Simple prime number generator in Python

Question

Could someone please tell me what I\'m doing wrong with this code? It is just printing \'count\' anyway. I just want a very simple prime generator (nothing fancy).

Answer 1

Just studied the topic, look for the examples in the thread and try to make my version:

from collections import defaultdict
# from pprint import pprint

import re


def gen_primes(limit=None):
    """Sieve of Eratosthenes"""
    not_prime = defaultdict(list)
    num = 2
    while limit is None or num <= limit:
        if num in not_prime:
            for prime in not_prime[num]:
                not_prime[prime + num].append(prime)
            del not_prime[num]
        else:  # Prime number
            yield num
            not_prime[num * num] = [num]
        # It's amazing to debug it this way:
        # pprint([num, dict(not_prime)], width=1)
        # input()
        num += 1


def is_prime(num):
    """Check if number is prime based on Sieve of Eratosthenes"""
    return num > 1 and list(gen_primes(limit=num)).pop() == num


def oneliner_is_prime(num):
    """Simple check if number is prime"""
    return num > 1 and not any([num % x == 0 for x in range(2, num)])


def regex_is_prime(num):
    return re.compile(r'^1?$|^(11+)\1+$').match('1' * num) is None


def simple_is_prime(num):
    """Simple check if number is prime
    More efficient than oneliner_is_prime as it breaks the loop
    """
    for x in range(2, num):
        if num % x == 0:
            return False
    return num > 1


def simple_gen_primes(limit=None):
    """Prime number generator based on simple gen"""
    num = 2
    while limit is None or num <= limit:
        if simple_is_prime(num):
            yield num
        num += 1


if __name__ == "__main__":
    less1000primes = list(gen_primes(limit=1000))
    assert less1000primes == list(simple_gen_primes(limit=1000))
    for num in range(1000):
        assert (
            (num in less1000primes)
            == is_prime(num)
            == oneliner_is_prime(num)
            == regex_is_prime(num)
            == simple_is_prime(num)
        )
    print("Primes less than 1000:")
    print(less1000primes)

    from timeit import timeit

    print("\nTimeit:")
    print(
        "gen_primes:",
        timeit(
            "list(gen_primes(limit=1000))",
            setup="from __main__ import gen_primes",
            number=1000,
        ),
    )
    print(
        "simple_gen_primes:",
        timeit(
            "list(simple_gen_primes(limit=1000))",
            setup="from __main__ import simple_gen_primes",
            number=1000,
        ),
    )
    print(
        "is_prime:",
        timeit(
            "[is_prime(num) for num in range(2, 1000)]",
            setup="from __main__ import is_prime",
            number=100,
        ),
    )
    print(
        "oneliner_is_prime:",
        timeit(
            "[oneliner_is_prime(num) for num in range(2, 1000)]",
            setup="from __main__ import oneliner_is_prime",
            number=100,
        ),
    )
    print(
        "regex_is_prime:",
        timeit(
            "[regex_is_prime(num) for num in range(2, 1000)]",
            setup="from __main__ import regex_is_prime",
            number=100,
        ),
    )
    print(
        "simple_is_prime:",
        timeit(
            "[simple_is_prime(num) for num in range(2, 1000)]",
            setup="from __main__ import simple_is_prime",
            number=100,
        ),
    )

The result of running this code show interesting results:

$ python prime_time.py
Primes less than 1000:
[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, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]

Timeit:
gen_primes: 0.6738066330144648
simple_gen_primes: 4.738092333020177
is_prime: 31.83770858097705
oneliner_is_prime: 3.3708438930043485
regex_is_prime: 8.692703998007346
simple_is_prime: 0.4686249239894096

So I can see that we have right answers for different questions here; for a prime number generator gen_primes looks like the right answer; but for a prime number check, the simple_is_prime function is better suited.

This works, but I am always open to better ways to make is_prime function.