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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
    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])/log(v[i]) for i in range(len(v)-1)])

%time t = prime_g(10^7); t
[1.4427, 1.8205, 1.2427, 2.0556, 0.8341 ... 0.3723, 1.7372, 0.1241, 1.1168, 1.7372] CPU time: 1.13 s, Wall time: 1.13 s 
%time show(t.plot_histogram(bins=1000))
CPU time: 2.16 s, Wall time: 2.10 s 
show(t.plot_histogram(bins=1000),xmax=4)

%time t = prime_g(10^8); t
[1.4427, 1.8205, 1.2427, 2.0556, 0.8341 ... 0.5429, 0.9772, 0.6514, 0.9772, 0.9772] CPU time: 9.19 s, Wall time: 9.19 s 
%time show(t.plot_histogram(bins=1000))
CPU time: 2.10 s, Wall time: 2.05 s 
show(t.plot_histogram(bins=1000),xmax=4)

show(t.plot_histogram(bins=3000),xmax=4)

%time t = prime_g(10^9); t
[1.4427, 1.8205, 1.2427, 2.0556, 0.8341 ... 4.1499, 0.4825, 1.7372, 0.3860, 3.3778] CPU time: 91.92 s, Wall time: 91.87 s 
%time show(t.plot_histogram(bins=2000))
CPU time: 6.19 s, Wall time: 6.10 s 

show(t.plot_histogram(bins=4000),xmax=4)