Gap size : 90 (r=45)

Generated by program gapCounts : Mon Jun 27 12:44:40 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+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+030-0-0.00-0.00
5.4000e+030-0-0.00-0.00
5.6000e+030-0-0.00-0.00
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+04000.000.00
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+04000.010.00
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+04000.010.00
7.0000e+04000.010.00
7.2000e+04000.010.00
7.4000e+04000.010.00
7.6000e+04000.010.00
7.8000e+04000.020.00
8.0000e+04000.020.00
8.2000e+04000.020.00
8.4000e+04000.020.00
8.6000e+04000.020.00
8.8000e+04000.020.00
9.0000e+04000.020.00
9.2000e+04000.020.00
9.4000e+04000.030.00
9.6000e+04000.030.00
9.8000e+04000.030.00
1.0000e+05000.030.00
1.0500e+05000.030.00
1.1000e+05000.040.00
1.1500e+05000.040.00
1.2000e+05000.050.00
1.2500e+05000.050.00
1.3000e+05000.060.00
1.3500e+05000.060.00
1.4000e+05000.070.00
1.4500e+05000.070.00
1.5000e+05000.080.00
1.5500e+05000.080.00
1.6000e+05000.090.00
1.6500e+05000.100.00
1.7000e+05000.100.00
1.7500e+05000.110.00
1.8000e+05000.120.00
1.8500e+05000.130.00
1.9000e+05000.130.00
1.9500e+05000.140.00
2.0000e+05000.150.00
2.1000e+05000.170.00
2.2000e+05000.180.00
2.3000e+05000.200.01
2.4000e+05000.220.01
2.5000e+05000.240.01
2.6000e+05000.260.01
2.7000e+05000.280.01
2.8000e+05000.310.01
2.9000e+05000.330.01
3.0000e+05000.350.01
3.1000e+05000.380.01
3.2000e+05000.400.01
3.3000e+05000.430.01
3.4000e+05000.460.01
3.5000e+05000.480.01
3.6000e+05010.510.01
3.7000e+05010.540.01
3.8000e+05010.570.01
3.9000e+05010.600.01
4.0000e+05010.630.01
4.1000e+0511-0.34-0.01
4.2000e+0511-0.31-0.01
4.3000e+0511-0.27-0.01
4.4000e+0511-0.24-0.00
4.5000e+0511-0.20-0.00
4.6000e+0511-0.17-0.00
4.7000e+0511-0.14-0.00
4.8000e+0511-0.10-0.00
4.9000e+0511-0.06-0.00
5.0000e+0511-0.03-0.00
5.2000e+05110.050.00
5.4000e+05110.130.00
5.6000e+05110.210.00
5.8000e+0521-0.71-0.01
6.0000e+0521-0.62-0.01
6.2000e+0521-0.54-0.01
6.4000e+0522-0.45-0.01
6.6000e+0522-0.36-0.01
6.8000e+0522-0.26-0.00
7.0000e+0522-0.17-0.00
7.2000e+0522-0.07-0.00
7.4000e+05220.030.00
7.6000e+05220.130.00
7.8000e+05220.230.00
8.0000e+05220.340.01
8.2000e+0532-0.56-0.01
8.4000e+0533-0.45-0.01
8.6000e+0543-1.34-0.02
8.8000e+0543-1.22-0.02
9.0000e+0543-1.11-0.02
9.2000e+0543-0.99-0.01
9.4000e+0543-0.88-0.01
9.6000e+0543-0.76-0.01
9.8000e+0543-0.64-0.01
1.0000e+0643-0.52-0.01
1.0500e+0644-0.20-0.00
1.1000e+0654-0.88-0.01
1.1500e+0664-1.55-0.02
1.2000e+0665-1.20-0.02
1.2500e+0665-0.85-0.01
1.3000e+0676-1.49-0.02
1.3500e+0676-1.12-0.01
1.4000e+0676-0.75-0.01
1.4500e+0677-0.36-0.00
1.5000e+0687-0.97-0.01
1.5500e+0687-0.57-0.01
1.6000e+0688-0.16-0.00
1.6500e+06880.260.00
1.7000e+06890.690.01
1.7500e+06891.120.01
1.8000e+068101.560.02
1.8500e+068102.000.02
1.9000e+069101.460.02
1.9500e+069111.920.02
2.0000e+061211-0.62-0.01
2.1000e+061312-0.66-0.01
2.2000e+0613130.320.00
2.3000e+061514-0.68-0.01
2.4000e+0615150.350.00
2.5000e+061716-0.60-0.01
2.6000e+061917-1.53-0.01
2.7000e+062119-2.43-0.02
2.8000e+062120-1.31-0.01
2.9000e+062221-1.18-0.01
3.0000e+062322-1.02-0.01
3.1000e+0623230.160.00
3.2000e+062724-2.64-0.02
3.3000e+062826-2.42-0.02
3.4000e+062927-2.19-0.02
