Gap size : 16 (r=8)

Generated by program gapCounts : Mon Jun 27 12:33:00 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+020-0-0.01-0.00
2.0000e+020-0-0.03-0.01
3.0000e+02000.050.02
4.0000e+02000.180.05
5.0000e+02000.340.10
6.0000e+02010.530.14
7.0000e+02010.740.18
8.0000e+02010.960.23
9.0000e+02011.200.27
1.0000e+03011.440.31
1.1000e+03021.690.36
1.2000e+03021.950.40
1.3000e+03022.220.44
1.4000e+03022.490.48
1.5000e+03032.760.52
1.6000e+03033.040.56
1.7000e+03033.330.60
1.8000e+03043.610.64
1.9000e+03142.900.50
2.0000e+03242.190.37
2.1000e+03242.490.41
2.2000e+03351.780.29
2.3000e+03550.080.01
2.4000e+03550.380.06
2.5000e+03560.680.11
2.6000e+03560.980.15
2.7000e+03660.290.04
2.8000e+03670.600.09
2.9000e+0377-0.10-0.01
3.0000e+03770.210.03
3.1000e+03780.520.08
3.2000e+0388-0.17-0.02
3.3000e+03880.140.02
3.4000e+0398-0.54-0.08
3.5000e+03119-2.23-0.31
3.6000e+03119-1.92-0.26
3.7000e+03129-2.60-0.35
3.8000e+031210-2.28-0.31
3.9000e+031210-1.97-0.26
4.0000e+031210-1.65-0.22
4.1000e+031311-2.33-0.30
4.2000e+031411-3.01-0.39
4.3000e+031411-2.69-0.34
4.4000e+031412-2.38-0.30
4.5000e+031412-2.06-0.26
4.6000e+031512-2.73-0.34
4.7000e+031613-3.41-0.42
4.8000e+031613-3.09-0.38
4.9000e+031613-2.77-0.34
5.0000e+031614-2.45-0.29
5.2000e+031714-2.80-0.33
5.4000e+031815-3.15-0.37
5.6000e+031815-2.51-0.29
5.8000e+031916-2.86-0.33
6.0000e+032017-3.21-0.36
6.2000e+032017-2.55-0.28
6.4000e+032018-1.90-0.21
6.6000e+032019-1.25-0.14
6.8000e+032219-2.59-0.28
7.0000e+032420-3.94-0.42
7.2000e+032421-3.28-0.34
7.4000e+032521-3.63-0.38
7.6000e+032622-3.97-0.41
7.8000e+032623-3.31-0.34
8.0000e+032623-2.65-0.27
8.2000e+032724-3.00-0.30
8.4000e+032725-2.34-0.23
8.6000e+032825-2.68-0.26
8.8000e+032926-3.02-0.29
9.0000e+032927-2.36-0.23
9.2000e+033027-2.70-0.26
9.4000e+033128-3.04-0.29
9.6000e+033129-2.38-0.22
9.8000e+033229-2.72-0.25
1.0000e+043330-3.05-0.28
1.0500e+043432-2.40-0.22
1.1000e+043733-3.75-0.33
1.1500e+043935-4.09-0.36
1.2000e+044137-4.43-0.38
1.2500e+044338-4.78-0.40
1.3000e+044440-4.12-0.34
1.3500e+044542-3.46-0.28
1.4000e+044843-4.81-0.39
1.4500e+044845-3.15-0.25
1.5000e+045247-5.49-0.43
1.5500e+045248-3.83-0.30
1.6000e+045350-3.18-0.24
1.6500e+045451-2.52-0.19
1.7000e+045653-2.86-0.21
1.7500e+045955-4.21-0.31
1.8000e+046256-5.55-0.41
1.8500e+046458-5.90-0.43
1.9000e+046660-6.24-0.45
1.9500e+046861-6.59-0.47
2.0000e+046963-5.93-0.42
2.1000e+047366-6.63-0.46
2.2000e+047470-4.32-0.29
2.3000e+047873-5.02-0.33
2.4000e+048276-5.72-0.37
2.5000e+048580-5.42-0.35
2.6000e+049183-8.13-0.51
2.7000e+049486-7.84-0.49
2.8000e+0410189-11.55-0.71
2.9000e+0410593-12.26-0.74
3.0000e+0410896-11.98-0.71
3.1000e+0411099-10.70-0.63
3.2000e+04113103-10.42-0.60
3.3000e+04117106-11.15-0.64
3.4000e+04120109-10.87-0.62
3.5000e+04122112-9.60-0.54
3.6000e+04124116-8.34-0.46
3.7000e+04126119-7.07-0.39
3.8000e+04133122-10.81-0.58
3.9000e+04140125-14.55-0.78
4.0000e+04143129-14.29-0.76
4.1000e+04145132-13.04-0.68
4.2000e+04151135-15.79-0.82
4.3000e+04153138-14.54-0.75
4.4000e+04157142-15.29-0.78
4.5000e+04161145-16.05-0.81
4.6000e+04163148-14.80-0.74
4.7000e+04165151-13.56-0.67
4.8000e+04167155-12.33-0.61
4.9000e+04169158-11.09-0.54
5.0000e+04175161-13.86-0.67
5.2000e+04182168-14.40-0.69
5.4000e+04184174-9.95-0.47
