Gap size : 68 (r=34)

Generated by program gapCounts : Mon Jun 27 12:44:10 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+030-0-0.00-0.00
2.1000e+030-0-0.00-0.00
2.2000e+030-0-0.00-0.00
2.3000e+030-0-0.00-0.00
2.4000e+030-0-0.00-0.00
2.5000e+030-0-0.00-0.00
2.6000e+030-0-0.00-0.00
2.7000e+030-0-0.00-0.00
2.8000e+030-0-0.00-0.00
2.9000e+030-0-0.00-0.00
3.0000e+030-0-0.00-0.00
3.1000e+030-0-0.00-0.00
3.2000e+030-0-0.00-0.00
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+03000.000.00
3.9000e+03000.000.00
4.0000e+03000.000.00
4.1000e+03000.000.00
4.2000e+03000.000.00
4.3000e+03000.000.00
4.4000e+03000.000.00
4.5000e+03000.000.00
4.6000e+03000.000.00
4.7000e+03000.000.00
4.8000e+03000.000.00
4.9000e+03000.000.00
5.0000e+03000.000.00
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+04000.010.00
1.9500e+04000.010.00
2.0000e+04000.010.00
2.1000e+04000.010.00
2.2000e+04000.010.00
2.3000e+04000.010.00
2.4000e+04000.010.00
2.5000e+04000.010.00
2.6000e+04000.010.00
2.7000e+04000.010.00
2.8000e+04000.020.00
2.9000e+04000.020.00
3.0000e+04000.020.00
3.1000e+04000.020.00
3.2000e+04000.020.00
3.3000e+04000.020.00
3.4000e+04000.030.00
3.5000e+04000.030.00
3.6000e+04000.030.00
3.7000e+04000.030.00
3.8000e+04000.030.00
3.9000e+04000.040.00
4.0000e+04000.040.00
4.1000e+04000.040.00
4.2000e+04000.040.00
4.3000e+04000.040.00
4.4000e+04000.050.00
4.5000e+04000.050.00
4.6000e+04000.050.00
4.7000e+04000.050.00
4.8000e+04000.060.00
4.9000e+04000.060.00
5.0000e+04000.060.00
5.2000e+04000.070.00
5.4000e+04000.080.00
5.6000e+04000.080.00
5.8000e+04000.090.00
6.0000e+04000.090.00
6.2000e+04000.100.00
6.4000e+04000.110.00
6.6000e+04000.120.01
6.8000e+04000.120.01
7.0000e+04000.130.01
7.2000e+04000.140.01
7.4000e+04000.150.01
7.6000e+04000.160.01
7.8000e+04000.170.01
8.0000e+04000.170.01
8.2000e+04000.180.01
8.4000e+04000.190.01
8.6000e+04000.200.01
8.8000e+04000.210.01
9.0000e+04000.220.01
9.2000e+04000.230.01
9.4000e+04000.240.01
9.6000e+04000.250.01
9.8000e+04000.260.01
1.0000e+05000.280.01
1.0500e+05000.300.01
1.1000e+05000.330.01
1.1500e+05000.360.01
1.2000e+05000.390.01
1.2500e+05000.430.01
1.3000e+05000.460.02
1.3500e+0510-0.51-0.02
1.4000e+0511-0.47-0.01
1.4500e+0511-0.43-0.01
1.5000e+0511-0.40-0.01
1.5500e+0511-0.36-0.01
1.6000e+0511-0.32-0.01
1.6500e+0511-0.28-0.01
1.7000e+0511-0.24-0.01
1.7500e+0511-0.20-0.01
1.8000e+0511-0.16-0.00
1.8500e+0511-0.11-0.00
1.9000e+0511-0.07-0.00
1.9500e+0511-0.02-0.00
2.0000e+05110.020.00
2.1000e+05110.110.00
2.2000e+05110.210.01
2.3000e+05110.310.01
2.4000e+05110.410.01
2.5000e+05120.520.01
2.6000e+05120.620.02
2.7000e+05120.730.02
2.8000e+05120.850.02
2.9000e+05120.960.02
3.0000e+05220.080.00
3.1000e+05220.200.00
3.2000e+05220.320.01
3.3000e+0532-0.56-0.01
3.4000e+0533-0.43-0.01
3.5000e+0533-0.30-0.01
3.6000e+0533-0.17-0.00
3.7000e+0533-0.04-0.00
