A prime number is a natural number greater than 1 with only two positive factors (1 and itself).
Prime numbers play an important role in number theory and are widely used in cryptography, computer science, and other fields. Premium short** plan
Definitions and judgment methods.
A prime number is a natural number greater than 1 and has no other factors than 1 and itself.
The most basic way to tell if a number is prime is trial division, which is to try to divide the number by all integers from 2 to its square root, and if it is divisible, it is not prime, otherwise it is prime.
Python programming implements prime number judgment.
In Python, we can write a function to determine whether a number is prime or not. Here's a simple example:
def is_prime(n): tab)if n <= 1: (2tab)return false (tab)elif n <= 3: (2tab)return true (tab)elif n % 2 == 0 or n % 3 == 0: (2tab)return false (tab)i = 5 (tab)while i * i <= n: (2tab)if n % i == 0 or n % i + 2) == 0: (3tab)return false (2tab)i += 6 (tab)return true
This function first handles some special cases (n is less than or equal to 1, n is equal to 2 or 3) and then checks whether n is divisible by 2 or 3.
Next, the function uses an optimization that only needs to check the square root of n, and increments by 6 at a time, because all prime numbers are either divisible by 6 or are the number before or after 6.
Finally, if n is not divisible by any integer between 2 and its square root, then the function returns true, indicating that n is a prime number.
Outputs prime numbers within the specified range.
Next, we can use the above function to find out all the prime numbers in the specified range. For example, if we want to find out all prime numbers between 1 and 100, we can use the following:
def print_primes(start, end): tab)for i in range(start, end + 1): 2tab)if is_prime(i): 3tab)print(i)
This function takes two parameters: the start and end ranges. For each number in the range, it calls the previously defined is prime function to check if the number is prime.
If yes, print it out. This way we can get all the primes in the specified range.
Summary. Prime numbers are a very interesting and important mathematical concept that has a wide range of applications in many fields. By understanding the definition and judgment methods of prime numbers, we can better understand and use prime numbers.
Hopefully, this article will be helpful for readers to quickly master python programming to implement prime numbers.