Rules are simple (Edit: they were supposed to be)-

• First n primes (not primes below n), should be printed to standard output separated by newlines (primes should be generated within the code)

• primes cannot be generated by an inbuilt function or through a library, i.e. use of a inbuilt or library function such as, prime = get_nth_prime(n), is_a_prime(number), or factorlist = list_all_factors(number) won't be very creative.

• Scoring - Say, we define Score = f([number of chars in the code]), O(f(n)) being the complexity of your algorithm where n is the number of primes it finds. So for example, if you have a 300 char code with O(n^2) complexity, score is 300^2 = 90000, for 300 chars with O(nln(n)), score becomes 3005.7 = 1711.13 (let's assume all logs to be natural logs for simplicity)

• Use any existing programming language, lowest score wins

Edit: Problem has been changed from finding 'first 1000000 primes' to 'first n primes' because of a confusion about what 'n' in O(f(n)) is, n is the number of primes you find (finding primes is the problem here and so complexity of the problem depends on the number of primes found)

Note: to clarify some confusions on complexity, if 'n' is the number of primes you find and 'N' is the nth prime found, complexity in terms of n is and N are not equivalent i.e. O(f(n)) != O(f(N)) as , f(N) != constant * f(n) and N != constant * n, because we know that nth prime function is not constant, I though since we were finding 'n' primes complexity should be easily expressible in terms of 'n'.

To verify your solutions, a list of million primes is available here, (it's on google docs, pastebin won't let me upload an 8 Mb file without paying)

Please Include these in your solution -

• what complexity your program has (include basic analysis if not trivial)

• character length of code

• the final calculated score

This is my first CodeGolf Question so, if there is a mistake or loophole in above rules please do point them out.