3.8000e+0543-0.91-0.02
3.9000e+0543-0.77-0.02
4.0000e+0543-0.63-0.01
4.1000e+0544-0.49-0.01
4.2000e+0544-0.35-0.01
4.3000e+0544-0.21-0.00
4.4000e+0544-0.06-0.00
4.5000e+0554-0.91-0.02
4.6000e+0554-0.76-0.01
4.7000e+0554-0.61-0.01
4.8000e+0555-0.46-0.01
4.9000e+0555-0.31-0.01
5.0000e+0555-0.15-0.00
5.2000e+0565-0.83-0.02
5.4000e+0565-0.51-0.01
5.6000e+0566-0.18-0.00
5.8000e+0586-1.85-0.03
6.0000e+0586-1.51-0.03
6.2000e+0587-1.16-0.02
6.4000e+0587-0.81-0.01
6.6000e+0598-1.45-0.02
6.8000e+0598-1.09-0.02
7.0000e+05108-1.72-0.03
7.2000e+05109-1.35-0.02
7.4000e+05109-0.97-0.02
7.6000e+05109-0.59-0.01
7.8000e+051010-0.21-0.00
8.0000e+0510100.180.00
8.2000e+0510110.580.01
8.4000e+051111-0.02-0.00
8.6000e+0511110.380.01
8.8000e+0511120.790.01
9.0000e+0511121.200.02
9.2000e+0511131.620.02
9.4000e+0512131.040.01
9.6000e+0512131.460.02
9.8000e+0513140.890.01
1.0000e+0613141.320.02
1.0500e+0615150.420.01
1.1000e+0616170.540.01
1.1500e+0616181.680.02
1.2000e+0618190.830.01
1.2500e+0618202.010.03
1.3000e+0619212.210.03
1.3500e+0619223.430.04
1.4000e+0620243.670.04
1.4500e+0620254.920.06
1.5000e+0620266.190.07
1.5500e+0623274.470.05
1.6000e+0624294.780.05
1.6500e+0626304.100.05
1.7000e+0626315.430.06
1.7500e+0627335.780.06
1.8000e+0628346.140.07
1.8500e+0631364.520.05
1.9000e+0633373.910.04
1.9500e+0633385.310.06
2.0000e+0634405.730.06
2.1000e+0637435.600.06
2.2000e+0639466.520.06
2.3000e+0642486.490.06
2.4000e+0643528.500.08
2.5000e+0648556.560.06
2.6000e+0651586.660.06
2.7000e+0654616.800.06
2.8000e+0656647.980.07
2.9000e+06566711.200.10
3.0000e+0662708.460.07
3.1000e+0667746.750.06
3.2000e+0670777.070.06
3.3000e+0673807.430.06
3.4000e+0678845.830.05
3.5000e+0683874.250.03
3.6000e+0690910.710.01
3.7000e+0690944.190.03
3.8000e+0691986.710.05
3.9000e+06961015.250.04
4.0000e+061011053.830.03
4.1000e+061031085.430.04
4.2000e+061051127.060.05
4.3000e+061081167.710.06
4.4000e+061141195.390.04
4.5000e+061161237.100.05
4.6000e+061201276.830.05
4.7000e+061221318.580.06
4.8000e+061251349.360.07
4.9000e+0612813810.160.07
5.0000e+061391422.980.02
5.2000e+061491500.700.00
5.4000e+061541583.500.02
5.6000e+061641651.390.01
5.8000e+06177173-3.64-0.02
6.0000e+06183181-1.60-0.01
6.2000e+06193190-3.48-0.02
6.4000e+06200198-2.28-0.01
6.6000e+06212206-6.02-0.04
6.8000e+06225214-10.68-0.06
7.0000e+06228223-5.28-0.03
7.2000e+06238231-6.81-0.04
7.4000e+06243240-3.28-0.02
7.6000e+06252248-3.68-0.02
7.8000e+062562570.970.01
8.0000e+062622663.680.02
8.2000e+06276274-1.54-0.01
8.4000e+062832830.290.00
8.6000e+06293292-0.83-0.00
8.8000e+062973014.110.02
9.0000e+063093101.100.01
9.2000e+063183191.140.01
9.4000e+063233285.230.03
9.6000e+06339337-1.63-0.01
9.8000e+06351347-4.44-0.02
1.0000e+07358356-2.20-0.01
1.0500e+073753794.100.02
1.1000e+073994033.670.02
1.1500e+074214275.520.03
1.2000e+0743945111.610.05
1.2500e+074674757.950.04
