Gap size : 150 (r=75)

Generated by program gapCounts : Mon Jun 27 12:46:04 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+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+03000.000.00
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+030-0-0.00-0.00
5.6000e+030-0-0.00-0.00
5.8000e+030-0-0.00-0.00
6.0000e+030-0-0.00-0.00
6.2000e+030-0-0.00-0.00
6.4000e+030-0-0.00-0.00
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+030-0-0.00-0.00
9.4000e+030-0-0.00-0.00
9.6000e+030-0-0.00-0.00
9.8000e+030-0-0.00-0.00
1.0000e+040-0-0.00-0.00
1.0500e+040-0-0.00-0.00
1.1000e+040-0-0.00-0.00
1.1500e+040-0-0.00-0.00
1.2000e+040-0-0.00-0.00
1.2500e+040-0-0.00-0.00
1.3000e+040-0-0.00-0.00
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+04000.000.00
4.5000e+04000.000.00
4.6000e+04000.000.00
4.7000e+04000.000.00
4.8000e+04000.000.00
4.9000e+04000.000.00
5.0000e+04000.000.00
5.2000e+04000.000.00
5.4000e+04000.000.00
5.6000e+04000.000.00
5.8000e+04000.000.00
6.0000e+04000.000.00
6.2000e+04000.000.00
6.4000e+04000.000.00
6.6000e+04000.000.00
6.8000e+04000.000.00
7.0000e+04000.000.00
7.2000e+04000.000.00
7.4000e+04000.000.00
7.6000e+04000.000.00
7.8000e+04000.000.00
8.0000e+04000.000.00
8.2000e+04000.000.00
8.4000e+04000.000.00
8.6000e+04000.000.00
8.8000e+04000.000.00
9.0000e+04000.000.00
9.2000e+04000.000.00
9.4000e+04000.000.00
9.6000e+04000.000.00
9.8000e+04000.000.00
1.0000e+05000.000.00
1.0500e+05000.000.00
1.1000e+05000.000.00
1.1500e+05000.000.00
1.2000e+05000.000.00
1.2500e+05000.000.00
1.3000e+05000.000.00
1.3500e+05000.000.00
1.4000e+05000.000.00
1.4500e+05000.000.00
1.5000e+05000.000.00
1.5500e+05000.000.00
1.6000e+05000.000.00
1.6500e+05000.000.00
1.7000e+05000.000.00
1.7500e+05000.000.00
1.8000e+05000.000.00
1.8500e+05000.000.00
1.9000e+05000.000.00
1.9500e+05000.000.00
2.0000e+05000.000.00
2.1000e+05000.000.00
2.2000e+05000.000.00
2.3000e+05000.000.00
2.4000e+05000.000.00
2.5000e+05000.000.00
2.6000e+05000.000.00
2.7000e+05000.000.00
2.8000e+05000.000.00
2.9000e+05000.000.00
3.0000e+05000.000.00
3.1000e+05000.000.00
3.2000e+05000.000.00
3.3000e+05000.000.00
3.4000e+05000.000.00
3.5000e+05000.000.00
3.6000e+05000.000.00
3.7000e+05000.000.00
3.8000e+05000.000.00
3.9000e+05000.000.00
4.0000e+05000.000.00
4.1000e+05000.000.00
4.2000e+05000.000.00
4.3000e+05000.000.00
4.4000e+05000.000.00
4.5000e+05000.000.00
4.6000e+05000.000.00
4.7000e+05000.000.00
4.8000e+05000.000.00
4.9000e+05000.000.00
5.0000e+05000.000.00
5.2000e+05000.000.00
5.4000e+05000.000.00
5.6000e+05000.000.00
5.8000e+05000.000.00
6.0000e+05000.000.00
6.2000e+05000.000.00
6.4000e+05000.000.00
6.6000e+05000.000.00
6.8000e+05000.000.00
7.0000e+05000.000.00
7.2000e+05000.000.00
7.4000e+05000.000.00
