def pr_log(xmax):
y = float(0)
v = [y]
for p in prime_range(xmax):
y += 1r
x = float(p)
v.append((y-x/math.log(x))/(math.log(x)*math.sqrt(x)))
return v
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time v_log = pr_log(10^7)
T_log = finance.TimeSeries(v_log[2:])
Time: CPU 1.96 s, Wall: 1.98 s Time: CPU 1.96 s, Wall: 1.98 s |
T_log
[-0.3840, -0.0296, 0.0782, 0.0519, 0.1007 ... 0.8664, 0.8664, 0.8664, 0.8664, 0.8664] [-0.3840, -0.0296, 0.0782, 0.0519, 0.1007 ... 0.8664, 0.8664, 0.8664, 0.8664, 0.8664] |
def pr_Li(xmax):
y = float(0)
v = [y]
for p in prime_range(xmax):
y += 1r
x = float(p)
v.append((y-float(Li(x)))/(math.log(x)*math.sqrt(x)))
return v
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time v = pr_Li(10^5)
T = finance.TimeSeries(v[2:])
Time: CPU 6.69 s, Wall: 6.89 s Time: CPU 6.69 s, Wall: 6.89 s |
T
[0.4633, 0.1141, 0.0560, -0.0686, -0.0380 ... -0.0095, -0.0100, -0.0100, -0.0101, -0.0099] [0.4633, 0.1141, 0.0560, -0.0686, -0.0380 ... -0.0095, -0.0100, -0.0100, -0.0101, -0.0099] |
T.plot_histogram(bins=5000).show(xmax=0,frame=True)
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time v = pr_Li(10^6)
T = finance.TimeSeries(v[2:])
Time: CPU 58.29 s, Wall: 60.19 s Time: CPU 58.29 s, Wall: 60.19 s |
T
[0.4633, 0.1141, 0.0560, -0.0686, -0.0380 ... -0.0093, -0.0093, -0.0092, -0.0093, -0.0092] [0.4633, 0.1141, 0.0560, -0.0686, -0.0380 ... -0.0093, -0.0093, -0.0092, -0.0093, -0.0092] |
T.min()
-0.09275610952168295 -0.09275610952168295 |
T[4:].min()
-0.09275610952168295 -0.09275610952168295 |
T.plot_histogram(bins=5000).show(xmax=0,frame=True)
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T.plot_histogram(bins=5000).show(xmin=-0.03, xmax=0,frame=True)
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T[1000:].plot_histogram(bins=5000).show(xmax=0,frame=True)
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prime_pi(10^5)
9592 9592 |
len(T)
78497 78497 |
T[10000:].plot_histogram(bins=1000).show(xmax=0,frame=True)
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T[50000:].plot_histogram(bins=1000).show(xmax=0,frame=True)
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T[50000:].plot_histogram(bins=100).show(xmax=0,frame=True)
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T[50000:].plot_histogram(bins=2000).show(xmax=0,frame=True)
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T[70000:].plot_histogram(bins=300).show(xmax=0,frame=True)
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