Summary of all prime numbers less than or equal to n.

prime_sum.py

#! /usr/bin/env python
# -*- coding: utf-8 -*-

from time import time
import math

def prime_sum_impl(n):
    r = int(math.sqrt(n))
    v = [n//i for i in range(1, r+1)]
    v += list(range(v[-1]-1, 0, -1))
    s = {i:(2+i)*(i-1)//2 for i in v}
    for p in range(2, r+1):
        if not s[p] > s[p-1]:
            continue
        for k in v:
            if k < p*p:
                break
            else:
                s[k] -= p*(s[k//p] - s[p-1])
    return s[n]

def prime_sum(n):
    t = time()
    return prime_sum_impl(n), time()-t

setup-with-cython.py

from distutils.core import setup
from Cython.Build import cythonize

setup(
    ext_modules = cythonize(
        "prime_sum.py",
        compiler_directives = {
            'boundscheck': False,
            'wraparound': True,
            'initializedcheck': False,
            'nonecheck': False,
            'overflowcheck': False,
            'overflowcheck.fold': False,
            'embedsignature': False,
            'cdivision': True,
            'cdivision_warnings': False,
            'linetrace': False,
            'infer_types': True,
            'unraisable_tracebacks': False,
        })
)