How to Generate Primes with a Generator in Python

Generate prime numbers up to a limit using the Sieve of Eratosthenes wrapped in a generator expression for lazy evaluation.

Medium Python 3.9+ Aug 9, 2026 Comprehensions & generators 15 views 0 copies

generators sieve primes performance math

Python code

16 lines

Python 3.9+

def prime_generator(limit):
    sieve = [True] * (limit + 1)
    sieve[0] = sieve[1] = False

    for i in range(2, int(limit ** 0.5) + 1):
        if sieve[i]:
            for j in range(i * i, limit + 1, i):
                sieve[j] = False

    return (num for num, is_prime in enumerate(sieve) if is_prime)


if __name__ == "__main__":
    limit = 30
    primes = list(prime_generator(limit))
    print(f"Primes up to {limit}: {primes}")

Output

stdout

Primes up to 30: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]

How it works

The code builds a boolean sieve where each index represents a number and True marks it as prime. It iterates only up to the square root of the limit, marking multiples of each prime as composite. The generator expression (num for num, is_prime in enumerate(sieve) if is_prime) lazily yields each prime when iterated, avoiding a full list in memory. This combines the efficiency of the sieve algorithm with the memory benefits of generators, ideal for large limits.

Common mistakes

Forgetting to mark 0 and 1 as not prime before starting the sieve
Iterating the inner loop from `i` instead of `i*i`, causing redundant work
Returning a list instead of a generator, defeating the lazy-evaluation goal

Variations

Use a set or list comprehension to return a list directly when memory isn't a concern
Implement the same logic with `itertools.compress` for a more concise generator

Real-world use cases

Generating a list of primes for cryptography key generation in security modules.
Precomputing prime numbers for hashing algorithms or collision-free table sizing.
Streaming primes in a data pipeline to filter or analyze number-theoretic sequences.

How to Generate Primes with a Generator in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

More from Comprehensions & generators

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