.09
4.6000e+0410122.050.10
4.7000e+0411121.420.07
4.8000e+0412130.790.04
4.9000e+0412131.150.06
5.0000e+0412141.530.07
5.2000e+0413141.270.06
5.4000e+0414151.030.05
5.6000e+041616-0.21-0.01
5.8000e+0416170.560.03
6.0000e+0416171.340.06
6.2000e+0417181.120.05
6.4000e+0418190.910.04
6.6000e+0419200.710.03
6.8000e+042121-0.49-0.02
7.0000e+042221-0.69-0.03
7.2000e+0422220.120.01
7.4000e+042323-0.06-0.00
7.6000e+0423240.760.03
7.8000e+0423251.590.06
8.0000e+0424251.420.06
8.2000e+0425261.260.05
8.4000e+0426271.100.04
8.6000e+0427280.940.04
8.8000e+0427291.790.07
9.0000e+0428301.640.06
9.2000e+0428302.500.09
9.4000e+0428313.360.13
9.6000e+0430322.220.08
9.8000e+0430333.090.11
1.0000e+0532341.960.07
1.0500e+0535361.160.04
1.1000e+0535383.370.12
1.1500e+0537413.600.12
1.2000e+0537435.860.20
1.2500e+0541454.130.14
1.3000e+0542475.410.18
1.3500e+0548501.720.06
1.4000e+0549523.030.10
1.4500e+0551543.370.11
1.5000e+0553573.710.11
1.5500e+0554595.070.15
1.6000e+0557614.440.13
1.6500e+0559644.830.14
1.7000e+0560666.230.18
1.7500e+0560698.630.25
1.8000e+0563718.050.23
1.8500e+0564739.480.27
1.9000e+0566769.920.28
1.9500e+05667812.370.34
2.0000e+05688112.830.35
2.1000e+05718614.780.40
2.2000e+0581919.760.26
2.3000e+05859610.780.28
2.4000e+05911019.830.25
2.5000e+05971068.900.22
2.6000e+059811113.010.32
2.7000e+0510511611.140.27
2.8000e+0511012111.300.27
2.9000e+0511412612.490.29
3.0000e+0511913212.700.29
3.1000e+0512313713.930.32
3.2000e+0512714215.180.34
3.3000e+0513514712.450.28
3.4000e+051431539.740.21
3.5000e+051501588.060.17
3.6000e+051561637.390.16
3.7000e+051601698.740.18
3.8000e+051661748.100.17
3.9000e+051741795.490.11
4.0000e+051811853.890.08
4.1000e+051881902.300.05
4.2000e+05198196-2.27-0.05
4.3000e+05207201-5.82-0.12
4.4000e+05210207-3.36-0.07
4.5000e+05216212-3.89-0.08
4.6000e+05220218-2.40-0.05
4.7000e+05226223-2.90-0.06
4.8000e+05229229-0.39-0.01
4.9000e+052312343.140.06
5.0000e+052372402.680.05
5.2000e+052472513.790.07
5.4000e+052562625.950.11
5.6000e+052672736.150.11
5.8000e+052802844.390.08
6.0000e+052932962.670.05
6.2000e+053023074.980.08
6.4000e+053183180.340.01
6.6000e+05333330-3.28-0.05
6.8000e+053393412.150.03
7.0000e+05361353-8.40-0.14
7.2000e+05371364-6.92-0.11
7.4000e+05383376-7.40-0.12
7.6000e+05395387-7.86-0.12
7.8000e+05412399-13.29-0.20
8.0000e+05421410-10.70-0.16
8.2000e+05430422-8.07-0.12
8.4000e+05445434-11.43-0.17
8.6000e+05457445-11.76-0.17
8.8000e+05468457-11.06-0.16
9.0000e+05476469-7.34-0.11
9.2000e+05487480-6.60-0.09
9.4000e+05502492-9.84-0.14
9.6000e+05519504-15.06-0.21
9.8000e+05532516-16.26-0.23
1.0000e+06550528-22.44-0.31
1.0500e+06582557-24.80-0.34
1.1000e+06613587-26.04-0.35
1.1500e+06643617-26.19-0.34
1.2000e+06672647-25.23-0.32
1.2500e+06712677-35.17-0.44
1.3000e+06742707-35.03-0.43
1.3500e+06765737-27.80-0.34
1.4000e+06801768-33.49-0.40
1.4500e+06831798-33.11-0.39
1.5000e+06856828-27.65-0.32
1.5500e+06885859-26.12-0.30
1.6000e+06913889-23.52-0.27
1.6500e+06952920-31.86-0.36
1.7000e+06983951-32.13-0.35
1.7500e+061008982-26.35-0.29
1.8000e+0610301012-17.51-0.19
1.8500e+0610691043-25.61-0.27
1.9000e+0610941074-19.66-0.21
1.9500e+0611221105-16.67-0.17
2.0000e+0611491136-12.62-0.13
2.1000e+0612091199-10.38-0.10
2.2000e+0612631261-1.96-0.02
2.3000e+06131813245.630.05
2.4000e+06138213864.370.04
2.5000e+0614531449-3.74-0.03
2.6000e+0615321512-19.70-0.18
