Gap size : 148 (r=74)

Generated by program gapCounts : Mon Jun 27 12:46:01 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+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+030-0-0.00-0.00
6.8000e+030-0-0.00-0.00
7.0000e+030-0-0.00-0.00
7.2000e+030-0-0.00-0.00
7.4000e+030-0-0.00-0.00
7.6000e+03000.000.00
7.8000e+03000.000.00
8.0000e+030-0-0.00-0.00
8.2000e+030-0-0.00-0.00
8.4000e+030-0-0.00-0.00
8.6000e+030-0-0.00-0.00
8.8000e+030-0-0.00-0.00
9.0000e+030-0-0.00-0.00
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+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+04000.000.00
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+06000.000.00
1.0500e+06000.000.00
1.1000e+06000.000.00
1.1500e+06000.000.00
1.2000e+06000.000.00
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+06000.010.00
1.6000e+06000.010.00
1.6500e+06000.010.00
1.7000e+06000.010.00
1.7500e+06000.010.00
1.8000e+06000.010.00
1.8500e+06000.010.00
1.9000e+06000.010.00
1.9500e+06000.020.00
2.0000e+06000.020.00
2.1000e+0610-0.98-0.01
2.2000e+0610-0.98-0.01
2.3000e+0610-0.98-0.01
2.4000e+0610-0.98-0.01
2.5000e+0610-0.97-0.01
2.6000e+0610-0.97-0.01
2.7000e+0610-0.97-0.01
2.8000e+0610-0.97-0.01
2.9000e+0610-0.96-0.01
3.0000e+0610-0.96-0.01
3.1000e+0610-0.96-0.01
3.2000e+0610-0.96-0.01
3.3000e+0610-0.95-0.01
3.4000e+0610-0.95-0.01
3.5000e+0610-0.95-0.01
3.6000e+0610-0.94-0.01
3.7000e+0610-0.94-0.01
3.8000e+0610-0.94-0.01
3.9000e+0610-0.93-0.01
4.0000e+0610-0.93-0.01
4.1000e+0610-0.93-0.01
4.2000e+0610-0.92-0.01
4.3000e+0610-0.92-0.01
4.4000e+0610-0.91-0.01
4.5000e+0610-0.91-0.01
4.6000e+0610-0.91-0.01
4.7000e+0610-0.90-0.01
4.8000e+0610-0.90-0.01
4.9000e+0610-0.89-0.01
5.0000e+0610-0.89-0.01
5.2000e+0610-0.88-0.01
5.4000e+0610-0.87-0.01
5.6000e+0610-0.86-0.01
5.8000e+0610-0.85-0.01
6.0000e+0610-0.84-0.01
6.2000e+0610-0.83-0.01
6.4000e+0610-0.82-0.01
6.6000e+0610-0.80-0.00
6.8000e+0610-0.79-0.00
7.0000e+0610-0.78-0.00
7.2000e+0610-0.77-0.00
7.4000e+0620-1.76-0.01
7.6000e+0620-1.74-0.01
7.8000e+0620-1.73-0.01
8.0000e+0620-1.72-0.01
8.2000e+0620-1.70-0.01
8.4000e+0620-1.69-0.01
8.6000e+0620-1.67-0.01
8.8000e+0620-1.66-0.01
9.0000e+0620-1.64-0.01
9.2000e+0620-1.63-0.01
9.4000e+0620-1.61-0.01
9.6000e+0620-1.60-0.01
9.8000e+0620-1.58-0.01
1.0000e+0720-1.57-0.01
1.0500e+0720-1.52-0.01
1.1000e+0721-1.48-0.01
1.1500e+0721-1.44-0.01
1.2000e+0721-1.39-0.01
1.2500e+0721-1.34-0.01
1.3000e+0721-1.29-0.01
1.3500e+0721-1.24-0.01
1.4000e+0721-1.19-0.01