1.3000e+0748450015.530.07
1.3500e+0751352411.330.05
1.4000e+075425497.360.03
1.4500e+0756457510.590.05
1.5000e+075996001.020.00
1.5500e+076256260.660.00
1.6000e+076446517.480.03
1.6500e+076686779.490.04
1.7000e+076987045.680.02
1.7500e+077247306.040.02
1.8000e+077497577.570.03
1.8500e+077807833.270.01
1.9000e+078028108.130.03
1.9500e+0782383714.140.05
2.0000e+0785186413.310.05
2.1000e+079119198.080.03
2.2000e+079709744.420.02
2.3000e+071019103011.300.04
2.4000e+071066108720.700.07
2.5000e+071121114422.590.08
2.6000e+07119212018.960.03
2.7000e+071228125930.790.10
2.8000e+071280131737.060.12
2.9000e+071340137635.760.11
3.0000e+071402143532.870.10
3.1000e+071470149424.370.08
3.2000e+071525155429.260.09
3.3000e+071586161528.520.09
3.4000e+071640167535.140.10
3.5000e+071713173623.120.07
3.6000e+071773179724.430.07
3.7000e+071838185921.070.06
3.8000e+071900192121.040.06
3.9000e+071969198314.320.04
4.0000e+072023204622.900.06
4.1000e+072082210926.780.07
4.2000e+072144217227.960.08
4.3000e+072199223536.410.10
4.4000e+072269229930.140.08
4.5000e+072326236337.150.10
4.6000e+072393242734.410.09
4.7000e+072475249216.940.04
4.8000e+072531255725.720.07
4.9000e+072596262225.740.07
5.0000e+072650268737.010.09
5.2000e+072792281826.250.06
5.4000e+072923295027.410.07
5.6000e+073061308322.450.05
5.8000e+07321232175.330.01
6.0000e+0733573352-4.97-0.01
6.2000e+0735183488-30.49-0.07
6.4000e+0736563624-32.24-0.07
6.6000e+0737833761-22.25-0.05
6.8000e+0739263898-27.54-0.06
7.0000e+0740564037-19.14-0.04
7.2000e+0741964176-20.06-0.04
7.4000e+0743204316-4.33-0.01
7.6000e+0744644456-7.97-0.02
7.8000e+0745984597-0.98-0.00
8.0000e+0747544739-15.39-0.03
8.2000e+0749104881-29.21-0.06
8.4000e+0750345024-10.46-0.02
8.6000e+0751805167-13.15-0.03
8.8000e+0753225311-11.30-0.02
9.0000e+0754675455-11.91-0.02
9.2000e+0756065600-6.00-0.01
9.4000e+0757665745-20.58-0.04
9.6000e+0758935891-1.66-0.00
9.8000e+0760386038-0.26-0.00
1.0000e+0862006185-15.37-0.03
1.0500e+0866066554-52.15-0.09
1.1000e+0869836926-57.14-0.10
1.1500e+0873747301-73.48-0.13
1.2000e+0877627678-84.30-0.14
1.2500e+0881218057-63.70-0.11
1.3000e+0885188439-78.78-0.13
1.3500e+0889028823-78.63-0.13
1.4000e+0892799210-69.35-0.11
1.4500e+0896709598-72.00-0.11
1.5000e+08100409988-51.66-0.08
1.5500e+081043610381-55.40-0.08
1.6000e+081084510775-70.29-0.10
1.6500e+081123411171-63.39-0.09
1.7000e+081159511568-26.75-0.04
1.7500e+081197011968-2.43-0.00
1.8000e+081241312369-44.47-0.06
1.8500e+081281512771-43.92-0.06
1.9000e+081320913175-33.84-0.05
1.9500e+081365113581-70.25-0.10
2.0000e+081408613988-98.21-0.13
2.1000e+081489314806-86.90-0.11
2.2000e+081577615630-146.18-0.19
2.3000e+081661616459-157.32-0.20
2.4000e+081747117292-178.56-0.22
2.5000e+081832018131-189.10-0.23
2.6000e+081911518974-141.14-0.17
2.7000e+081992319821-101.86-0.12
2.8000e+082080520673-132.44-0.15
