Gap size : 46 (r=23)

Generated by program gapCounts : Mon Jun 27 12:41:24 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+020-0-0.00-0.00
3.0000e+020-0-0.00-0.00
4.0000e+020-0-0.00-0.00
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+030-0-0.00-0.00
1.2000e+030-0-0.00-0.00
1.3000e+030-0-0.00-0.00
1.4000e+030-0-0.00-0.00
1.5000e+030-0-0.00-0.00
1.6000e+030-0-0.00-0.00
1.7000e+030-0-0.00-0.00
1.8000e+030-0-0.00-0.00
1.9000e+030-0-0.00-0.00
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+03000.000.00
3.4000e+03000.000.00
3.5000e+03000.000.00
3.6000e+03000.000.00
3.7000e+03000.000.00
3.8000e+03000.000.00
3.9000e+03000.010.00
4.0000e+03000.010.00
4.1000e+03000.010.00
4.2000e+03000.010.00
4.3000e+03000.010.00
4.4000e+03000.010.00
4.5000e+03000.010.00
4.6000e+03000.010.00
4.7000e+03000.010.00
4.8000e+03000.010.00
4.9000e+03000.010.00
5.0000e+03000.010.00
5.2000e+03000.010.00
5.4000e+03000.020.00
5.6000e+03000.020.00
5.8000e+03000.020.00
6.0000e+03000.020.00
6.2000e+03000.020.00
6.4000e+03000.030.00
6.6000e+03000.030.00
6.8000e+03000.030.00
7.0000e+03000.030.00
7.2000e+03000.040.00
7.4000e+03000.040.00
7.6000e+03000.040.00
7.8000e+03000.050.00
8.0000e+03000.050.00
8.2000e+03000.050.01
8.4000e+03000.060.01
8.6000e+03000.060.01
8.8000e+03000.060.01
9.0000e+03000.070.01
9.2000e+03000.070.01
9.4000e+03000.070.01
9.6000e+03000.080.01
9.8000e+03000.080.01
1.0000e+04000.090.01
1.0500e+04000.100.01
1.1000e+04000.110.01
1.1500e+04000.120.01
1.2000e+04000.130.01
1.2500e+04000.140.01
1.3000e+04000.160.01
1.3500e+04000.170.01
1.4000e+04000.190.01
1.4500e+04000.200.02
1.5000e+04000.220.02
1.5500e+04000.230.02
1.6000e+04000.250.02
1.6500e+04000.260.02
1.7000e+04000.280.02
1.7500e+04000.300.02
1.8000e+04000.310.02
1.8500e+04000.330.02
1.9000e+04000.350.03
1.9500e+04000.370.03
2.0000e+04000.390.03
2.1000e+04000.430.03
2.2000e+04000.470.03
2.3000e+04010.510.03
2.4000e+04010.550.04
2.5000e+04010.600.04
2.6000e+04010.650.04
2.7000e+04010.690.04
2.8000e+04010.740.05
2.9000e+04010.790.05
3.0000e+04010.840.05
3.1000e+04010.890.05
3.2000e+04010.950.05
3.3000e+04011.000.06
3.4000e+04011.060.06
3.5000e+04011.110.06
3.6000e+04011.170.06
3.7000e+04011.230.07
3.8000e+04011.290.07
3.9000e+04011.350.07
4.0000e+04011.410.07
4.1000e+04011.470.08
4.2000e+04021.530.08
4.3000e+04021.600.08
4.4000e+04021.660.08
4.5000e+04021.720.09
4.6000e+04021.790.09
4.7000e+04021.860.09
4.8000e+04021.920.09
4.9000e+04021.990.10
5.0000e+04022.060.10
5.2000e+04022.200.10
5.4000e+04022.340.11
5.6000e+04022.490.12
5.8000e+04032.640.12
6.0000e+04032.790.13
6.2000e+04032.940.13
6.4000e+04033.100.14
6.6000e+04033.260.14
6.8000e+04033.420.15
7.0000e+04043.580.15
7.2000e+04043.740.16
7.4000e+04043.910.16
7.6000e+04044.080.17
7.8000e+04044.250.17
8.0000e+04044.420.18
8.2000e+04153.600.14
8.4000e+04153.780.15
8.6000e+04153.950.15
8.8000e+04154.140.16
9.0000e+04154.320.16
9.2000e+04263.500.13
9.4000e+04461.690.06
9.6000e+04461.870.07
9.8000e+04462.060.08
1.0000e+05462.250.08
1.0500e+05670.740.03
1.1000e+05671.230.04
1.1500e+05780.730.03
1.2000e+0598-0.76-0.03
1.2500e+05109-1.24-0.04
1.3000e+05129-2.71-0.09
1.3500e+051210-2.18-0.07
1.4000e+051310-2.64-0.08
