Gap size : 64 (r=32)

Generated by program gapCounts : Mon Jun 27 12:44:05 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+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+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+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+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+04000.010.00
1.3500e+04000.010.00
1.4000e+04000.010.00
1.4500e+04000.010.00
1.5000e+04000.010.00
1.5500e+04000.010.00
1.6000e+04000.010.00
1.6500e+04000.010.00
1.7000e+04000.010.00
1.7500e+04000.010.00
1.8000e+04000.010.00
1.8500e+04000.010.00
1.9000e+04000.020.00
1.9500e+04000.020.00
2.0000e+04000.020.00
2.1000e+04000.020.00
2.2000e+04000.020.00
2.3000e+04000.030.00
2.4000e+04000.030.00
2.5000e+04000.030.00
2.6000e+04000.030.00
2.7000e+04000.040.00
2.8000e+04000.040.00
2.9000e+04000.040.00
3.0000e+04000.050.00
3.1000e+04000.050.00
3.2000e+04000.060.00
3.3000e+04000.060.00
3.4000e+04000.060.00
3.5000e+04000.070.00
3.6000e+04000.070.00
3.7000e+04000.080.00
3.8000e+04000.080.00
3.9000e+04000.090.00
4.0000e+04000.090.00
4.1000e+04000.100.01
4.2000e+04000.100.01
4.3000e+04000.110.01
4.4000e+04000.110.01
4.5000e+04000.120.01
4.6000e+04000.130.01
4.7000e+04000.130.01
4.8000e+04000.140.01
4.9000e+04000.140.01
5.0000e+04000.150.01
5.2000e+04000.160.01
5.4000e+04000.180.01
5.6000e+04000.190.01
5.8000e+04000.210.01
6.0000e+04000.220.01
6.2000e+04000.240.01
6.4000e+04000.250.01
6.6000e+04000.270.01
6.8000e+04000.280.01
7.0000e+04000.300.01
7.2000e+04000.320.01
7.4000e+04000.340.01
7.6000e+04000.350.01
7.8000e+04000.370.01
8.0000e+04000.390.02
8.2000e+04000.410.02
8.4000e+04000.430.02
8.6000e+04000.450.02
8.8000e+04000.470.02
9.0000e+0410-0.51-0.02
9.2000e+0411-0.49-0.02
9.4000e+0411-0.47-0.02
9.6000e+0411-0.45-0.02
9.8000e+0411-0.43-0.02
1.0000e+0511-0.40-0.01
1.0500e+0511-0.35-0.01
1.1000e+0521-1.29-0.05
1.1500e+0521-1.23-0.04
1.2000e+0521-1.16-0.04
1.2500e+0521-1.10-0.04
1.3000e+0521-1.03-0.03
1.3500e+0521-0.97-0.03
1.4000e+0521-0.90-0.03
1.4500e+0521-0.83-0.03
1.5000e+0521-0.75-0.02
1.5500e+0521-0.68-0.02
1.6000e+0521-0.60-0.02
1.6500e+0521-0.53-0.02
1.7000e+0522-0.45-0.01
1.7500e+0522-0.37-0.01
1.8000e+0522-0.29-0.01
1.8500e+0522-0.21-0.01
1.9000e+0522-0.12-0.00
1.9500e+0522-0.04-0.00
2.0000e+05220.050.00
2.1000e+05220.230.01
2.2000e+05220.410.01
2.3000e+05230.590.02
2.4000e+05230.780.02
2.5000e+05230.980.02
2.6000e+05231.180.03
2.7000e+05231.380.03
2.8000e+05241.590.04
2.9000e+05340.800.02
3.0000e+05341.010.02
3.1000e+05341.230.03
3.2000e+05341.450.03
3.3000e+05351.680.04
3.4000e+05351.910.04
3.5000e+05352.140.05
3.6000e+05352.370.05
3.7000e+05461.610.03
3.8000e+05461.850.04
3.9000e+05561.100.02
4.0000e+05561.340.03
4.1000e+05670.600.01
4.2000e+05670.850.02
4.3000e+05671.100.02
4.4000e+05671.360.03
