Prime-counting function and x/ln(x) plot

prime.py

#!python
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches

def pi(x):
    prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541]
    assert x <= prime[-1]
    i = 0
    while prime[i] < x:
            i += 1
    return i

x = np.arange(0, 500, 0.1)

y = x / np.log(x) # Natural log
p = [pi(i) for i in x]

plt.plot(x, y, label='$f(x) = x / \ln(x)$', color='red')
plt.plot(x, p, label='$\pi(x)$', color='black')

plt.legend(loc='upper left')
plt.ylim([0, 100])

plt.show()

nice work