1.4500e+051311-2.09-0.07
1.5000e+051311-1.53-0.05
1.5500e+051312-0.97-0.03
1.6000e+051413-1.40-0.04
1.6500e+051613-2.82-0.08
1.7000e+051614-2.24-0.07
1.7500e+051614-1.65-0.05
1.8000e+051615-1.06-0.03
1.8500e+051716-1.46-0.04
1.9000e+051716-0.86-0.02
1.9500e+051817-1.25-0.03
2.0000e+052017-2.63-0.07
2.1000e+052119-2.39-0.06
2.2000e+052220-2.12-0.06
2.3000e+052321-1.84-0.05
2.4000e+052422-1.54-0.04
2.5000e+052424-0.23-0.01
2.6000e+0524251.110.03
2.7000e+052826-1.54-0.04
2.8000e+052828-0.18-0.00
2.9000e+0529290.200.00
3.0000e+0530310.590.01
3.1000e+053232-0.01-0.00
3.2000e+0533330.410.01
3.3000e+0534350.840.02
3.4000e+0535361.290.03
3.5000e+053838-0.26-0.01
3.6000e+0538391.210.03
3.7000e+054141-0.32-0.01
3.8000e+054442-1.83-0.04
3.9000e+054844-4.33-0.09
4.0000e+054945-3.82-0.08
4.1000e+055047-3.30-0.07
4.2000e+055248-3.77-0.08
4.3000e+055550-5.23-0.10
4.4000e+055751-5.69-0.11
4.5000e+055953-6.13-0.12
4.6000e+056054-5.56-0.11
4.7000e+056156-4.99-0.10
4.8000e+056358-5.41-0.10
4.9000e+056559-5.82-0.11
5.0000e+056761-6.22-0.12
5.2000e+057464-10.00-0.18
5.4000e+058067-12.75-0.23
5.6000e+058171-10.47-0.19
5.8000e+058474-10.16-0.18
6.0000e+058977-11.82-0.20
6.2000e+059481-13.46-0.23
6.4000e+059784-13.07-0.22
6.6000e+059887-10.66-0.18
6.8000e+0510191-10.23-0.17
7.0000e+0510594-10.77-0.17
7.2000e+0510998-11.29-0.18
7.4000e+05112101-10.79-0.17
7.6000e+05113105-8.26-0.13
7.8000e+05114108-5.72-0.09
8.0000e+05116112-4.16-0.06
8.2000e+05119115-3.58-0.05
8.4000e+05122119-2.98-0.04
8.6000e+05126123-3.36-0.05
8.8000e+05130126-3.72-0.05
9.0000e+05136130-6.07-0.09
9.2000e+05140134-6.40-0.09
9.4000e+05144137-6.71-0.10
9.6000e+05147141-6.01-0.08
9.8000e+05150145-5.29-0.07
1.0000e+06155148-6.55-0.09
1.0500e+06160158-2.15-0.03
1.1000e+061661671.340.02
1.1500e+06184177-7.08-0.09
1.2000e+06195187-8.43-0.11
1.2500e+06204196-7.69-0.10
1.3000e+06219206-12.88-0.16
1.3500e+06228216-12.00-0.15
1.4000e+06241226-15.06-0.18
1.4500e+06247236-11.04-0.13
1.5000e+06262246-15.97-0.19
1.5500e+06270256-13.83-0.16
1.6000e+06282266-15.63-0.18
1.6500e+06294277-17.38-0.19
1.7000e+06303287-16.08-0.18
1.7500e+06315297-17.72-0.19
1.8000e+06323308-15.31-0.16
1.8500e+06331318-12.85-0.14
1.9000e+06336329-7.34-0.08
1.9500e+06343339-3.79-0.04
2.0000e+06350350-0.19-0.00
2.1000e+063673714.140.04
2.2000e+06396393-3.36-0.03
2.3000e+064114143.290.03
2.4000e+06441436-4.90-0.05
2.5000e+06460458-1.95-0.02
2.6000e+06484480-3.86-0.04
2.7000e+064975025.360.05
2.8000e+065205254.700.04
2.9000e+065415476.170.05
3.0000e+0655757012.750.11
3.1000e+0657459218.450.16
3.2000e+0659561520.250.17
3.3000e+0661263826.160.22
3.4000e+0664466117.170.14
3.5000e+0666268422.270.18
3.6000e+0668270725.470.20
3.7000e+0670673124.760.19
3.8000e+0672175433.140.26
3.9000e+0673977838.600.30
4.0000e+0676080141.150.31
4.1000e+0677782547.780.36
4.2000e+0681184837.490.28
4.3000e+0683687236.270.27
4.4000e+0686489632.130.23
4.5000e+0688592035.060.25
4.6000e+0691094434.060.24
4.7000e+0693496834.130.24
4.8000e+0695699236.270.25
4.9000e+06987101629.480.21
5.0000e+061016104124.740.17
5.2000e+061067108922.470.15
5.4000e+061111113827.430.18
5.6000e+061158118829.620.19
5.8000e+061208123729.040.19
6.0000e+061255128731.660.20