3.5000e+063028-1.93-0.02
3.6000e+063129-1.66-0.01
3.7000e+063231-1.37-0.01
3.8000e+063432-2.06-0.02
3.9000e+063533-1.74-0.01
4.0000e+063635-1.40-0.01
4.1000e+063736-1.04-0.01
4.2000e+064037-2.67-0.02
4.3000e+064139-2.28-0.02
4.4000e+064240-1.87-0.01
4.5000e+064242-0.45-0.00
4.6000e+064643-3.02-0.02
4.7000e+064944-4.57-0.03
4.8000e+064946-3.11-0.02
4.9000e+065047-2.63-0.02
5.0000e+065149-2.14-0.01
5.2000e+065652-4.11-0.03
5.4000e+066155-6.03-0.04
5.6000e+066358-4.90-0.03
5.8000e+066461-2.72-0.02
6.0000e+066765-2.49-0.02
6.2000e+066868-0.22-0.00
6.4000e+067371-1.89-0.01
6.6000e+067674-1.52-0.01
6.8000e+067978-1.11-0.01
7.0000e+0681810.350.00
7.2000e+0683851.850.01
7.4000e+0686882.400.01
7.6000e+069492-2.02-0.01
7.8000e+0610096-4.39-0.02
8.0000e+0610399-3.73-0.02
8.2000e+06104103-1.03-0.01
8.4000e+06107107-0.29-0.00
8.6000e+06111110-0.51-0.00
8.8000e+06118114-3.70-0.02
9.0000e+06121118-2.85-0.02
9.2000e+06123122-0.97-0.01
9.4000e+06127126-1.05-0.01
9.6000e+06132130-2.10-0.01
9.8000e+06136134-2.11-0.01
1.0000e+07141138-3.09-0.02
1.0500e+07154148-5.91-0.03
1.1000e+07167158-8.53-0.04
1.1500e+07182169-12.97-0.06
1.2000e+07196180-16.22-0.08
1.2500e+07201191-10.30-0.05
1.3000e+07210202-8.21-0.04
1.3500e+07215213-1.96-0.01
1.4000e+07233224-8.56-0.04
1.4500e+07241236-5.00-0.02
1.5000e+07259248-11.29-0.05
1.5500e+07276260-16.43-0.07
1.6000e+07288272-16.43-0.07
1.6500e+07310284-26.30-0.11
1.7000e+07325296-29.03-0.12
1.7500e+07342308-33.63-0.13
1.8000e+07356321-35.11-0.14
1.8500e+07367334-33.46-0.13
1.9000e+07383346-36.69-0.14
1.9500e+07395359-35.80-0.14
2.0000e+07406372-33.79-0.13
2.1000e+07433399-34.44-0.13
2.2000e+07459425-33.64-0.12
2.3000e+07506453-53.43-0.19
2.4000e+07540480-59.81-0.21
2.5000e+07571508-62.80-0.21
2.6000e+07601537-64.42-0.22
2.7000e+07632565-66.66-0.22
2.8000e+07669594-74.56-0.24
2.9000e+07691624-67.11-0.21
3.0000e+07715654-61.33-0.19
3.1000e+07747684-63.23-0.20
3.2000e+07777714-62.81-0.19
3.3000e+07806745-61.08-0.18
3.4000e+07827776-51.06-0.15
3.5000e+07859807-51.75-0.15
3.6000e+07886839-47.16-0.14
3.7000e+07917871-46.29-0.13
3.8000e+07941903-38.15-0.11
3.9000e+07965935-29.75-0.08
4.0000e+071005968-37.09-0.10
4.1000e+0710431001-42.18-0.12
4.2000e+0710751034-41.02-0.11
4.3000e+0711091067-41.63-0.11
4.4000e+0711411101-39.99-0.11
4.5000e+0711791135-44.13-0.12
4.6000e+0712141169-45.03-0.12
4.7000e+0712471203-43.72-0.11
4.8000e+0712851238-47.19-0.12
4.9000e+0713161273-43.44-0.11
5.0000e+0713591308-51.48-0.13
5.2000e+0714211378-42.95-0.11
5.4000e+0714891449-39.62-0.10
5.6000e+0715621521-40.51-0.10
5.8000e+0716331594-38.66-0.09
6.0000e+0717151668-47.08-0.11
6.2000e+0717961742-53.80-0.12
6.4000e+0718741817-56.84-0.13
6.6000e+0719461893-53.21-0.12
6.8000e+0720241969-54.93-0.12
7.0000e+0721072046-61.03-0.13
7.2000e+0721892123-65.51-0.14
7.4000e+0722682202-66.40-0.14
7.6000e+0723672280-86.70-0.18
7.8000e+0724512360-91.44-0.19
8.0000e+0725342439-94.61-0.19
8.2000e+0725982520-78.25-0.16
8.4000e+0726792601-78.35-0.16
8.6000e+0727482682-65.94-0.13
8.8000e+0728322764-68.01-0.13
9.0000e+0729352846-88.59-0.17
9.2000e+0730022929-72.67-0.14
9.4000e+0730853013-72.28-0.14
9.6000e+0731743097-77.42-0.15
9.8000e+0732483181-67.10-0.12
1.0000e+0833373266-71.33-0.13
1.0500e+0835753480-95.47-0.17
