Lists Samuel Marateck © 2010

The Sieve of Eratosthenes

Place a 0 in all slots X = 26*[0]

Place 0’s in all slots

Start with 2 for j in range(2, √25):

Start with 2 for j in range(2, √25): if x[j] == 0:

Start with 2 for j in range(2, √25): if x[j] == 0: index = 2*j

Start with the 2 slot

for j in range(2, √25): if x[j] == 0: index = 2*j while index < 25: x[index] = 1

Place a 1 in the 4 slot

for j in range(2, √25): if x[j] == 0: index = 2*j while index < 25: x[index] = 1 index = index + j

Then in the 6 slot

Continue

Place 1’s in all multiples of 2 slots

Since there is a 0 in the 3 slot, 3 is prime

There is a 1 already in the 6 slot

Place a 1 in the 9 slot

The 12 slot already has a

Then a 1 in the 15 slot

Then a 1 in the 21 slot

Now there is a 1 in all multiple of 3 slots

Skip the 4 slot since it has a

There is a 0 in the 5 slot, so 5 is prime

Place a 1 in multiple of 5 slots

The only non-zero slot is

Since √25 is 5 we stop here

Starting with 2, all the slots with 0’s are prime numbers