Python Eratosthenes Sieve Algorithm Optimization

Question

I\'m attempting to implement the Sieve of Eratosthenes. The output seems to be correct (minus \"2\" that needs to be added) but if the input to the function is larger than 1

Answer 1

You can try the same way Eratosthenes did. Take an array with all numbers you need to check order ascending, go to number 2 and mark it. Now scratch every second number till the end of the array. Then go to 3 and mark it. After that scratch every third number . Then go to 4 - it is already scratched, so skip it. Repeat this for every n+1 which is not already scratched.

In the end, the marked numbers are the prime one. This algorithm is faster, but sometimes need lots of memory. You can optimize it a little by drop all even numbers (cause they are not prime) and add 2 manually to the list. This will twist the logic a little, but will take half the memory.

Here is an illustration of what I'm talking about: http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes