This isn't a Sieve of Eratosthenes algorithm, but it's too good not to share it.
select r from ( select rownum+1 r from dual connect by rownum < 10000 ) where r=2 or 0 not in( select mod(r,rownum+1) from dual connect by rownum<sqrt(r) )
This is an Oracle query that will generate all of the primes up to 10,000. The query is not even close to fast, but I think it's kind of funny. It's just your typical everyday brute force method of calculating prime numbers.