#/usr/bin/env python3

import numpy as np
import matplotlib.pyplot as plt
from sympy import primepi

# Define the range of n
n_values = np.arange(2, 1000, 1) # 2 - 1000 in steps of 1

# Compute the prime counting function π(n)
pi_values = [primepi(n) for n in n_values]

# Plot the prime counting function
plt.figure(figsize=(10, 6))
plt.plot(n_values, pi_values, label=r'$\pi(n)$ (Prime Counting Function)', color='blue')
plt.xlabel(r'$n$', fontsize=12)
plt.ylabel(r'$\pi(n)$', fontsize=12)
plt.title(r'Prime Counting Function $\pi(n)$ for $n = 2$ to $1000$', fontsize=14)
plt.legend()
plt.grid(True)
plt.show()