6.2000e+061313133623.490.15
6.4000e+061375138711.520.07
6.6000e+061418143718.740.11
6.8000e+061463148724.140.15
7.0000e+061516153821.710.13
7.2000e+061560158828.460.17
7.4000e+061612163927.370.16
7.6000e+061669169021.440.12
7.8000e+061712174229.670.17
8.0000e+061769179324.040.14
8.2000e+061824184520.570.11
8.4000e+061878189618.230.10
8.6000e+061927194821.040.11
8.8000e+06199120008.980.05
9.0000e+06204620526.050.03
9.2000e+06210021044.240.02
9.4000e+06214721579.570.05
9.6000e+0622162209-6.99-0.04
9.8000e+0622632262-1.43-0.01
1.0000e+0723262314-11.75-0.06
1.0500e+0724502446-3.56-0.02
1.1000e+07257025799.290.05
1.1500e+07271127131.770.01
1.2000e+072828284718.860.09
1.2500e+072969298212.520.06
1.3000e+07311131175.720.03
1.3500e+0732563252-3.56-0.02
1.4000e+0734013389-12.34-0.05
1.4500e+0735473525-21.64-0.09
1.5000e+0736913663-28.48-0.12
1.5500e+0738263800-25.88-0.11
1.6000e+0739603938-21.86-0.09
1.6500e+0740874077-10.43-0.04
1.7000e+0742314215-15.61-0.06
1.7500e+0743884355-33.40-0.13
1.8000e+0745454494-50.83-0.20
1.8500e+0746664634-31.91-0.12
1.9000e+0748034774-28.63-0.11
1.9500e+0749464915-31.03-0.12
2.0000e+0750775056-21.10-0.08
2.1000e+0753685339-29.31-0.11
2.2000e+0756325623-9.34-0.03
2.3000e+0759375908-29.24-0.10
2.4000e+0762106194-16.08-0.06
2.5000e+0765056481-23.90-0.08
2.6000e+0768136769-43.76-0.15
2.7000e+0771407058-81.70-0.27
2.8000e+0774647348-115.75-0.38
2.9000e+0777197639-79.97-0.26
3.0000e+0780227931-91.37-0.29
3.1000e+0783138223-90.00-0.28
3.2000e+0786278516-110.88-0.34
3.3000e+0789308810-120.04-0.36
3.4000e+0792159104-110.51-0.33
3.5000e+0794829400-82.31-0.24
3.6000e+0797819696-85.46-0.25
3.7000e+07100619992-68.98-0.20
3.8000e+071034910289-59.90-0.17
3.9000e+071063810587-51.24-0.14
4.0000e+071094710885-62.00-0.17
4.1000e+071124811184-64.22-0.18
4.2000e+071155911483-75.90-0.21
4.3000e+071183511783-52.06-0.14
4.4000e+071210612083-22.72-0.06
4.5000e+071242212384-37.88-0.10
4.6000e+071275212685-66.56-0.17
4.7000e+071303112987-43.78-0.11
4.8000e+071332813289-38.55-0.10
4.9000e+071362413592-31.87-0.08
5.0000e+071391313895-17.76-0.04
5.2000e+0714494145038.720.02
5.4000e+071514515112-33.20-0.08
5.6000e+071577015722-47.57-0.11
5.8000e+071636916335-34.48-0.08
6.0000e+071702516948-76.97-0.18
6.2000e+071763417563-71.11-0.16
6.4000e+071820018179-20.95-0.05
6.6000e+071881418796-17.54-0.04
6.8000e+071942619415-10.92-0.02
7.0000e+0720033200351.870.00
7.2000e+07205962065659.780.13
7.4000e+07212212127856.770.12
7.6000e+07218542190146.810.10
7.8000e+072253322525-8.12-0.02
8.0000e+0723148231501.920.00
8.2000e+072377823776-2.08-0.00
8.4000e+07243752440327.850.06
8.6000e+07250132503117.680.03
8.8000e+07256292565930.390.06
9.0000e+07262472628941.940.08
9.2000e+07268472691972.320.14
9.4000e+07274942755156.510.11
9.6000e+07281082818274.490.14
9.8000e+07287312881584.230.16
1.0000e+082932729449121.710.22
1.0500e+08309383103697.570.18
1.1000e+08325333262793.720.17
1.1500e+083411434222107.920.19
1.2000e+08357533582167.950.12
1.2500e+08373993742424.630.04
1.3000e+08389883903041.760.07
1.3500e+08406064063933.200.05
1.4000e+08422044225247.780.08
1.4500e+08437884386779.380.12
1.5000e+084537945486106.860.16