2.7000e+0616031575-27.54-0.25
2.8000e+0616661639-27.24-0.24
2.9000e+0617471702-44.83-0.39
3.0000e+0618101766-44.30-0.38
3.1000e+0618711829-41.66-0.35
3.2000e+0619341893-40.92-0.34
3.3000e+0619941957-37.08-0.31
3.4000e+0620452021-24.14-0.20
3.5000e+0620982085-13.11-0.11
3.6000e+0621592149-10.00-0.08
3.7000e+0622232213-9.79-0.08
3.8000e+0622922277-14.51-0.11
3.9000e+0623512342-9.15-0.07
4.0000e+0624202406-13.71-0.10
4.1000e+0624902471-19.20-0.14
4.2000e+0625472535-11.61-0.09
4.3000e+0626232600-22.96-0.17
4.4000e+0627042665-39.25-0.29
4.5000e+0627762730-46.47-0.34
4.6000e+0628452794-50.62-0.36
4.7000e+0628982859-38.72-0.27
4.8000e+0629572924-32.76-0.23
4.9000e+0630282989-38.75-0.27
5.0000e+0630883054-33.67-0.23
5.2000e+0632283185-43.37-0.29
5.4000e+0633703315-54.87-0.37
5.6000e+0634923446-46.18-0.30
5.8000e+0636333577-56.30-0.36
6.0000e+0637693708-61.25-0.39
6.2000e+0638933839-54.04-0.34
6.4000e+0640193970-48.68-0.30
6.6000e+0641364102-34.16-0.21
6.8000e+0642824233-48.50-0.29
7.0000e+0644204365-54.71-0.33
7.2000e+0645654497-67.78-0.40
7.4000e+0646884629-58.73-0.34
7.6000e+0648254761-63.56-0.37
7.8000e+0649534894-59.28-0.34
8.0000e+0650855026-58.88-0.33
8.2000e+0652245159-65.37-0.36
8.4000e+0653285291-36.76-0.20
8.6000e+0654655424-41.06-0.22
8.8000e+0655965557-39.25-0.21
9.0000e+0657165690-26.35-0.14
9.2000e+0658255823-2.36-0.01
9.4000e+06594959566.710.04
9.6000e+0660916089-2.13-0.01
9.8000e+0662256222-2.89-0.01
1.0000e+0763646355-8.57-0.04
1.0500e+076676668913.060.07
1.1000e+07702170232.140.01
1.1500e+07735173586.630.03
1.2000e+0777007693-7.49-0.04
1.2500e+0780558028-27.25-0.13
1.3000e+0783698363-5.67-0.03
1.3500e+07869386996.230.03
1.4000e+0790589035-22.57-0.10
1.4500e+0794099372-37.08-0.16
1.5000e+0797679709-58.32-0.25
1.5500e+071010510046-59.31-0.25
1.6000e+071044210383-59.06-0.24
1.6500e+071080510720-84.57-0.35
1.7000e+071113211058-73.87-0.30
1.7500e+071147111396-74.95-0.30
1.8000e+071178811734-53.84-0.21
1.8500e+071213912072-66.54-0.26
1.9000e+071245512411-44.06-0.17
1.9500e+071281512750-65.40-0.25
2.0000e+071317713088-88.58-0.33
2.1000e+071380713767-40.46-0.15
2.2000e+071448914445-43.75-0.16
2.3000e+071515715125-32.49-0.11
2.4000e+071582115804-16.74-0.06
2.5000e+071654616484-61.51-0.21
2.6000e+071722817165-62.84-0.21
2.7000e+071791717846-70.77-0.23
2.8000e+071859818528-70.32-0.23
2.9000e+071931819209-108.51-0.35
3.0000e+071997019892-78.36-0.25
3.1000e+072070320574-128.90-0.40
3.2000e+072139821257-141.14-0.43
3.3000e+072211721940-177.10-0.53
3.4000e+072277922623-155.79-0.46
3.5000e+072349023307-183.24-0.54
3.6000e+072415523991-164.45-0.48
3.7000e+072481324675-138.43-0.40
3.8000e+072549825359-139.20-0.39
3.9000e+072618226043-138.77-0.39
4.0000e+072684726728-119.14-0.33
4.1000e+072756827413-155.34-0.43
4.2000e+072823028098-132.35-0.36
4.3000e+072891928783-136.21-0.37
4.4000e+072960829468-139.90-0.37
4.5000e+073027030154-116.45-0.31
4.6000e+073098230839-142.85-0.37
4.7000e+073167931525-154.12-0.40
4.8000e+073231032211-99.25-0.25
4.9000e+073304732897-150.26-0.38
5.0000e+073369733583-114.15-0.29
5.2000e+073502934955-73.58-0.18
5.4000e+073638136328-52.60-0.13
5.6000e+073777937702-77.23-0.18
5.8000e+073916939075-93.51-0.22
6.0000e+074051440450-64.46-0.15
6.2000e+074185641824-32.11-0.07
6.4000e+074326343199-64.49-0.14
6.6000e+074468644573-112.61-0.25
6.8000e+074610945949-160.49-0.35
7.0000e+074752547324-201.16-0.43
