I enjoyed this - tried to write a solution that was easy to read and understand. I made it a bit more flexible to test for any number rather than just 1000.
#Problem Set 1a ( Problem 1 )
primeswanted = int(input("This program will find the nth prime. \nPlease enter n:"))
if primeswanted <=0:
print "n must be >= 1"
else:
lastprime = 2
primesfound = 1
primecandidate = lastprime + 1
while primesfound < primeswanted: # range of search
possibly_prime = True
for divisor in range(2, primecandidate, 1): # testing
if possibly_prime:
possibly_prime = ((primecandidate % divisor) != 0) # testing continued
if possibly_prime:
lastprime = primecandidate # moving the marker
primesfound = primesfound + 1
primecandidate = primecandidate + 1
print "The nth prime is:", lastprime
#Problem Set 1b ( Problem 2 )
from math import *
primeswanted = int(input("This program will sum logs of primes through the nth and give the ratio between the sum and n.\nPlease enter n:"))
if primeswanted <=0:
print "n must be >= 1"
else:
lastprime = 2
primelogs = log(2) # giving initial value for primelogs
primesfound = 1
primecandidate = lastprime + 1
while primesfound < primeswanted:
possibly_prime = True
for divisor in range(2, primecandidate, 1): # searching
if possibly_prime:
possibly_prime = ((primecandidate % divisor) != 0) # testing
if possibly_prime:
lastprime = primecandidate # moving the marker
primesfound = primesfound + 1
newprimelog = log(primecandidate)
primelogs = primelogs + newprimelog # summing the logs of primes
primecandidate = primecandidate + 1
print "The sum of the logs of the primes is:", primelogs
print "The number of primes was (or n equals):", primeswanted
print "The ratio between the sum of the logs of primes and n is:", primelogs / primeswanted
