检查N是否为弱质数

给定正整数N ，任务是检查N是否为弱质数。

In number theory, a weak prime is a prime number that is less than the arithmetic mean of nearest prime numbers i.e next and previous prime numbers.
First few weak prime numbers are 3, 7, 13, 19, 23, 31, 43, 47, 61, …
A weak prime P_n can be represented as-

where n is its index in the ordered set of prime numbers.

例子：

Input: N = 13
Output: Yes
13 is 6th prime number, the arithmetic mean of 5th and 7th prime number i.e. 11 and 17 is 14.
13 is less than 14 so 13 is a weak prime.

Input: N = 11
Output: No

方法：

• 如果N不是素数或它是第一个素数，即2，则打印No。
• 否则，找到最接近N的素数(左边一个，右边一个)，并将它们的算术平均值存储在mean中。
  • 如果N <表示打印是。
  • 其他打印号。

下面是上述方法的实现：

C++14

// C++ program to check
// if a given number is weak prime
#include 
using namespace std;
 
// Utility function to check
// if a number is prime or not
bool isPrime(int 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 || n % 3 == 0)
        return false;
 
    for(int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// Function that returns true
// if n is a weak prime
bool isWeakPrime(int n)
{
     
    // If n is not a prime number or
    // n is the first prime then return false
    if (!isPrime(n) || n == 2)
        return false;
 
    // Initialize previous_prime to n - 1
    // and next_prime to n + 1
    int previous_prime = n - 1;
    int next_prime = n + 1;
 
    // Find next prime number
    while (!isPrime(next_prime))
        next_prime++;
 
    // Find previous prime number
    while (!isPrime(previous_prime))
        previous_prime--;
 
    // Arithmetic mean
    int mean = (previous_prime +
                next_prime) / 2;
 
    // If n is a weak prime
    if (n < mean)
        return true;
    else
        return false;
}
 
// Driver code
int main()
{
    int n = 13;
 
    if (isWeakPrime(n))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}
 
// This code is contributed by himanshu77

Java

// Java program to check
// if a given number is weak prime
import java.util.*;
class GFG{
 
// Utility function to check
// if a number is prime or not
static boolean isPrime(int 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 || n % 3 == 0)
        return false;
 
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
 
    return true;
}
 
// Function that returns true
// if n is a weak prime
static boolean isWeakPrime(int n)
{
    // If n is not a prime number or
    // n is the first prime then return false
    if (!isPrime(n) || n == 2)
        return false;
 
    // Initialize previous_prime to n - 1
    // and next_prime to n + 1
    int previous_prime = n - 1;
    int next_prime = n + 1;
 
    // Find next prime number
    while (!isPrime(next_prime))
        next_prime++;
 
    // Find previous prime number
    while (!isPrime(previous_prime))
        previous_prime--;
 
    // Arithmetic mean
    int mean = (previous_prime +
                next_prime) / 2;
 
    // If n is a weak prime
    if (n < mean)
        return true;
    else
        return false;
}
 
// Driver code
public static void main(String args[])
{
    int n = 13;
 
    if (isWeakPrime(n))
        System.out.print("Yes");
    else
        System.out.print("No");
}
}
 
// This code is contributed by Code_Mech

Python3

# Python3 program to check if a given
# number is weak prime
 
# Utility function to check
# if a number is prime or not
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
 
# Function that returns true
# if n is a weak prime
def isWeakPrime(n):
 
    # declaring variables as global
    global next_prime, previous_prime
 
    # If n is not a prime number or n is
    # the first prime then return false
    if(not isPrime(n) or n == 2):
        return False
 
    # Initialize previous_prime to n - 1
    # and next_prime to n + 1
    previous_prime = n - 1
    next_prime = n + 1
 
    # Find next prime number
    while(not isPrime(next_prime)):
        next_prime += 1
 
    # Find previous prime number
    while (not isPrime(previous_prime)):
        previous_prime -= 1
 
    # Arithmetic mean
    mean = (previous_prime + next_prime) // 2
 
    # If n is a weak prime
    if(n < mean):
        return True
    else:
        return False
 
# