Fastest way to list all primes below N

Answer

Below is a script which compares a number of implementations:

• ambi_sieve_plain,
• rwh_primes,
• rwh_primes1,
• rwh_primes2,
• sieveOfAtkin,
• sieveOfEratosthenes,
• sundaram3,
• sieve_wheel_30,
• ambi_sieve (requires numpy)
• primesfrom3to (requires numpy)
• primesfrom2to (requires numpy)

Many thanks to stephan for bringing sieve_wheel_30 to my attention. Credit goes to Robert William Hanks for primesfrom2to, primesfrom3to, rwh_primes, rwh_primes1, and rwh_primes2.

Of the plain Python methods tested, with psyco, for n=1000000, rwh_primes1 was the fastest tested.