7.6000e+05000.000.00
7.8000e+05000.000.00
8.0000e+05000.000.00
8.2000e+05000.000.00
8.4000e+05000.000.00
8.6000e+05000.000.00
8.8000e+05000.000.00
9.0000e+05000.000.00
9.2000e+05000.000.00
9.4000e+05000.000.00
9.6000e+05000.000.00
9.8000e+05000.000.00
1.0000e+06000.010.00
1.0500e+06000.010.00
1.1000e+06000.010.00
1.1500e+06000.010.00
1.2000e+06000.010.00
1.2500e+06000.010.00
1.3000e+06000.010.00
1.3500e+06000.010.00
1.4000e+06000.010.00
1.4500e+06000.010.00
1.5000e+06000.010.00
1.5500e+06000.020.00
1.6000e+06000.020.00
1.6500e+06000.020.00
1.7000e+06000.020.00
1.7500e+06000.020.00
1.8000e+06000.020.00
1.8500e+06000.020.00
1.9000e+06000.020.00
1.9500e+06000.030.00
2.0000e+06000.030.00
2.1000e+06000.030.00
2.2000e+06000.030.00
2.3000e+06000.040.00
2.4000e+06000.040.00
2.5000e+06000.050.00
2.6000e+06000.050.00
2.7000e+06000.050.00
2.8000e+06000.060.00
2.9000e+06000.060.00
3.0000e+06000.070.00
3.1000e+06000.070.00
3.2000e+06000.080.00
3.3000e+06000.080.00
3.4000e+06000.090.00
3.5000e+06000.090.00
3.6000e+06000.100.00
3.7000e+06000.110.00
3.8000e+06000.110.00
3.9000e+06000.120.00
4.0000e+06000.130.00
4.1000e+06000.130.00
4.2000e+06000.140.00
4.3000e+06000.150.00
4.4000e+06000.150.00
4.5000e+06000.160.00
4.6000e+06000.170.00
4.7000e+06000.180.00
4.8000e+06000.180.00
4.9000e+06000.190.00
5.0000e+06000.200.00
5.2000e+06000.220.00
5.4000e+06000.230.00
5.6000e+06000.250.00
5.8000e+06000.270.00
6.0000e+06000.290.00
6.2000e+06000.310.00
6.4000e+06000.330.00
6.6000e+06000.350.00
6.8000e+06000.370.00
7.0000e+06000.390.00
7.2000e+06000.420.00
7.4000e+06000.440.00
7.6000e+06000.460.00
7.8000e+06000.490.00
8.0000e+06010.510.00
8.2000e+06010.540.00
8.4000e+06010.560.00
8.6000e+06010.590.00
8.8000e+06010.620.00
9.0000e+06010.640.00
9.2000e+06010.670.00
9.4000e+06010.700.00
9.6000e+06010.730.00
9.8000e+06010.760.00
1.0000e+07010.790.00
1.0500e+07010.870.00
1.1000e+07010.950.00
1.1500e+07011.030.00
1.2000e+07011.120.01
1.2500e+07011.200.01
1.3000e+07011.300.01
1.3500e+07011.390.01
1.4000e+07110.490.00
1.4500e+07120.590.00
1.5000e+07120.690.00
1.5500e+07120.800.00
1.6000e+07120.910.00
1.6500e+07121.020.00
1.7000e+07121.130.00
1.7500e+07121.250.00
1.8000e+07220.370.00
1.8500e+07220.490.00
1.9000e+07230.610.00
1.9500e+07230.740.00
2.0000e+07230.870.00
2.1000e+07231.130.00
2.2000e+07231.400.01
2.3000e+07340.690.00
2.4000e+07340.980.00
2.5000e+07341.280.00
2.6000e+07450.580.00
2.7000e+07450.900.00
2.8000e+07550.220.00
2.9000e+07560.560.00
3.0000e+07560.900.00
3.1000e+07561.250.00
3.2000e+07571.600.00
3.3000e+07571.970.01
3.4000e+07671.340.00
3.5000e+07681.710.01
3.6000e+07781.100.00
3.7000e+07781.490.00
3.8000e+07890.890.00
3.9000e+07891.300.00
4.0000e+079100.710.00
4.1000e+0710100.130.00
4.2000e+0710110.560.00