1.4500e+0721-1.14-0.00
1.5000e+0721-1.08-0.00
1.5500e+0721-1.02-0.00
1.6000e+0721-0.97-0.00
1.6500e+0721-0.91-0.00
1.7000e+0721-0.85-0.00
1.7500e+0721-0.78-0.00
1.8000e+0721-0.72-0.00
1.8500e+0721-0.66-0.00
1.9000e+0721-0.59-0.00
1.9500e+0721-0.53-0.00
2.0000e+0732-1.46-0.01
2.1000e+0732-1.32-0.00
2.2000e+0732-1.17-0.00
2.3000e+0732-1.02-0.00
2.4000e+0732-0.87-0.00
2.5000e+0732-0.71-0.00
2.6000e+0732-0.55-0.00
2.7000e+0733-0.38-0.00
2.8000e+0733-0.21-0.00
2.9000e+0733-0.04-0.00
3.0000e+07330.140.00
3.1000e+07330.320.00
3.2000e+0754-1.49-0.00
3.3000e+0764-2.30-0.01
3.4000e+0764-2.11-0.01
3.5000e+0764-1.91-0.01
3.6000e+0774-2.71-0.01
3.7000e+0774-2.51-0.01
3.8000e+0775-2.30-0.01
3.9000e+0775-2.09-0.01
4.0000e+0775-1.87-0.01
4.1000e+0785-2.65-0.01
4.2000e+0786-2.43-0.01
4.3000e+0786-2.21-0.01
4.4000e+0796-2.98-0.01
4.5000e+0796-2.75-0.01
4.6000e+0796-2.51-0.01
4.7000e+07107-3.27-0.01
4.8000e+07127-5.03-0.01
4.9000e+07137-5.79-0.01
5.0000e+07137-5.54-0.01
5.2000e+07138-5.04-0.01
5.4000e+07148-5.53-0.01
5.6000e+07149-5.00-0.01
5.8000e+071510-5.47-0.01
6.0000e+071610-5.92-0.01
6.2000e+071711-6.36-0.01
6.4000e+071811-6.79-0.02
6.6000e+071812-6.22-0.01
6.8000e+072012-7.63-0.02
7.0000e+072413-11.03-0.02
7.2000e+072414-10.42-0.02
7.4000e+072414-9.80-0.02
7.6000e+072515-10.18-0.02
7.8000e+072615-10.54-0.02
8.0000e+072916-12.89-0.03
8.2000e+072917-12.24-0.02
8.4000e+073017-12.58-0.03
8.6000e+073018-11.90-0.02
8.8000e+073019-11.22-0.02
9.0000e+073119-11.54-0.02
9.2000e+073220-11.84-0.02
9.4000e+073221-11.13-0.02
9.6000e+073222-10.42-0.02
9.8000e+073222-9.70-0.02
1.0000e+083423-10.97-0.02
1.0500e+083525-10.11-0.02
1.1000e+083727-10.20-0.02
1.1500e+084229-13.25-0.02
1.2000e+084431-13.26-0.02
1.2500e+084633-13.22-0.02
1.3000e+085035-15.13-0.02
1.3500e+085337-16.01-0.03
1.4000e+085439-14.85-0.02
1.4500e+085441-12.64-0.02
1.5000e+085944-15.40-0.02
1.5500e+086046-14.12-0.02
1.6000e+086148-12.81-0.02
1.6500e+086351-12.46-0.02
1.7000e+086353-10.07-0.01
1.7500e+086555-9.65-0.01
1.8000e+086758-9.19-0.01
1.8500e+087060-9.70-0.01
1.9000e+087163-8.18-0.01
1.9500e+087465-8.62-0.01
2.0000e+087668-8.04-0.01
2.1000e+087773-3.77-0.00
2.2000e+088479-5.39-0.01
2.3000e+089284-7.89-0.01
2.4000e+089490-4.27-0.01
2.5000e+0810295-6.55-0.01
2.6000e+08105101-3.71-0.00
2.7000e+08112107-4.78-0.01
2.8000e+08120113-6.74-0.01
2.9000e+08128119-8.61-0.01
3.0000e+08131126-5.37-0.01
3.1000e+08138132-6.05-0.01
3.2000e+08143138-4.63-0.01
3.3000e+08150145-5.12-0.01