5.6000e+04192180-11.51-0.53
5.8000e+04199187-12.08-0.55
6.0000e+04208193-14.66-0.66
6.2000e+04215200-15.25-0.68
6.4000e+04218206-11.84-0.52
6.6000e+04228213-15.44-0.67
6.8000e+04234219-15.06-0.64
7.0000e+04241225-15.67-0.66
7.2000e+04253232-21.30-0.89
7.4000e+04256238-17.93-0.74
7.6000e+04263244-18.57-0.76
7.8000e+04270251-19.22-0.78
8.0000e+04277257-19.88-0.79
8.2000e+04285263-21.54-0.85
8.4000e+04291270-21.21-0.83
8.6000e+04298276-21.89-0.85
8.8000e+04303282-20.57-0.79
9.0000e+04308289-19.26-0.73
9.2000e+04315295-19.95-0.75
9.4000e+04322301-20.66-0.77
9.6000e+04333308-25.36-0.94
9.8000e+04335314-21.08-0.77
1.0000e+05339320-18.80-0.68
1.0500e+05356336-20.13-0.72
1.1000e+05372352-20.49-0.72
1.1500e+05389367-21.89-0.75
1.2000e+05400383-17.32-0.58
1.2500e+05415398-16.78-0.56
1.3000e+05426414-12.27-0.40
1.3500e+05445429-15.80-0.51
1.4000e+05457445-12.35-0.39
1.4500e+05472460-11.93-0.37
1.5000e+05490475-14.54-0.45
1.5500e+05503491-12.18-0.37
1.6000e+05515506-8.84-0.26
1.6500e+05534521-12.53-0.37
1.7000e+05554537-17.24-0.50
1.7500e+05567552-14.97-0.43
1.8000e+05581567-13.73-0.39
1.8500e+05595582-12.51-0.35
1.9000e+05610598-12.32-0.34
1.9500e+05624613-11.15-0.31
2.0000e+05637628-8.99-0.25
2.1000e+05664658-5.75-0.15
2.2000e+05694688-5.59-0.15
2.3000e+05731718-12.50-0.32
2.4000e+05761749-12.49-0.32
2.5000e+05789778-10.55-0.26
2.6000e+05817808-8.67-0.21
2.7000e+05842838-3.86-0.09
2.8000e+05882868-14.12-0.33
2.9000e+05905898-7.43-0.17
3.0000e+05929927-1.81-0.04
3.1000e+05957957-0.24-0.01
3.2000e+05987986-0.73-0.02
3.3000e+0510241016-8.28-0.18
3.4000e+0510611045-15.87-0.35
3.5000e+0510931074-18.52-0.40
3.6000e+0511231104-19.22-0.41
3.7000e+0511441133-10.96-0.23
3.8000e+0511701162-7.76-0.16
3.9000e+0511991191-7.60-0.16
4.0000e+0512321221-11.48-0.23
4.1000e+0512671250-17.41-0.35
4.2000e+0512951279-16.38-0.33
4.3000e+0513161308-8.39-0.17
4.4000e+0513461337-9.45-0.19
4.5000e+0513701365-4.54-0.09
4.6000e+05139213942.330.04
4.7000e+05141814235.160.10
4.8000e+0514541452-2.05-0.04
4.9000e+0514851481-4.30-0.08
5.0000e+0515121509-2.58-0.05
5.2000e+0515701567-3.25-0.06
5.4000e+05162316240.950.02
5.6000e+05167816813.010.05
5.8000e+05173317384.950.09
6.0000e+051782179512.760.22
6.2000e+051837185114.460.24
6.4000e+051897190811.040.18
6.6000e+05195519659.510.16
6.8000e+05201420216.880.11
7.0000e+05207120776.140.10
7.2000e+05212621337.290.12
7.4000e+05218821891.350.02
7.6000e+0522462245-0.69-0.01
7.8000e+05229623015.180.08
8.0000e+052337235719.960.30
8.2000e+052393241319.650.30
8.4000e+052446246822.250.33
8.6000e+052501252422.760.34
8.8000e+052553257926.200.38
9.0000e+052606263528.550.41
9.2000e+052651269038.820.56
9.4000e+052711274534.020.48
9.6000e+052767280033.140.47
9.8000e+052820285535.190.49
1.0000e+062881291029.160.40
1.0500e+063010304737.290.50
1.1000e+063132318451.990.69
1.1500e+063279332041.290.54
1.2000e+063407345649.210.63
1.2500e+063552359239.750.50
1.3000e+063662372764.940.80
1.3500e+063813386248.790.59
1.4000e+063960399636.310.43
1.4500e+064105413125.510.30
1.5000e+064229426435.410.41
1.5500e+064371439827.020.31
1.6000e+064493453138.340.43
1.6500e+064621466443.380.48
1.7000e+064749479748.160.53
1.7500e+064903493026.680.29
1.8000e+065037506224.950.27
1.8500e+065173519420.970.22
1.9000e+065289532636.760.39
