OCW Problem Set 1

These are my solutions from the second set of assignments in my OpenCourseWare study.

ps1a.py

#lists prime numbers up to the 1000th prime

def testPrime(x):
    factor = 2
    while factor**2 <= x:
        if x % factor == 0:
            return False
        else:
            factor = factor + 1
    
    return True

candidate = 3
numPrime = 1

while numPrime < 1000:
    if testPrime(candidate):
        numPrime = numPrime + 1
    candidate = candidate + 2

print "The 1000th prime number is", candidate - 2

ps1b.py

#asks for an upper limit
#calculates all primes and the sum of their logs up to the upper limit
#prints out the sum of the logs, the upper limit,
#and the ratio between the two

from math import *

def testPrime(x):
    factor = 2
    while factor**2 <= x:
        if x % factor == 0:
            return False
        else:
            factor = factor + 1
    
    return True


candidate = 3
primeLogSum = log(2)

n = int(raw_input("What is n? "))

while candidate < n:
    if testPrime(candidate):
        primeLogSum = primeLogSum + log(candidate)
    candidate = candidate + 2

print primeLogSum, n, primeLogSum/n