When I run this code, even for just counting to the 10th prime number (instead of 1000) I get a skewed/jacked output--all "not prime" titles for my is_composite variable, my test_num is giving me prime and composite numbers, and my prime_count is off
Some of the answers that developers have shared use functions and the math import--that's something we haven't yet covered. I am not trying to get the most efficient answer; I am just trying to write workable python code to understand the basics of looping.
# test a prime by diving number by previous sequence of number(s) (% == 0). Do this by
# counting up from 1 all the way to 1000.
test_num = 2 #these are the numbers that are being tested for primality
is_composite = 'not prime' # will be counted by prime_count
prime_count = 0 #count the number of primes
while (prime_count<10): #counts number primes and make sures that loop stops after the 1000th prime (here: I am just running it to the tenth for quick testing)
test_num = test_num + 1 # starts with two, tested for primality and counted if so
x = test_num - 1 #denominator for prime equation
while (x>2):
if test_num%(x) == 0:
is_composite = 'not prime'
else:
prime_count = prime_count + 1
x = x - 1
print is_composite
print test_num
print prime_count
See the hints given by MIT for your assignment. I quote them below:
Initialize some state variables
Generate all (odd) integers > 1 as candidates to be prime
For each candidate integer, test whether it is prime
3.1. One easy way to do this is to test whether any other integer > 1 evenly divides the candidate with 0 remainder. To do this, you can use modular arithmetic, for example, the expression a%b returns the remainder after dividing the integer a by the integer b.
3.2. You might think about which integers you need to check as divisors – certainly you don’t need to go beyond the candidate you are checking, but how much sooner can you stop checking?
If the candidate is prime, print out some information so you know where you are in the computation, and update the state variables
Stop when you reach some appropriate end condition. In formulating this condition, don’t forget that your program did not generate the first prime (2).
It could look like this:
def primes(n):
# http://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188
""" Returns a list of primes < n """
sieve = [True] * n
for i in xrange(3,int(n**0.5)+1,2):
if sieve[i]:
sieve[i*i::2*i]=[False]*((n-i*i-1)/(2*i)+1)
return [2] + [i for i in xrange(3,n,2) if sieve[i]]