I haven't had time to edit Problem 2 yet, but will post it as soon as I do.
PS 1: Problem 1
# Initialize state variables. primes =  count = 1 sum_candidates = 0 sum_tests = 0 # Do this until we have 1000 primes while len(primes) < 1000: # Increment counter by 2. (Eliminates all divisible by 2.) count += 2 # Set prime switch true. is_prime = True # Loop through the testing slice. for prime in primes: # Check to see if count is prime. if count % prime == 0: # Not a prime, set switch to false. is_prime = False # Don't waste any more time on this number. break # Check for prime limit. if prime**2 > count: break # Check the switch; if it's still true... if is_prime: #...count is prime. Add it to the primes array. primes.append(count) # print ordinal = str(len(primes)) + 'th' print 'The', ordinal, 'prime is', count print ' '