4.5000e+05780.630.01
4.6000e+05780.890.02
4.7000e+05781.160.02
4.8000e+05781.430.03
4.9000e+05791.700.03
5.0000e+05791.970.04
5.2000e+057102.530.05
5.4000e+057103.090.06
5.6000e+057113.670.06
5.8000e+057114.250.07
6.0000e+057124.840.08
6.2000e+057125.440.09
6.4000e+0510133.050.05
6.6000e+0510143.670.06
6.8000e+0510144.290.07
7.0000e+0510154.920.08
7.2000e+0511164.560.07
7.4000e+0512164.210.07
7.6000e+0512174.860.08
7.8000e+0513184.520.07
8.0000e+0513185.190.08
8.2000e+0515193.860.06
8.4000e+0517202.540.04
8.6000e+0518202.220.03
8.8000e+0518212.920.04
9.0000e+0519222.610.04
9.2000e+0521221.320.02
9.4000e+0521232.030.03
9.6000e+0522241.740.02
9.8000e+0522242.460.03
1.0000e+0624251.190.02
1.0500e+0625272.020.03
1.1000e+062929-0.11-0.00
1.1500e+063131-0.21-0.00
1.2000e+063333-0.28-0.00
1.2500e+0633351.680.02
1.3000e+0634372.670.03
1.3500e+063939-0.32-0.00
1.4000e+064241-1.29-0.02
1.4500e+064443-1.22-0.01
1.5000e+064845-3.14-0.04
1.5500e+065047-3.03-0.03
1.6000e+065549-5.90-0.07
1.6500e+065951-7.75-0.09
1.7000e+066253-8.57-0.09
1.7500e+066356-7.38-0.08
1.8000e+066358-5.16-0.06
1.8500e+066660-5.93-0.06
1.9000e+066962-6.67-0.07
1.9500e+067165-6.40-0.07
2.0000e+067467-7.11-0.07
2.1000e+068072-8.48-0.09
2.2000e+068476-7.78-0.08
2.3000e+068781-6.01-0.06
2.4000e+069286-6.18-0.06
2.5000e+069791-6.29-0.06
2.6000e+0610096-4.35-0.04
2.7000e+06106101-5.35-0.05
2.8000e+06115106-9.29-0.08
2.9000e+06121111-10.18-0.09
3.0000e+06125116-9.03-0.08
3.1000e+06129121-7.82-0.07
3.2000e+06135126-8.57-0.07
3.3000e+06143132-11.27-0.09
3.4000e+06150137-12.93-0.11
3.5000e+06160142-17.55-0.14
3.6000e+06173148-25.12-0.20
3.7000e+06181153-27.66-0.22
3.8000e+06185159-26.15-0.20
3.9000e+06195164-30.61-0.24
4.0000e+06201170-31.02-0.24
4.1000e+06209176-33.41-0.25
4.2000e+06217181-35.75-0.27
4.3000e+06225187-38.06-0.28
4.4000e+06229193-36.34-0.26
4.5000e+06233198-34.58-0.25
4.6000e+06234204-29.79-0.21
4.7000e+06242210-31.97-0.23
4.8000e+06249216-33.12-0.23
4.9000e+06260222-38.23-0.27
5.0000e+06262228-34.32-0.24
5.2000e+06273240-33.40-0.23
5.4000e+06281252-29.37-0.20
5.6000e+06289264-25.23-0.17
5.8000e+06301276-24.99-0.16
6.0000e+06313288-24.64-0.16
6.2000e+06325301-24.20-0.15
6.4000e+06335313-21.66-0.13
6.6000e+06349326-23.02-0.14
6.8000e+06358339-19.30-0.12
7.0000e+06368352-16.49-0.10
7.2000e+06384364-19.60-0.12
7.4000e+06396377-18.62-0.11
7.6000e+06411390-20.56-0.12
7.8000e+06419404-15.43-0.09
8.0000e+06436417-19.21-0.11
8.2000e+06453430-22.93-0.13
8.4000e+06463443-19.57-0.11
8.6000e+06480457-23.14-0.13
8.8000e+06487470-16.65-0.09
9.0000e+06501484-17.08-0.09
9.2000e+06515498-17.45-0.09
9.4000e+06526511-14.76-0.08
9.6000e+06532525-7.00-0.04
9.8000e+06540539-1.18-0.01
1.0000e+07559553-6.30-0.03
1.0500e+075865881.660.01
1.1000e+076196233.970.02
