File:Digits in largest prime found as a function of time.svg
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This is a file from the Wikimedia Commons. The description on its description page there is shown below.
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Summary
| Description |
English: Plot of the number of digits in largest known prime by year, since the electronic computer. Note that the vertical scale is logarithmic. The green line is the exponential curve of best fit that was followed roughly until 1999; the red curve is a linear fit, more accurate after 1999. Run the source code below to get actual
Русский: График зависимости числа цифр в наибольшем известном простом числе по годам с момента появления первого компьютера. Вертикальная шкала логарифмическая. Зеленая линия - экспоненциальная кривая наилучшего приближения, которой примерно следовал рост числа цифр до 1999 года; красная кривая - это линейная аппроксимация, более точное приближение после 1999 г. |
| Date | |
| Source | Own work |
| Author | Nicoguaro |
| Other versions |
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| SVG development |  This plot was created with Matplotlib. |
| Source code | Python code"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from matplotlib import rcParams
rcParams['font.size'] = 14
# 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, 2018, 2018],
[ 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]])
year = data[0, :]
primes = data[1, :]
year_of_lin_growth = 1998
plt.plot(year, primes, color="#377eb8", marker=".", drawstyle='steps-post')
plt.yscale('log')
# Fit function
def lin_fun(x, a, b):
return a*x + b
def exp_fun(x, a, b):
return np.exp(a*x + b)
## 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
## 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))
# 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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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 05:09, 22 August 2020 | 540 × 408 (59 KB) | Gap9551 | fixed error in linear rate (red line fit) in legend |
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