4.3000e+0710110.990.00
4.4000e+0710111.430.00
4.5000e+0711120.880.00
4.6000e+0711121.330.00
4.7000e+0711131.790.00
4.8000e+0711132.250.01
4.9000e+0711142.720.01
5.0000e+0712142.200.01
5.2000e+0712153.170.01
5.4000e+0712164.170.01
5.6000e+0712175.180.01
5.8000e+0713185.220.01
6.0000e+0715194.280.01
6.2000e+0718202.370.01
6.4000e+0719212.470.01
6.6000e+0720232.600.01
6.8000e+0722241.740.00
7.0000e+0722252.910.01
7.2000e+0724262.090.00
7.4000e+0724273.300.01
7.6000e+0724294.520.01
7.8000e+0726303.760.01
8.0000e+0728313.020.01
8.2000e+0728324.300.01
8.4000e+0728345.600.01
8.6000e+0729355.910.01
8.8000e+0730366.250.01
9.0000e+0732385.600.01
9.2000e+0732396.960.01
9.4000e+0734406.350.01
9.6000e+0737424.750.01
9.8000e+0737436.160.01
1.0000e+0837457.590.01
1.0500e+0841487.240.01
1.1000e+0843528.990.02
1.1500e+0848567.830.01
1.2000e+0855604.770.01
1.2500e+0859644.790.01
1.3000e+0861686.900.01
1.3500e+0863729.090.01
1.4000e+08657611.370.02
1.4500e+08698111.720.02
1.5000e+08718514.160.02
1.5500e+08759014.670.02
1.6000e+08779417.260.03
1.6500e+08849914.930.02
1.7000e+088710416.670.02
1.7500e+088910819.470.03
1.8000e+089611317.350.02
1.8500e+0810111817.300.02
1.9000e+0810812315.320.02
1.9500e+0811312815.400.02
2.0000e+0811713416.550.02
2.1000e+0812714417.030.02
2.2000e+081451559.770.01
2.3000e+081601665.750.01
2.4000e+0816617710.960.01
2.5000e+0817718811.400.01
2.6000e+081922008.070.01
2.7000e+0820121210.950.01
2.8000e+0820922415.040.02
2.9000e+0822523611.330.01
3.0000e+082462492.830.00
3.1000e+082562625.520.01
3.2000e+082702744.410.00
3.3000e+082842873.480.00
3.4000e+083003010.740.00
3.5000e+08316314-1.82-0.00
3.6000e+08332328-4.21-0.00
3.7000e+083413420.580.00
3.8000e+083553560.530.00
3.9000e+083673702.660.00
4.0000e+083833840.950.00
4.1000e+083903988.390.01
4.2000e+084084135.000.00
4.3000e+084264281.760.00
4.4000e+084404432.680.00
4.5000e+08460458-2.26-0.00
4.6000e+08479473-6.04-0.01
4.7000e+08494488-5.68-0.01
4.8000e+08507504-3.18-0.00
4.9000e+08522519-2.53-0.00
5.0000e+08541535-5.75-0.01
5.2000e+08570567-2.77-0.00
5.4000e+08602600-2.26-0.00
5.6000e+08636633-3.22-0.00
5.8000e+08673666-6.68-0.01
6.0000e+08706700-5.64-0.00
6.2000e+08744735-9.12-0.01
6.4000e+08782770-12.13-0.01
6.6000e+08816805-10.68-0.01
6.8000e+08861841-19.77-0.02
7.0000e+08895878-17.43-0.01
7.2000e+08927914-12.65-0.01
7.4000e+08962952-10.45-0.01
7.6000e+081012989-22.84-0.02
7.8000e+0810481027-20.82-0.02
8.0000e+0810851066-19.40-0.01
8.2000e+0811301104-25.59-0.02
8.4000e+0811601144-16.39-0.01
8.6000e+0812011183-17.82-0.01
8.8000e+0812421223-18.88-0.01
9.0000e+0812771263-13.57-0.01
9.2000e+0813181304-13.90-0.01
9.4000e+0813571345-11.88-0.01
9.6000e+0814061386-19.51-0.01
9.8000e+0814411428-12.80-0.01