1.1500e+076556593.620.02
1.2000e+076916953.580.02
1.2500e+077227318.860.04
1.3000e+07771767-3.57-0.02
1.3500e+07808804-3.71-0.02
1.4000e+07853841-11.58-0.05
1.4500e+07891879-12.19-0.05
1.5000e+07939916-22.54-0.10
1.5500e+07980954-25.65-0.11
1.6000e+071006992-13.52-0.06
1.6500e+0710511031-20.15-0.08
1.7000e+0710851069-15.57-0.06
1.7500e+0711351108-26.77-0.11
1.8000e+0711771147-29.76-0.12
1.8500e+0712241186-37.55-0.15
1.9000e+0712711226-45.14-0.17
1.9500e+0713131265-47.53-0.18
2.0000e+0713471305-41.74-0.16
2.1000e+0714341385-48.61-0.18
2.2000e+0715121466-45.79-0.17
2.3000e+0715981548-50.30-0.18
2.4000e+0716881630-58.18-0.20
2.5000e+0717691713-56.46-0.19
2.6000e+0718531796-57.15-0.19
2.7000e+0719341880-54.28-0.18
2.8000e+0720241964-59.88-0.19
2.9000e+0721052049-55.96-0.18
3.0000e+0721932134-58.55-0.18
3.1000e+0722842220-63.65-0.20
3.2000e+0723822307-75.29-0.23
3.3000e+0724752394-81.48-0.25
3.4000e+0725512481-70.23-0.21
3.5000e+0726442568-75.56-0.22
3.6000e+0727152657-58.48-0.17
3.7000e+0728082745-63.01-0.18
3.8000e+0728822834-48.14-0.14
3.9000e+0729612923-37.91-0.11
4.0000e+0730463013-33.30-0.09
4.1000e+0731183103-15.34-0.04
4.2000e+0732093193-16.04-0.04
4.3000e+0733023284-18.39-0.05
4.4000e+0733843375-9.42-0.02
4.5000e+0734913466-25.12-0.07
4.6000e+0735743557-16.51-0.04
4.7000e+0736613649-11.59-0.03
4.8000e+0737553742-13.37-0.03
4.9000e+0738503834-15.86-0.04
5.0000e+07392639270.940.00
5.2000e+07411041133.380.01
5.4000e+074279430121.900.05
5.6000e+074457448932.460.08
5.8000e+074644467935.020.08
6.0000e+074836487033.540.08
6.2000e+075017506143.990.10
6.4000e+075203525350.340.11
6.6000e+075388544758.560.13
6.8000e+075590564150.620.11
7.0000e+075788583547.490.10
7.2000e+075973603158.140.12
7.4000e+076207622820.570.04
7.6000e+07641764257.740.02
7.8000e+076611662311.630.02
8.0000e+076797682124.220.05
8.2000e+076987702133.500.07
8.4000e+077179722041.450.08
8.6000e+077395742126.040.05
8.8000e+077594762228.270.06
9.0000e+077787782437.120.07
9.2000e+078011802715.570.03
9.4000e+078204823025.620.05
9.6000e+078405843328.230.05
9.8000e+078623863714.410.03
1.0000e+088823884219.150.04
1.0500e+089315935641.320.07
1.1000e+089847987426.680.05
1.1500e+08103551039439.100.07
1.2000e+08108381091779.420.13
1.2500e+08113851144458.510.10
1.3000e+08119061197266.260.11
1.3500e+081239312504110.550.18
1.4000e+08129431303794.290.15
1.4500e+08134911357382.380.13
1.5000e+08140341411277.730.12
1.5500e+08145721465280.270.12
1.6000e+08151251519569.910.10
1.6500e+08156941574045.580.07
1.7000e+081629016286-3.77-0.01
1.7500e+081691816835-83.22-0.12
1.8000e+081742817385-42.82-0.06
1.8500e+081795417937-16.63-0.02
1.9000e+081853218491-40.70-0.06
1.9500e+081907819047-31.08-0.04
2.0000e+081961319604-8.81-0.01
2.1000e+08206832072340.470.05
2.2000e+082185321849-4.18-0.01