1.5500e+08470804710727.110.04
1.6000e+08487104873121.010.03
1.6500e+08503175035740.470.06
1.7000e+08518925198694.390.14
1.7500e+085351353618104.670.15
1.8000e+085509555251156.250.22
1.8500e+085671156887176.030.25
1.9000e+085827958525245.940.34
1.9500e+085987460165290.920.40
2.0000e+086152161807285.900.39
2.1000e+086480365097293.600.39
2.2000e+086805968394334.610.43
2.3000e+087139471697303.490.39
2.4000e+087463275008375.890.47
2.5000e+087792778324397.470.49
2.6000e+088130881647338.910.41
2.7000e+088462284975352.940.42
2.8000e+088803388308275.300.32
2.9000e+089138991647257.750.29
3.0000e+089465994990331.080.37
3.1000e+089807598338263.070.29
3.2000e+08101404101691286.550.31
3.3000e+08104684105047363.330.39
3.4000e+08108100108408308.260.33
3.5000e+08111543111773230.170.24
3.6000e+08114986115142155.930.16
3.7000e+08118358118514156.400.16
3.8000e+08121659121890231.450.23
3.9000e+08124976125270293.980.29
4.0000e+08128361128653291.850.29
4.1000e+08131791132039247.980.24
4.2000e+08135091135428337.250.33
4.3000e+08138508138821312.580.30
4.4000e+08141873142216342.870.33
4.5000e+08145324145614290.040.27
4.6000e+08148803149015212.000.20
4.7000e+08152228152419190.690.18
4.8000e+08155604155825221.020.20
4.9000e+08158960159234273.930.25
5.0000e+08162403162645242.350.22
5.2000e+08169271169475204.470.18
5.4000e+08176207176315107.900.09
5.6000e+08183044183163119.200.10
5.8000e+08189844190020175.970.15
6.0000e+08196656196885228.830.19
6.2000e+08203443203757314.440.26
6.4000e+08210247210637390.490.31
6.6000e+08217156217525368.670.29
6.8000e+08224053224419365.710.29
7.0000e+08230913231319406.350.31
7.2000e+08237797238226429.340.33
7.4000e+08244682245139457.460.34
7.6000e+08251560252059498.500.37
7.8000e+08258470258983513.260.38
8.0000e+08265305265914608.540.44
8.2000e+08272228272849621.180.45
8.4000e+08279162279790627.990.45
8.6000e+08286186286736549.820.39
8.8000e+08293174293687512.530.36
9.0000e+08300108300642533.960.37
9.2000e+08306941307602660.980.45
9.4000e+08314050314566516.460.35
9.6000e+08320973321535562.280.38
9.8000e+08327744328508764.310.51
1.0000e+09334720335485765.460.50
1.0500e+09352358352946587.610.38
1.1000e+09369788370429641.220.40
1.1500e+09387164387935770.920.47
1.2000e+09404671405461790.440.48
1.2500e+09422110423008897.660.53
1.3000e+09439693440573879.540.51
1.3500e+09457279458155876.140.50
1.4000e+09474927475755827.600.47
1.4500e+09492700493370670.120.37
1.5000e+09510307511001693.970.38
1.5500e+09527964528646682.480.37
1.6000e+09545723546306583.020.31
1.6500e+09563241563979738.010.39
1.7000e+09581015581665649.920.34
1.7500e+09598670599363693.220.35
1.8000e+09616394617073679.460.34
1.8500e+09634000634795795.180.39
1.9000e+09651616652528911.980.45
1.9500e+09669366670271905.470.44
2.0000e+09687135688025890.270.43
2.1000e+09723092723562470.470.22
2.2000e+09758797759137340.020.16
2.3000e+09794084794747662.650.30
2.4000e+09829720830389669.300.30
2.5000e+09865624866063439.120.19
2.6000e+09901139901766627.410.27
2.7000e+09936985937498512.650.21
2.8000e+09972830973255425.410.17
2.9000e+091008961100903877.410.03
3.0000e+0910446791044845166.460.07
3.1000e+0910802581080675417.450.16
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