10 examples of 'python prime number list' in Python

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12def primes():
13 yield 2
14 yield 3
15
16 for i in itertools.count(start=5, step=2):
17 if is_prime(i):
18 yield i
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746def prime_number_factorisation(n):
747 if n < 2:
748 return [n]
749 i = 2
750 factors = []
751 while i * i <= n:
752 if n % i:
753 i += 1
754 else:
755 n //= i
756 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 smallest
52 :param n: Natural integer
53 :rtype : list of all prime factors of the given natural n
54 """
55 i = 2
56 while i <= sqrt(n):
57 if n % i == 0:
58 l = prime_factors(n/i)
59 l.append(i)
60 return l
61 i += 1
62 return [n] # n is prime
7def isPrime(num):
8 # Returns True if num is a prime number, otherwise False.
9
10 # Note: Generally, isPrime() is slower than primeSieve().
11
12 # all numbers less than 2 are not prime
13 if num < 2:
14 return False
15
16 # see if num is divisible by any number up to the square root of num
17 for i in range(2, int(math.sqrt(num)) + 1):
18 if num % i == 0:
19 return False
20 return True
16def primeGen(n):
17 for i in xrange(2, n):
18 prime = True
19 if i % 2 == 0 and i != 2:
20 continue
21 sqrtp = int(i ** 1 / 2)
22 for j in xrange(2, sqrtp):
23 if j % 2 == 0:
24 continue
25 if i % j == 0:
26 prime = False
27 break
28 if prime:
29 yield i
20def prime(num):
21 # num is actually a string because input() returns strings. We'll convert it to int
22 num = int(num)
23
24 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 function
30 # 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 thing
33 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 valid
35 return True
36 if num % 2 == 0: # excluding all even numbers except two.
37 return False
38 else:
39 # Here we are starting counter variable from 3 in range. Second argument excludes numbers above one third
40 # of the given argument. Third argument in range sets steps to take to 2. This makes loop to iterate odds
41 for x in range(3, int(num/3), 2):
42 # Checking if argument is divisible by counter. % is modulus operator which returns remainder of division
43 if num % x == 0:
44 return False
45 # 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 True
20 elif no % 2 == 0:
21 return False
22 sq = int(math.sqrt(no)) + 1
23 for i in range(3, sq, 2):
24 if no % i == 0:
25 return False
26 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 2
10 yield 3
11 yield 5
12 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))
14
15 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] = q
21 yield q
22 else:
23 x = q + 2 * p
24 while x in D or (x % 30) not in MODULOS:
25 x += 2 * p
26 D[x] = p
1def is_prime(n):
2 if n < 2:
3 return False
4
5 i = 2
6
7 while i * i <= n:
8 if n % i == 0:
9 return False
10
11 i += 1
12
13 return True

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