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# Python Program to Check Prime Number

Given a positive integer, check if the number is prime or not. A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples of first few prime numbers are {2, 3, 5,

Examples:

Input:  n = 11
Output: true

Input:  n = 15
Output: false

Input:  n = 1
Output: false

School Method :

 # A school method based Python3 # program to check if a number# is prime  def isPrime(n):      # Corner case    if n <= 1:        return False      # Check from 2 to n-1    for i in range(2, n):        if n % i == 0:            return False;      return True  # Driver Program to test above functionprint("true") if isPrime(11) else print("false")print("true") if isPrime(14) else print("false")  # This code is contributed by Smitha Dinesh Semwal

Output:

true
false

Time complexity of this solution is O(n)

Optimized School Method :

 # A optimized school method based  # Python3 program to check # if a number is prime         def isPrime(n) :     # Corner cases     if (n <= 1) :         return False    if (n <= 3) :         return True        # This is checked so that we can skip      # middle five numbers in below loop     if (n % 2 == 0 or n % 3 == 0) :         return False        i = 5    while(i * i <= n) :         if (n % i == 0 or n % (i + 2) == 0) :             return False        i = i + 6        return True        # Driver Program      if(isPrime(11)) :     print(" true") else :     print(" false")         if(isPrime(15)) :     print(" true") else :      print(" false")                 # This code is contributed  # by Nikita Tiwari.

Output:

true
false

Please refer complete article on Primality Test | Set 1 (Introduction and School Method) for more details!

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