from math import *

def primes_upto_n(n):
    primes = [2]
    choice = 1
    while len(primes) < n:
        choice += 2
        rt = sqrt(choice)
        isPrime = True
        # since we need all primes from 2 to n, this optimization works
        # we can prime-factor all non-prime numbers.
        for i in range(0, len(primes)):
            poss = primes[i]
            if (choice % poss) == 0:
                isPrime = False
                break
            if (poss >= rt):
                break
        if isPrime:
            primes.append(choice)
    return primes

primes = primes_upto_n(1000)
nthPrime = primes[-1]
sums = reduce(lambda sum,prime: sum+log(prime),primes)
print "Sum: ", sums
print "Nth Prime: ", nthPrime
print "sums / Nth Prime: ", sums/nthPrime