Optimize Sieve of Eratosthenes Further

Question

I have written a Sieve of Eratosthenes--I think--but it seems like it\'s not as optimized as it could be. It works, and it gets all the primes up to N, but not as quickly as

Answer 1

a slightly different approach: use a bitarray to represent the odd numbers 3,5,7,... saving some space compared to a list of booleans.

this may save some space only and not help speedup...

from bitarray import bitarray

def index_to_number(i): return 2*i+3
def number_to_index(n): return (n-3)//2

LIMIT_NUMBER = 50
LIMIT_INDEX = number_to_index(LIMIT_NUMBER)+1

odd_primes = bitarray(LIMIT_INDEX)
# index  0 1 2 3
# number 3 5 7 9

odd_primes.setall(True)

for i in range(LIMIT_INDEX):
    if odd_primes[i] is False:
        continue
    n = index_to_number(i)
    for m in range(n**2, LIMIT_NUMBER, 2*n):
        odd_primes[number_to_index(m)] = False

primes = [index_to_number(i) for i in range(LIMIT_INDEX)
          if odd_primes[i] is True]
primes.insert(0,2)

print('primes: ', primes)

the same idea again; but this time let bitarray handle the inner loop using slice assignment. this may be faster.

for i in range(LIMIT_INDEX):
    if odd_primes[i] is False:
        continue
    odd_primes[2*i**2 + 6*i + 3:LIMIT_INDEX:2*i+3] = False

(none of this code has been seriously checked! use with care)

---

in case you are looking for a primes generator based on a different method (wheel factorizaition) have a look at this excellent answer.