Portfolio: Sieve of Eratosthenes

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View raw: eratosthenes.py

#!/usr/bin/env python2
# -*- coding: utf-8 -*-
# 
# Copyright by Scott Severance
# 
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# 
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.

# This is a library to implement the Sieve of Eratosthenes
# <https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>.
#
# This module has only been tested in Python 2. No attempt has been made to make
# it compatible with Python 3.

'''
This module contains functions for handling prime numbers.

All prime number operations are done by means of the Sieve
of Eratosthenes.

Functions:
    list_primes(upper_limit)
        Lists all primes up to a given limit
    
    is_prime(num)
        Tests whether a given integer is prime

    prime_factors(num)
        Returns a list of num's prime factors
'''

import math

def list_primes(upper_limit):
    '''
    This function implements the Sieve of Eratosthenes
    to find all prime numbers up to a given integer.
    
    Parameter:
        upper_limit: the highest integer to search.
        (raises ValueError if upper_limit < 2 or isn't
        an integer.)
    
    Returns: a list of prime numbers
    '''

    if upper_limit != int(upper_limit):
        raise ValueError, "%d isn't an integer!" % upper_limit
    if upper_limit < 2:
        raise ValueError, "%d doesn't make sense as an upper limit!" % upper_limit
    loop_limit = math.sqrt(upper_limit)
    ints = range(2, upper_limit + 1)
    primes = []
    while True:
        i = ints[0]
        primes.append(i)
        del ints[0]
        if i <= loop_limit:
            ints = [x for x in ints if x % i != 0]
        else:
            return primes + ints # All remaining ints are prime

def is_prime(num):
    'Tests whether num is prime. Returns bool.'
    return num in list_primes(num)

def prime_factors(num):
    "Returns a list of num's prime factors."
    if num != int(num):
        raise ValueError, "Can't find the prime factors of a non-integer."
    num = abs(num)
    try:
        primes = list_primes(int(math.sqrt(num)))
    except ValueError:
        # num is either small or invalid
        if num == 1:
            return [num]
        primes = list_primes(num)
    factors = []
    for i in primes:
        # I use a while loop instead of an if statement because some
        # factors might occur more than once.
        while num % i == 0:
            factors.append(i)
            num /= i
        if num == 1:
            return factors
        elif num in primes:
            break
    factors.append(num)
    return factors


# For testing purposes, this module can be called directly from the command line
# with an integer specified on the command line. Each function in this module
# will be called with that integer. Don't try this with too large an integer
# unless you have a lot of time to spare. Better to import the module and call
# just the functions you need.
# 
# The code below only executes if this module is run directly as opposed to
# being imported.
if __name__ == '__main__':
    from sys import argv, stderr, exit
    if len(argv) != 2:
        stderr.write('ERROR: You must pass exactly one argument, an integer.\n')
        exit(1)
    try:
        number = int(argv[1])
    except ValueError:
        stderr.write('ERROR: You must pass an integer.\n')
        exit(1)
    primes = list_primes(number)
    print 'Primes up to %d:' % number, primes
    print '%d is prime:' % number, number in primes
    print 'The prime factors of %d are:' % number, prime_factors(number)