File:Chebyshevplotfrom0to1000.png

#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
from mpmath import *
from pylab import rcParams
rcParams['figure.figsize'] = 10, 10

def  isValid(n):
        if (n <=0):
                return 0
        elif (n-int(n) != 0):
                return 0
        return 1

def  isPrime(n):
        return  not (n < 2 or any(n % i == 0 for i in  range(2, int(n**0.5)+1)))

def  Chebyshev(n):
        if not  isValid(n):
                return 0
        chebyshev = 0
        for p in  range(1,n):
                if (isPrime(p)):
                        chebyshev  += log(p)
        return  chebyshev

x=np.arange(0,1000,0.01);
f=np.vectorize(lambda x: Chebyshev(floor(x)))
y=f(x)

fig, ax = plt.subplots()

plt.xlabel(r'$x$')
plt.ylabel(r'$\vartheta(x)$')

plt.plot(x,y,linewidth=2,color='Black')

plt.savefig('chebyshevplot.png',bbox_inches='tight',pad_inches=0.15)