1.1000e+0837903696-93.96-0.17
1.1500e+0840253915-109.90-0.19
1.2000e+0842514137-114.41-0.19
1.2500e+0844764360-115.56-0.19
1.3000e+0847164587-129.46-0.21
1.3500e+0849524815-137.17-0.22
1.4000e+0851885045-142.77-0.23
1.4500e+0854125278-134.34-0.21
1.5000e+0856575512-144.94-0.22
1.5500e+0858985748-149.62-0.23
1.6000e+0861525987-165.45-0.25
1.6500e+0863966227-169.48-0.25
1.7000e+0866326468-163.76-0.24
1.7500e+0868676712-155.34-0.22
1.8000e+0870856957-128.26-0.18
1.8500e+0873187203-114.56-0.16
1.9000e+0875717452-119.29-0.16
1.9500e+0878047702-102.49-0.14
2.0000e+0880797953-126.19-0.17
2.1000e+0885668460-106.24-0.14
2.2000e+0891078972-134.69-0.17
2.3000e+0896369490-145.79-0.19
2.4000e+081015910013-145.76-0.18
2.5000e+081065310541-111.79-0.14
2.6000e+081117611074-102.08-0.12
2.7000e+081170011611-88.79-0.10
2.8000e+081225812153-105.08-0.12
2.9000e+081280312699-104.11-0.12
3.0000e+081333513249-86.01-0.10
3.1000e+081385413803-50.91-0.06
3.2000e+081442114361-59.94-0.07
3.3000e+081499014923-67.21-0.07
3.4000e+081559615488-107.83-0.11
3.5000e+081617416057-116.90-0.12
3.6000e+081671816629-88.52-0.09
3.7000e+081724817205-42.77-0.04
3.8000e+081779617784-11.75-0.01
3.9000e+081839518366-28.54-0.03
4.0000e+081898718952-35.21-0.03
4.1000e+081956319540-22.84-0.02
4.2000e+082015820132-26.49-0.03
4.3000e+082073720726-11.25-0.01
4.4000e+08213012132321.830.02
4.5000e+08218992192323.680.02
4.6000e+082252822525-2.74-0.00
4.7000e+082313723130-6.51-0.01
4.8000e+0823729237389.330.01
4.9000e+082438024349-31.27-0.03
5.0000e+082498224962-20.37-0.02
5.2000e+082621026195-15.26-0.01
5.4000e+0827432274375.330.00
5.6000e+082871028689-20.97-0.02
5.8000e+08299102995039.550.03
6.0000e+08311453121973.590.06
6.2000e+0832491324964.870.00
6.4000e+083381133781-29.86-0.02
6.6000e+0835067350747.160.01
6.8000e+083640736375-32.30-0.03
7.0000e+083775737683-74.46-0.06
7.2000e+083903038997-32.52-0.02
7.4000e+084034840319-28.66-0.02
7.6000e+084168241648-34.07-0.03
7.8000e+084305742983-73.92-0.05
8.0000e+084434244325-17.37-0.01
8.2000e+084571345672-40.59-0.03
8.4000e+084705347026-26.71-0.02
8.6000e+08483704838616.130.01
8.8000e+08497124975239.770.03
9.0000e+085113451123-10.89-0.01
9.2000e+08524535250047.020.03
9.4000e+08538385388244.370.03
9.6000e+08552255527045.050.03
9.8000e+08566195666343.960.03
1.0000e+0958057580614.000.00
1.0500e+096162261578-44.15-0.03
1.1000e+096520365125-78.37-0.05
1.1500e+096881268700-111.98-0.07
1.2000e+0972295723037.800.00
1.2500e+09758377593294.850.06
1.3000e+097946079586126.140.07
1.3500e+098308783265177.710.10
1.4000e+098668086967286.680.16
1.4500e+099038390691308.230.17
1.5000e+099427294438165.590.09
1.5500e+099806398205142.050.08
1.6000e+09101862101993130.930.07
1.6500e+09105601105801199.610.10
1.7000e+09109418109627209.500.11
1.7500e+09113366113473107.030.05
1.8000e+09117417117337-80.31-0.04
1.8500e+09121281121218-63.03-0.03
1.9000e+09125264125116-147.60-0.07
1.9500e+09129121129032-89.47-0.04
2.0000e+09133019132963-56.05-0.03
2.1000e+09140932140873-58.95-0.03
2.2000e+09148973148844-129.32-0.06
2.3000e+0915686015687212.110.01
2.4000e+09165065164956-109.15-0.05
2.5000e+09173190173093-97.38-0.04
2.6000e+09181332181280-51.71-0.02
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