py1b2.py

py1b2.py

from math import *

def calculate_n_primes(n):

	primes = []
	prime_candidate = 1
	global its_a_prime
	its_a_prime = True

	while len(primes) < (n + 1):
		prime_candidate = prime_candidate + 1
		divisor = 1
		while divisor < prime_candidate-1:
			its_a_prime = True
			divisor = divisor + 1
			if prime_candidate % divisor == 0:
				its_a_prime = False
				break

		if its_a_prime == True:
			primes.append(prime_candidate)

	return primes


def calculate_nth_prime(n):

	primes = calculate_n_primes(n)
	return primes[n-1]


def calculate_primes_beneath_n(n):

	primes = []
	prime_candidate = 1

	global its_a_prime
	its_a_prime = True

	while prime_candidate < n:
		prime_candidate = prime_candidate + 1
		divisor = 1
		while divisor < prime_candidate-1:
			its_a_prime = True
			divisor = divisor + 1;
			if prime_candidate % divisor == 0:
				its_a_prime = False
				break

		if its_a_prime == True:
			primes.append(prime_candidate)

	return primes


def calculate_sum_of_logarithms_of_primes_beneath_n(n):
	
	primes = calculate_primes_beneath_n(n)
	sum_of_logs = 0

	for prime in primes:
		sum_of_logs = sum_of_logs + log(prime)

	return sum_of_logs

print "The 1000th prime is "+ str(calculate_nth_prime(1000))
print "The sum of the logarithms of all the primes beneath 100 is: " + str(calculate_sum_of_logarithms_of_primes_beneath_n(100))
print "The ratio of the sum of the logarithms of all the primes beneath n (100) to n (100) is: " + str(calculate_sum_of_logarithms_of_primes_beneath_n(100)/100)
print "The sum of the logarithms of all the primes beneath 2000 is: " + str(calculate_sum_of_logarithms_of_primes_beneath_n(2000))
print "The ratio of the sum of the logarithms of all the primes beneath n (2000) to n (2000) is: " + str(calculate_sum_of_logarithms_of_primes_beneath_n(2000)/2000)