# 10 examples of 'python prime number list' in Python

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``12def primes():13    yield 214    yield 31516    for i in itertools.count(start=5, step=2):17        if is_prime(i):18            yield i``
``746def prime_number_factorisation(n):747    if n < 2:748        return [n]749    i = 2750    factors = []751    while i * i <= n:752        if n % i:753            i += 1754        else:755            n //= i756            factors.append(i)757    if n > 1:758        factors.append(n)759    return factors``
``50def prime_factors(n):51    """Lists prime factors of a given natural integer, from greatest to smallest52    :param n: Natural integer53    :rtype : list of all prime factors of the given natural n54    """55    i = 256    while i <= sqrt(n):57        if n % i == 0:58            l = prime_factors(n/i)59            l.append(i)60            return l61        i += 162    return [n]      # n is prime``
``7def isPrime(num):8    # Returns True if num is a prime number, otherwise False.910    # Note: Generally, isPrime() is slower than primeSieve().1112    # all numbers less than 2 are not prime13    if num < 2:14        return False1516    # see if num is divisible by any number up to the square root of num17    for i in range(2, int(math.sqrt(num)) + 1):18        if num % i == 0:19            return False20    return True``
``16def primeGen(n):17    for i in xrange(2, n):18        prime = True19        if i % 2 == 0 and i != 2:20            continue21        sqrtp = int(i ** 1 / 2)22        for j in xrange(2, sqrtp):23            if j % 2 == 0:24                continue25            if i % j == 0:26                prime = False27                break28        if prime:29            yield i``
``20def prime(num):21    # num is actually a string because input() returns strings. We'll convert it to int22    num = int(num)2324    if num < 0:25        print("Negative integers can not be prime")26        quit()27    if num is 1:28        print("1 is neither prime nor composite")29        # See how I lazily terminated program otherwise it'd forward "None"(default behaviour of python when function30        # returns nothing) rather than True or False. Which could mess up the program.31        # If we hit this if statement above statement is printed then program exits.32        quit()  # Now you don't need to get sys.exit() to exit python has quit to handle the same thing33    if num in [2, 3]:34        # if given argument is 2 or 3, it is prime. We used list without defining a variable which is perfectly valid35        return True36    if num % 2 == 0:  # excluding all even numbers except two.37        return False38    else:39        # Here we are starting counter variable from 3 in range. Second argument excludes numbers above one third40        # of the given argument. Third argument in range sets steps to take to 2. This makes loop to iterate odds41        for x in range(3, int(num/3), 2):42            # Checking if argument is divisible by counter. % is modulus operator which returns remainder of division43            if num % x == 0:44                return False45    # It's okay to have more than one return statement when program hits return statement it exits the function.46    return True``
``17def isprime(no):18    if no == 2:19        return True20    elif no % 2 == 0:21        return False22    sq = int(math.sqrt(no)) + 123    for i in range(3, sq, 2):24        if no % i == 0:25            return False26    return True``
``23def findprimes(start, end):24	for i in range(start, end):25		if i not in Checked:26			Checked.append(i)27			if is_prime(i):28				Primes.append(i)``
``7def prime():8    D = {9: 3, 25: 5}9    yield 210    yield 311    yield 512    MASK = 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0,13    MODULOS = frozenset((1, 7, 11, 13, 17, 19, 23, 29))1415    for q in it.compress(16            it.islice(it.count(7), 0, None, 2),17            it.cycle(MASK)):18        p = D.pop(q, None)19        if p is None:20            D[q * q] = q21            yield q22        else:23            x = q + 2 * p24            while x in D or (x % 30) not in MODULOS:25                x += 2 * p26            D[x] = p``
``1def is_prime(n):2	if n < 2:3		return False45	i = 267	while i * i <= n:8		if n % i == 0:9			return False1011		i += 11213	return True``