3.4000e+08155151-3.53-0.00
3.5000e+081581580.160.00
3.6000e+081641650.920.00
3.7000e+081671724.770.00
3.8000e+081721796.700.01
3.9000e+081781867.710.01
4.0000e+081831939.800.01
4.1000e+081912008.970.01
4.2000e+0819620711.210.01
4.3000e+082062158.520.01
4.4000e+082152226.910.01
4.5000e+082212298.370.01
4.6000e+082342372.900.00
4.7000e+082402444.500.00
4.8000e+08253252-0.83-0.00
4.9000e+08260260-0.10-0.00
5.0000e+08270268-2.30-0.00
5.2000e+08292283-8.50-0.01
5.4000e+08307300-7.45-0.01
5.6000e+08319316-3.15-0.00
5.8000e+08335332-2.61-0.00
6.0000e+083463493.160.00
6.2000e+083573669.160.01
6.4000e+0837338310.390.01
6.6000e+083974013.830.00
6.8000e+084114187.490.01
7.0000e+084334363.360.00
7.2000e+084474547.430.01
7.4000e+084694733.690.00
7.6000e+084854916.160.00
7.8000e+085065103.820.00
8.0000e+08531529-2.34-0.00
8.2000e+08553548-5.31-0.00
8.4000e+08574567-7.10-0.01
8.6000e+08591586-4.71-0.00
8.8000e+08610606-4.14-0.00
9.0000e+08626626-0.41-0.00
9.2000e+086456450.500.00
9.4000e+08668666-2.43-0.00
9.6000e+08687686-1.20-0.00
9.8000e+087037063.200.00
1.0000e+097247272.750.00
1.0500e+097737795.810.00
1.1000e+09843832-11.19-0.01
1.1500e+09901886-15.28-0.01
1.2000e+09954941-13.50-0.01
1.2500e+091011996-14.87-0.01
1.3000e+0910561053-3.41-0.00
1.3500e+0911111110-1.16-0.00
1.4000e+0911791168-11.14-0.01
1.4500e+0912421227-15.36-0.01
1.5000e+0913021286-15.85-0.01
1.5500e+0913661346-19.63-0.01
1.6000e+0914471407-39.71-0.02
1.6500e+0914951469-26.11-0.01
1.7000e+0915611531-29.85-0.02
1.7500e+0916251594-30.95-0.02
1.8000e+0916991658-41.41-0.02
1.8500e+0917771722-55.25-0.03
1.9000e+0918311787-44.49-0.02
1.9500e+0918981852-46.14-0.02
2.0000e+0919661918-48.20-0.02
2.1000e+0921002051-48.63-0.02
2.2000e+0922132187-25.87-0.01
2.3000e+0923422325-17.00-0.01
2.4000e+0925012465-36.09-0.02
2.5000e+0926582607-51.22-0.02
2.6000e+0927902751-39.43-0.02
2.7000e+0929302896-33.80-0.01
2.8000e+0930823044-38.37-0.02
2.9000e+0932303193-37.20-0.02
3.0000e+0933963344-52.34-0.02
3.1000e+0935563496-59.83-0.02
3.2000e+0937293650-78.72-0.03
3.3000e+0938793806-73.04-0.03
3.4000e+0940233963-59.84-0.02
3.5000e+0941724122-50.15-0.02
3.6000e+0943144282-32.00-0.01
3.7000e+0944934444-49.44-0.02
3.8000e+0946574607-50.48-0.02
3.9000e+0948164771-45.16-0.02
4.0000e+0950114936-74.51-0.03
4.1000e+0951585103-54.56-0.02
4.2000e+0953395272-67.33-0.02
4.3000e+0954975441-55.84-0.02
4.4000e+0956795612-67.13-0.02
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