Summary

{{Information |description=

|date=2016-09-13 |source=Own work |author=Nicoguaro |permission= |other versions=

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  int .png
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  int .svg
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  Chinese .svg
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  English .svg
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|other fields={{Igen|Matplotlib|+|code= import numpy as np import matplotlib.pyplot as plt from scipy.optimize import curve_fit from matplotlib import rcParams

rcParams['font.size'] = 14

1. Data

data = np.array([[

           1952,     1952,     1957,     1961,     1961,     1963,
           1963,     1971,     1978,     1979,     1979,     1982,
           1983,     1985,     1989,     1992,     1994,     1996,
           1996,     1997,     1998,     1999,     2001,     2003,
           2004,     2005,     2005,     2006,     2008,     2013,
           2016,     2017,     2018,     2024],
      [     157,      687,      969,     1281,     1332,     2917,
           3376,     6002,     6533,     6987,    13395,    25962,
          39751,    65050,    65087,   227832,   258716,   378632,
         420921,   895932,   909526,  2098960,  4053946,  6320430,
        7235733,  7816230,  9152052,  9808358, 12978189, 17425170,
       22338618, 23249425, 24862048, 41024320]])

year = data[0, :] primes = data[1, :]

year_of_lin_growth = 1999

plt.plot(year, primes, color="#377eb8", marker=".", drawstyle='steps-post') plt.yscale('log')

1. Fit function

def lin_fun(x, a, b):

   return a*x + b

def exp_fun(x, a, b):

   return np.exp(a*x + b)

1. 1. Plot the older part which follows exponential growth of digits with time

popt, pcov = curve_fit(lin_fun, year[year <= year_of_lin_growth], np.log(primes[year <= year_of_lin_growth])) x_vals = np.linspace(np.min(year), year_of_lin_growth, 20) y_vals = exp_fun(x_vals, *popt) plt.plot(x_vals, y_vals, color="#1ae41c", linestyle="dashed", label='digit number doubling every {:.1f} y'.format(np.log(2)/popt[0])) print('Exponential fit (green curve): y = exp({:.4f} * t + {:.4f})'.format(*popt))

year_of_lin_growth = 1998

1. 1. Plot the newer part which follows linear growth of digits with time

popt, pcov = curve_fit(lin_fun, year[year >= year_of_lin_growth], primes[year >= year_of_lin_growth]) x_vals = np.linspace(year_of_lin_growth, np.max(year), 100) y_vals = lin_fun(x_vals, *popt) plt.plot(x_vals, y_vals, color="#e41a1c", linestyle="dashed", label='digit number growing by $10^6$ every {:.2f} y'.format(1e6/popt[0])) print('Linear fit (red curve): y = {:.4g} * t + {:.4g}'.format(*popt))

1. Plot details

plt.legend(prop={'size':10}) plt.xlabel("Year") plt.ylabel("Number of digits in largest known prime") plt.savefig("Digits_in_largest_found_prime_as_a_function_of_time.svg", bbox_inches="tight") plt.show()}}}}

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