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William Stein -- Talk for Mathematics is a long conversation: a celebration of Barry Mazur

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def prime_g(B):
    """
    Compute the numbers g(p) for all primes p <= B, as a time series.

    These are the numbers g(p)=(next_prime(p)-p)/p, which are numbers between 0 and 1.
    """
    from math import log, sqrt
    v = [float(p) for p in prime_range(next_prime(B)+1)]  # primes less than B and one more.
    return stats.TimeSeries([(v[i+1]-v[i])/sqrt(log(v[i])) for i in range(len(v)-1)])

%time t = prime_g(10^7); t
[1.2011, 1.9081, 1.5765, 2.8675, 1.2916 ... 1.4945, 6.9743, 0.4982, 4.4835, 6.9743] CPU time: 1.07 s, Wall time: 1.08 s 
%time show(t.plot_histogram(bins=1000))
CPU time: 1.83 s, Wall time: 1.74 s 
show(t.plot_histogram(bins=1000),xmax=13)

%time t = prime_g(10^8); t
[1.2011, 1.9081, 1.5765, 2.8675, 1.2916 ... 2.3300, 4.1939, 2.7959, 4.1939, 4.1939] CPU time: 9.14 s, Wall time: 9.14 s 
%time show(t.plot_histogram(bins=1000))
CPU time: 1.73 s, Wall time: 1.64 s 
show(t.plot_histogram(bins=1000),xmax=13)

show(t.plot_histogram(bins=3000),xmax=13)

%time t = prime_g(10^9); t
[1.2011, 1.9081, 1.5765, 2.8675, 1.2916 ... 18.8916, 2.1967, 7.9081, 1.7574, 15.3769] CPU time: 83.72 s, Wall time: 83.72 s 
%time show(t.plot_histogram(bins=2000))
CPU time: 6.02 s, Wall time: 5.92 s 

show(t.plot_histogram(bins=4000),xmax=13)