1.0000e+0914861470-15.75-0.01
1.0500e+0916011577-24.19-0.02
1.1000e+0917181685-32.62-0.02
1.1500e+0918491796-53.13-0.03
1.2000e+0919741908-65.76-0.04
1.2500e+0920802022-57.59-0.03
1.3000e+0922032138-64.66-0.04
1.3500e+0923102256-54.03-0.03
1.4000e+0924332375-57.74-0.03
1.4500e+0925502496-53.85-0.03
1.5000e+0926762619-57.38-0.03
1.5500e+0928262743-83.39-0.04
1.6000e+0929592868-90.91-0.05
1.6500e+0930812995-85.97-0.04
1.7000e+0932083123-84.61-0.04
1.7500e+0933433253-89.87-0.05
1.8000e+0934763384-91.77-0.05
1.8500e+0936073517-90.34-0.04
1.9000e+0937453650-94.61-0.05
1.9500e+0938853785-99.61-0.05
2.0000e+0940223922-100.36-0.05
2.1000e+0942754198-77.21-0.04
2.2000e+0945524479-73.34-0.03
2.3000e+0948104764-45.93-0.02
2.4000e+0950905054-36.13-0.02
2.5000e+0953915348-43.08-0.02
2.6000e+0956965646-49.92-0.02
2.7000e+0959775948-28.77-0.01
2.8000e+0963176254-62.75-0.03
2.9000e+0966326564-67.97-0.03
3.0000e+0969566877-78.52-0.03
3.1000e+0972487194-53.52-0.02
3.2000e+0975667515-51.05-0.02
3.3000e+0979077839-68.19-0.03
3.4000e+0982328166-66.02-0.02
3.5000e+0985708496-73.64-0.03
3.6000e+0989048830-74.10-0.03
3.7000e+0992489167-81.48-0.03
3.8000e+0995679506-60.85-0.02
3.9000e+0999169849-67.27-0.02
4.0000e+091026410194-69.79-0.02
4.1000e+091063210543-89.49-0.03
4.2000e+091098510894-91.41-0.03
4.3000e+091133811247-90.61-0.03
4.4000e+091168511604-81.14-0.03
4.5000e+091205111963-88.04-0.03
4.6000e+091244312325-118.37-0.04
4.7000e+091284112689-152.17-0.05
4.8000e+091321213056-156.48-0.05
4.9000e+091357413425-149.35-0.05
5.0000e+091395313796-156.81-0.05
5.2000e+091473014546-183.68-0.06
5.4000e+091554915306-243.39-0.07
5.6000e+091632416074-250.21-0.08
5.8000e+091708916851-238.40-0.07
6.0000e+091787617636-240.20-0.07
6.2000e+091868218429-252.86-0.07
6.4000e+091950219230-271.57-0.08
6.6000e+092034820039-308.54-0.09
6.8000e+092111520856-258.98-0.07
7.0000e+092194121680-261.05-0.07
7.2000e+092278922511-277.93-0.07
7.4000e+092362223349-272.79-0.07
7.6000e+092442924194-234.79-0.06
7.8000e+092524025046-194.07-0.05
8.0000e+092610325904-198.77-0.05
8.2000e+092693326769-164.04-0.04
8.4000e+092783627640-196.00-0.05
8.6000e+092869528517-177.77-0.04
8.8000e+092955129401-150.49-0.04
9.0000e+093043030290-140.25-0.03
9.2000e+093132431185-139.17-0.03
9.4000e+093219832086-112.36-0.03
9.6000e+093315132992-158.91-0.04
9.8000e+093406133904-156.94-0.04
1.0000e+103498134821-159.52-0.04
1.0500e+103724837138-109.75-0.02
1.1000e+103965639487-168.88-0.04
1.1500e+104198441867-117.13-0.03
1.2000e+104444144276-164.62-0.03
1.2500e+104682546715-110.39-0.02
1.3000e+104926449181-83.43-0.02
1.3500e+105174851673-74.61-0.01
1.4000e+105426554192-72.80-0.01
1.4500e+105679656736-59.76-0.01
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