2.3000e+082301722980-37.06-0.05
2.4000e+082417324117-56.44-0.07
2.5000e+082534725258-88.57-0.11
2.6000e+082648926405-83.68-0.10
2.7000e+082759927557-41.98-0.05
2.8000e+082872528713-11.66-0.01
2.9000e+082995029874-75.90-0.09
3.0000e+083109231039-52.87-0.06
3.1000e+083228532208-76.72-0.09
3.2000e+083346133381-79.60-0.09
3.3000e+083463434558-75.65-0.08
3.4000e+083578135739-41.98-0.04
3.5000e+08369033692320.280.02
3.6000e+083811638111-4.99-0.01
3.7000e+083931039302-7.88-0.01
3.8000e+084050840497-11.49-0.01
3.9000e+084175841694-63.93-0.06
4.0000e+084295642895-61.28-0.06
4.1000e+084415144098-52.62-0.05
4.2000e+084533445305-29.03-0.03
4.3000e+084656546514-50.60-0.05
4.4000e+084778747727-60.39-0.06
4.5000e+084901248942-70.47-0.07
4.6000e+085020450159-44.91-0.04
4.7000e+0851379513790.230.00
4.8000e+08525625260239.890.04
4.9000e+085384653827-18.99-0.02
5.0000e+08550385505516.530.01
5.2000e+08574295751787.590.08
5.4000e+085987959988108.660.09
5.6000e+086232662467141.390.12
5.8000e+086484264955113.420.10
6.0000e+08674216745130.450.03
6.2000e+087002669955-70.82-0.06
6.4000e+087255472466-87.66-0.07
6.6000e+087509974985-114.33-0.09
6.8000e+087768677510-176.06-0.14
7.0000e+088029280042-250.09-0.19
7.2000e+088288782580-306.61-0.23
7.4000e+088532485125-198.85-0.15
7.6000e+088785987676-182.97-0.14
7.8000e+089046690233-233.15-0.17
8.0000e+089308192795-285.58-0.21
8.2000e+089561995364-255.39-0.18
8.4000e+089821797937-279.76-0.20
8.6000e+08100810100516-293.81-0.21
8.8000e+08103417103100-316.69-0.22
9.0000e+08105982105689-292.53-0.20
9.2000e+08108553108284-269.44-0.18
9.4000e+08111070110882-187.56-0.13
9.6000e+08113619113486-132.99-0.09
9.8000e+08116267116094-172.83-0.11
1.0000e+09118951118707-244.20-0.16
1.0500e+09125538125257-280.69-0.18
1.1000e+09132088131834-254.25-0.16
1.1500e+09138638138435-203.20-0.13
1.2000e+09145293145059-233.71-0.14
1.2500e+09151972151706-265.89-0.16
1.3000e+09158669158374-294.71-0.17
1.3500e+09165265165063-202.09-0.12
1.4000e+09171948171771-176.88-0.10
1.4500e+09178687178498-188.85-0.10
1.5000e+09185409185243-165.72-0.09
1.5500e+09192284192006-278.17-0.15
1.6000e+09199069198785-283.82-0.15
1.6500e+09205950205581-369.26-0.19
1.7000e+09212802212392-410.04-0.21
1.7500e+09219621219218-402.67-0.20
1.8000e+09226440226059-380.63-0.19
1.8500e+09233247232915-332.38-0.16
1.9000e+09240152239784-368.35-0.18
1.9500e+09247013246666-346.94-0.17
2.0000e+09253846253561-284.54-0.14
2.1000e+09267790267390-400.19-0.19
2.2000e+09281537281266-270.99-0.12
2.3000e+09295547295188-359.38-0.16
2.4000e+09309541309152-388.57-0.17
2.5000e+09323719323158-560.57-0.24
2.6000e+09337785337204-581.23-0.25
2.7000e+09351906351287-619.24-0.26
2.8000e+09365933365406-527.18-0.22
2.9000e+09380117379560-557.48-0.23
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