Sieve2026-05-03

My Solution: Exercism Sieve solution

Instructions

Return all prime numbers less than or equal to a given limit.

If the limit is below 2, return an empty list.

Solution

def primes(limit):
    if limit < 2:
        return []

    is_prime = [True] * (limit + 1)
    is_prime[0] = is_prime[1] = False

    for p in range(2, int(limit ** .5) + 1):
        if is_prime[p]:
            for i in range(p * p, limit + 1, p):
                is_prime[i] = False

    return [p for p in range(2, limit + 1) if is_prime[p]]

Syntax Notes

• A boolean list tracks which numbers are still considered prime.
• Multiples of each discovered prime are marked False.
• The outer loop only needs to run up to the square root of the limit.
• The final list comprehension collects every number that remained prime.