1.9500e+065423545734.310.36
2.0000e+065550558938.640.40
2.1000e+065812585138.650.39
2.2000e+066074611237.830.37
2.3000e+066339637233.210.32
2.4000e+066596663235.840.34
2.5000e+066840689150.740.47
2.6000e+067100714948.940.45
2.7000e+067343740663.480.57
2.8000e+067607766356.370.50
2.9000e+067861792058.650.51
3.0000e+068126817549.330.42
3.1000e+068388843042.430.36
3.2000e+068630868554.980.46
3.3000e+068905893933.990.28
3.4000e+069144919248.490.40
3.5000e+069418944527.470.22
3.6000e+069662969835.970.29
3.7000e+069935995014.990.12
3.8000e+06101611020240.550.32
3.9000e+06104021045350.660.39
4.0000e+06106591070344.340.34
4.1000e+06109021095451.590.39
4.2000e+06111431120360.420.45
4.3000e+06113891145363.850.47
4.4000e+06116451170256.880.41
4.5000e+06119101195140.530.29
4.6000e+06121421219956.810.41
4.7000e+06123851244761.710.44
4.8000e+06126321269462.260.44
4.9000e+06128911294150.460.35
5.0000e+06131351318853.310.37
5.2000e+06135951368186.010.58
5.4000e+06140741417298.420.66
5.6000e+06146031466359.590.39
5.8000e+06151021515249.560.32
6.0000e+06155411563998.380.63
6.2000e+06160291612697.090.61
6.4000e+061650116612110.720.69
6.6000e+06170001709696.320.59
6.8000e+06174851758094.920.57
7.0000e+061796218063100.540.60
7.2000e+06184551854489.220.52
7.4000e+06189371902587.980.51
7.6000e+06194131950591.850.53
7.8000e+06199201998463.850.36
8.0000e+06203922046270.020.39
8.2000e+06208762093963.360.35
8.4000e+06213712141644.910.25
8.6000e+06218302189261.680.34
8.8000e+06222962236770.690.38
9.0000e+06227682284172.960.39
9.2000e+06232492331565.510.35
9.4000e+062367623787111.350.58
9.6000e+062415824260101.500.53
9.8000e+062461924731111.980.58
1.0000e+072509925202102.790.52
1.0500e+07263142637662.030.31
1.1000e+07274932754653.430.26
1.1500e+072861228713101.180.49
1.2000e+072974329876133.450.63
1.2500e+073090231036134.390.62
1.3000e+073205632193137.150.62
1.3500e+073323033347116.850.52
1.4000e+073435234498145.610.64
1.4500e+073546535646180.550.78
1.5000e+073659836791192.770.82
1.5500e+073771537933218.370.92
1.6000e+073882939073244.441.01
1.6500e+073991340211298.061.22
1.7000e+074110041346246.310.99
1.7500e+074224342479236.260.94
1.8000e+074340043610209.990.83
1.8500e+074448944739249.570.97
1.9000e+074564045865225.040.87
1.9500e+074679546989194.490.74
2.0000e+074795148112160.940.61
2.1000e+075017350351178.130.66
2.2000e+075247452583109.000.39
2.3000e+07547255480882.900.29
2.4000e+07569965702630.150.10
2.5000e+07591815923857.070.19
2.6000e+07613926144451.910.17
2.7000e+07635876364456.930.19
2.8000e+07657816583857.360.19
2.9000e+076803968027-11.59-0.04
3.0000e+077026370211-51.72-0.16
3.1000e+077241672390-25.84-0.08
3.2000e+07745497456415.220.05
3.3000e+077673776734-3.37-0.01
3.4000e+0778893788995.520.02
3.5000e+07810418105918.050.05
3.6000e+07831928321523.350.07
3.7000e+07853338536834.550.10
3.8000e+07874578751658.760.17
3.9000e+07896198966041.100.12
4.0000e+079185691801-55.33-0.15
4.1000e+079402593938-87.42-0.24
4.2000e+079618296071-111.08-0.30
4.3000e+079837998201-178.22-0.48
4.4000e+07100590100327-262.75-0.70
4.5000e+07102692102450-241.58-0.63
4.6000e+07104845104570-274.65-0.71
4.7000e+07106955106687-267.86-0.69
4.8000e+07109073108801-272.16-0.69
4.9000e+07111164110912-252.47-0.64
