Question

This is code an algorithm I found for Sieve of Eratosthenes for python3. What I want to do is edit it so the I can input a range of bottom and top and then input a list of primes up to the bottom one and it will output a list of primes within that range.
However, I am not quite sure how to do that.
If you can help that would be greatly appreciated.

from math import sqrt
def sieve(end):  
    if end < 2: return []  

    #The array doesn't need to include even numbers  
    lng = ((end//2)-1+end%2)  

    # Create array and assume all numbers in array are prime  
    sieve = [True]*(lng+1)  

    # In the following code, you're going to see some funky  
    # bit shifting and stuff, this is just transforming i and j  
    # so that they represent the proper elements in the array.  
    # The transforming is not optimal, and the number of  
    # operations involved can be reduced.  

    # Only go up to square root of the end  
    for i in range(int(sqrt(end)) >> 1):  

        # Skip numbers that aren’t marked as prime  
        if not sieve[i]: continue  

        # Unmark all multiples of i, starting at i**2  
        for j in range( (i*(i + 3) << 1) + 3, lng, (i << 1) + 3):  
            sieve[j] = False  

    # Don't forget 2!  
    primes = [2]  

    # Gather all the primes into a list, leaving out the composite numbers  
    primes.extend([(i << 1) + 3 for i in range(lng) if sieve[i]])  

    return primes

Answer 1

I think the following is working:

def extend_erathostene(A, B, prime_up_to_A):
    sieve = [ True ]* (B-A)
    for p in prime_up_to_A:
        # first multiple of p greater than A
        m0 = ((A+p-1)/p)*p
        for m in range( m0, B, p):
            sieve[m-A] = False
    limit = int(ceil(sqrt(B)))
    for p in range(A,limit+1):
        if sieve[p-A]:
            for m in range(p*2, B, p):
                sieve[m-A] = False 
    return prime_up_to_A + [ A+c for (c, isprime) in enumerate(sieve) if isprime]