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7 | 7 |
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8 | 8 |
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9 | 9 | def is_prime(number: int) -> bool: |
10 | | - """ |
| 10 | + """ |
11 | 11 | Check whether a given integer is a prime number. |
12 | 12 |
|
13 | | - :param n: integer to check |
14 | | - :return: True if n is prime, False otherwise |
15 | | - :raises ValueError: if n is less than 2 |
16 | | - """ |
17 | | - if n < 2: |
18 | | - raise ValueError("n must be an integer greater than or equal to 2") |
19 | | - """Checks to see if a number is a prime in O(sqrt(n)). |
20 | | -
|
21 | | - A number is prime if it has exactly two factors: 1 and itself. |
22 | | -
|
23 | | - >>> is_prime(0) |
24 | | - False |
25 | | - >>> is_prime(1) |
26 | | - False |
27 | | - >>> is_prime(2) |
28 | | - True |
29 | | - >>> is_prime(3) |
30 | | - True |
31 | | - >>> is_prime(27) |
32 | | - False |
33 | | - >>> is_prime(87) |
34 | | - False |
35 | | - >>> is_prime(563) |
36 | | - True |
37 | | - >>> is_prime(2999) |
38 | | - True |
39 | | - >>> is_prime(67483) |
40 | | - False |
41 | | - >>> is_prime(16.1) |
42 | | - Traceback (most recent call last): |
43 | | - ... |
44 | | - ValueError: is_prime() only accepts positive integers |
45 | | - >>> is_prime(-4) |
46 | | - Traceback (most recent call last): |
47 | | - ... |
48 | | - ValueError: is_prime() only accepts positive integers |
| 13 | + A prime number has exactly two distinct positive divisors: 1 and itself. |
| 14 | +
|
| 15 | + :param number: integer to check |
| 16 | + :return: True if number is prime, False otherwise |
| 17 | + :raises ValueError: if input is not a positive integer |
49 | 18 | """ |
50 | 19 |
|
| 20 | + # precondition |
| 21 | + if not isinstance(number, int) or number < 0: |
| 22 | + raise ValueError("is_prime() only accepts positive integers") |
| 23 | + |
| 24 | + if 1 < number < 4: |
| 25 | + return True |
| 26 | + if number < 2 or number % 2 == 0 or number % 3 == 0: |
| 27 | + return False |
| 28 | + |
| 29 | + for i in range(5, int(math.sqrt(number)) + 1, 6): |
| 30 | + if number % i == 0 or number % (i + 2) == 0: |
| 31 | + return False |
| 32 | + return True |
| 33 | + |
51 | 34 | # precondition |
52 | 35 | if not isinstance(number, int) or not number >= 0: |
53 | 36 | raise ValueError("is_prime() only accepts positive integers") |
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