5.0000e+07113262113019-242.72-0.61
5.2000e+07117374117226-147.81-0.36
5.4000e+07121633121422-210.95-0.51
5.6000e+07125768125607-160.70-0.38
5.8000e+07130053129782-270.66-0.64
6.0000e+07134181133948-233.45-0.54
6.2000e+07138260138103-156.70-0.36
6.4000e+07142398142250-148.10-0.33
6.6000e+07146561146388-173.33-0.38
6.8000e+07150720150517-203.12-0.44
7.0000e+07154875154638-237.17-0.51
7.2000e+07159010158751-259.25-0.55
7.4000e+07163128162856-272.11-0.57
7.6000e+07167215166953-261.52-0.54
7.8000e+07171306171044-262.27-0.54
8.0000e+07175455175127-328.16-0.67
8.2000e+07179653179203-450.00-0.91
8.4000e+07183658183272-385.59-0.77
8.6000e+07187746187335-410.77-0.81
8.8000e+07191724191392-332.38-0.65
9.0000e+07195765195442-323.25-0.62
9.2000e+07199662199486-176.24-0.34
9.4000e+07203646203524-122.19-0.23
9.6000e+07207697207556-140.98-0.26
9.8000e+07211762211583-179.48-0.33
1.0000e+08215804215603-200.55-0.37
1.0500e+08225796225632-163.85-0.30
1.1000e+08235762235628-133.52-0.24
1.1500e+08245769245594-174.97-0.30
1.2000e+08255721255530-190.75-0.32
1.2500e+08265596265438-157.54-0.26
1.3000e+08275416275320-96.14-0.16
1.3500e+08285243285176-67.42-0.11
1.4000e+08295058295007-51.37-0.08
1.4500e+08304831304814-17.03-0.03
1.5000e+08314675314598-76.52-0.12
1.5500e+08324584324361-223.01-0.34
1.6000e+08334281334102-178.73-0.27
1.6500e+08343985343823-161.98-0.24
1.7000e+08353606353524-82.08-0.12
1.7500e+0836313536320670.610.10
1.8000e+0837278237286986.670.12
1.8500e+08382534382514-20.33-0.03
1.9000e+08392270392141-128.87-0.18
1.9500e+08401856401752-104.44-0.14
2.0000e+08411449411345-103.58-0.14
2.1000e+08430489430485-3.78-0.00
2.2000e+0844953944956424.850.03
2.3000e+08468826468584-241.68-0.31
2.4000e+08487818487549-268.63-0.33
2.5000e+08506862506461-400.51-0.49
2.6000e+08525683525323-360.03-0.43
2.7000e+08544405544136-269.08-0.32
2.8000e+08563186562902-283.72-0.33
2.9000e+08581972581624-348.14-0.40
3.0000e+08600770600302-467.67-0.53
3.1000e+08619436618939-496.76-0.55
3.2000e+08638062637536-525.96-0.58
3.3000e+08656484656094-389.90-0.42
3.4000e+08675008674615-393.33-0.42
3.5000e+08693474693099-375.04-0.39
3.6000e+08712077711548-528.91-0.55
3.7000e+08730507729963-543.89-0.56
3.8000e+08748904748345-558.98-0.57
3.9000e+08767092766695-397.23-0.40
4.0000e+08785330785013-316.75-0.31
4.1000e+08803585803301-283.69-0.28
4.2000e+08821880821560-320.25-0.31
4.3000e+08840005839789-215.67-0.21
4.4000e+08858166857991-175.22-0.17
4.5000e+08876327876165-162.21-0.15
4.6000e+08894504894312-191.97-0.18
4.7000e+08912689912433-255.87-0.24
4.8000e+08930809930529-280.32-0.26
4.9000e+08948894948599-294.74-0.27
5.0000e+08967206966645-560.57-0.50
5.2000e+0810031961002667-529.37-0.47
5.4000e+0810389861038596-389.76-0.34
5.6000e+0810749541074438-516.05-0.44
5.8000e+0811105651110195-369.85-0.31
6.0000e+0811462351145871-363.99-0.30
6.2000e+0811817751181468-306.55-0.25
6.4000e+0812174791216990-488.78-0.39
6.6000e+0812528271252439-388.11-0.31
6.8000e+0812882401287817-423.16-0.33
7.0000e+0813234751323126-348.66-0.27
7.2000e+0813586621358370-292.49-0.22
7.4000e+0813940481393548-499.66-0.38
7.6000e+0814290681428665-403.28-0.30
7.8000e+0814638891463720-168.57-0.12
8.0000e+0814990761498717-358.85-0.26
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