7.2000e+074892348699-223.62-0.48
7.4000e+075026350075-187.90-0.40
7.6000e+075160951451-158.01-0.33
7.8000e+075299652827-168.96-0.35
8.0000e+075439754203-193.77-0.39
8.2000e+075575755580-177.44-0.36
8.4000e+075715456956-197.99-0.39
8.6000e+075850958333-176.43-0.35
8.8000e+075988059709-170.76-0.33
9.0000e+076125061086-164.00-0.32
9.2000e+076275262463-289.15-0.55
9.4000e+076412763840-287.22-0.54
9.6000e+076549965217-282.22-0.53
9.8000e+076687366594-279.15-0.52
1.0000e+086829167971-320.02-0.59
1.0500e+087177771414-362.97-0.65
1.1000e+087524874857-390.67-0.69
1.1500e+087875378301-452.19-0.78
1.2000e+088219381744-448.59-0.76
1.2500e+088565285188-463.92-0.77
1.3000e+088914288632-510.23-0.84
1.3500e+089260992075-533.57-0.86
1.4000e+089605995519-539.96-0.86
1.4500e+089940098963-437.45-0.68
1.5000e+08102852102406-446.06-0.69
1.5500e+08106355105849-505.82-0.77
1.6000e+08109739109292-446.74-0.67
1.6500e+08113232112735-496.86-0.73
1.7000e+08116661116178-483.19-0.70
1.7500e+08120025119620-404.73-0.58
1.8000e+08123549123062-486.52-0.69
1.8500e+08126926126504-421.56-0.59
1.9000e+08130334129946-387.87-0.54
1.9500e+08133812133388-424.44-0.58
2.0000e+08137197136829-368.30-0.50
2.1000e+08144099143710-388.90-0.51
2.2000e+08150958150590-367.73-0.48
2.3000e+08157807157469-337.81-0.43
2.4000e+08164625164347-278.20-0.35
2.5000e+08171569171223-345.92-0.42
2.6000e+08178577178098-478.99-0.58
2.7000e+08185332184972-360.43-0.43
2.8000e+08192173191844-329.25-0.38
2.9000e+08199039198715-324.45-0.37
3.0000e+08206004205584-420.05-0.47
3.1000e+08212871212452-419.05-0.47
3.2000e+08219687219319-368.45-0.40
3.3000e+08226609226184-425.24-0.46
3.4000e+08233672233048-624.43-0.67
3.5000e+08240614239910-704.00-0.74
3.6000e+08247390246771-618.96-0.64
3.7000e+08254352253631-721.31-0.74
3.8000e+08261358260489-869.02-0.88
3.9000e+08268163267346-817.10-0.82
4.0000e+08275143274201-941.53-0.93
4.1000e+08281967281056-911.31-0.89
4.2000e+08288932287909-1023.44-0.99
4.3000e+08295818294760-1057.89-1.01
4.4000e+08302674301610-1063.67-1.01
4.5000e+08309441308459-981.76-0.92
4.6000e+08316237315307-930.15-0.87
4.7000e+08323070322153-916.83-0.84
4.8000e+08329909328998-910.79-0.83
4.9000e+08336679335842-837.03-0.76
5.0000e+08343414342684-729.53-0.65
5.2000e+08357128356366-762.28-0.67
5.4000e+08370777370042-734.96-0.64
5.6000e+08384352383714-638.50-0.54
5.8000e+08397993397380-612.81-0.51
6.0000e+08411621411042-578.82-0.48
6.2000e+08425111424700-411.45-0.33
6.4000e+08438854438352-501.64-0.40
6.6000e+08452690452001-689.30-0.54
6.8000e+08466117465645-472.37-0.37
7.0000e+08479781479284-496.79-0.38
7.2000e+08493347492920-427.47-0.32
7.4000e+08506981506551-430.37-0.32
7.6000e+08520686520178-508.41-0.38
7.8000e+08534222533800-421.53-0.31
8.0000e+08548030547419-610.67-0.44
8.2000e+08561637561034-602.78-0.43
8.4000e+08575225574645-579.80-0.41
8.6000e+08588865588252-612.67-0.43
8.8000e+08602588601856-732.34-0.51
9.0000e+08616073615455-617.75-0.42
9.2000e+08629605629051-553.85-0.38
9.4000e+08643128642643-484.61-0.33
9.6000e+08656818656232-585.95-0.39
9.8000e+08670194669817-376.85-0.25
1.0000e+09683896683399-497.25-0.33
1.0500e+09717883717338-545.28-0.35
1.1000e+09751958751256-702.25-0.44
1.1500e+09785971785153-817.53-0.50
1.2000e+09819666819031-634.53-0.38
1.2500e+09853679852890-788.70-0.47
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