2.9000e+082168321528-155.03-0.18
3.0000e+082255922387-171.77-0.19
3.1000e+082342123250-170.80-0.19
3.2000e+082426024117-143.24-0.16
3.3000e+082508724987-100.22-0.11
3.4000e+082593225860-71.84-0.08
3.5000e+082682026737-83.21-0.09
3.6000e+082773927617-122.43-0.13
3.7000e+082859928499-99.59-0.10
3.8000e+082948629385-100.77-0.10
3.9000e+083040830274-134.06-0.13
4.0000e+083135231165-186.54-0.18
4.1000e+083227732060-217.29-0.21
4.2000e+083317032957-213.36-0.21
4.3000e+083409033856-233.84-0.22
4.4000e+083503034758-271.79-0.26
4.5000e+083590035663-237.26-0.22
4.6000e+083682936570-259.31-0.24
4.7000e+083775937479-280.00-0.26
4.8000e+083869038391-299.39-0.27
4.9000e+083960439304-299.52-0.27
5.0000e+084051540221-294.45-0.26
5.2000e+084230642059-246.86-0.22
5.4000e+084411543906-208.99-0.18
5.6000e+084595345761-192.16-0.16
5.8000e+084787647623-252.68-0.21
6.0000e+084974349493-249.81-0.21
6.2000e+085166051370-289.84-0.24
6.4000e+085357753254-322.99-0.26
6.6000e+085547855144-333.51-0.26
6.8000e+085730757041-265.60-0.21
7.0000e+085921558945-270.46-0.21
7.2000e+086110960854-255.30-0.19
7.4000e+086302862769-259.28-0.19
7.6000e+086492964689-239.57-0.18
7.8000e+086689666616-280.35-0.21
8.0000e+086884168547-293.74-0.21
8.2000e+087079870484-313.91-0.22
8.4000e+087273872426-311.99-0.22
8.6000e+087470174373-328.10-0.23
8.8000e+087667976325-354.38-0.25
9.0000e+087860778281-325.94-0.22
9.2000e+088049280242-249.88-0.17
9.4000e+088243082208-222.33-0.15
9.6000e+088435384178-175.38-0.12
9.8000e+088640586152-253.13-0.17
1.0000e+098839688130-265.67-0.17
1.0500e+099328593094-190.72-0.12
1.1000e+099831498083-231.36-0.15
1.1500e+09103427103094-332.78-0.20
1.2000e+09108485108128-357.07-0.22
1.2500e+09113423113183-240.22-0.14
1.3000e+09118521118258-263.15-0.15
1.3500e+09123660123352-307.68-0.18
1.4000e+09128687128465-221.61-0.12
1.4500e+09133811133596-214.64-0.12
1.5000e+09138891138745-146.44-0.08
1.5500e+09144074143909-164.62-0.09
1.6000e+09149331149090-240.78-0.13
1.6500e+09154476154287-189.45-0.10
1.7000e+09159770159498-272.14-0.14
1.7500e+09164998164724-274.33-0.14
1.8000e+09170251169964-287.46-0.14
1.8500e+09175498175217-280.95-0.14
1.9000e+09180737180484-253.22-0.12
1.9500e+09186001185763-237.63-0.12
2.0000e+09191321191055-265.54-0.13
2.1000e+09201824201676-148.20-0.07
2.2000e+09212558212342-215.71-0.10
2.3000e+09223230223053-177.36-0.08
2.4000e+09233992233805-187.22-0.08
2.5000e+09244858244597-261.17-0.11
2.6000e+09255459255427-31.96-0.01
2.7000e+0926621526629478.830.03
2.8000e+09277197277196-1.29-0.00
2.9000e+09288196288131-64.67-0.03
3.0000e+0929907229909927.410.01
3.1000e+09310237310099-138.22-0.05
3.2000e+09321211321128-82.67-0.03
3.3000e+0933217733218710.040.00
3.4000e+09342966343274307.950.12
3.5000e+09354096354388292.140.11
3.6000e+09365108365529420.770.15
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