5 examples of 'prime numbers from 1 to 10000' in Python

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def prime(num):
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    # num is actually a string because input() returns strings. We'll convert it to int
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    num = int(num)
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    if num < 0:
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        print("Negative integers can not be prime")
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        quit()
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    if num is 1:
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        print("1 is neither prime nor composite")
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        # See how I lazily terminated program otherwise it'd forward "None"(default behaviour of python when function
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        # returns nothing) rather than True or False. Which could mess up the program.
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        # If we hit this if statement above statement is printed then program exits.
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        quit()  # Now you don't need to get sys.exit() to exit python has quit to handle the same thing
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    if num in [2, 3]:
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        # if given argument is 2 or 3, it is prime. We used list without defining a variable which is perfectly valid
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        return True
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    if num % 2 == 0:  # excluding all even numbers except two.
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        return False
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    else:
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        # Here we are starting counter variable from 3 in range. Second argument excludes numbers above one third
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        # of the given argument. Third argument in range sets steps to take to 2. This makes loop to iterate odds
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        for x in range(3, int(num/3), 2):
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            # Checking if argument is divisible by counter. % is modulus operator which returns remainder of division
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            if num % x == 0:
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                return False
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    # It's okay to have more than one return statement when program hits return statement it exits the function.
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    return True

16
def primeGen(n):
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    for i in xrange(2, n):
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        prime = True
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        if i % 2 == 0 and i != 2:
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            continue
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        sqrtp = int(i ** 1 / 2)
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        for j in xrange(2, sqrtp):
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            if j % 2 == 0:
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                continue
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            if i % j == 0:
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                prime = False
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                break
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        if prime:
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            yield i

7
def isPrime(num):
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    # Returns True if num is a prime number, otherwise False.
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    # Note: Generally, isPrime() is slower than primeSieve().
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    # all numbers less than 2 are not prime
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    if num < 2:
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        return False
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    # see if num is divisible by any number up to the square root of num
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    for i in range(2, int(math.sqrt(num)) + 1):
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        if num % i == 0:
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            return False
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    return True

12
def genprime(n):
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  global isprime
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  isprime = [True] * (n+1)
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  sN = int(math.floor(math.sqrt(n)))
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  for i in range(3, n+1, 2): 
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      if (isprime[i]):
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          yield i
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          if (i < sN):
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              ni = 2*i
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              while (ni <= n):
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                  isprime[ni] = False
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                  ni += i

12
def primes():
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    yield 2
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    yield 3
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    for i in itertools.count(start=5, step=2):
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        if is_prime(i):
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            yield i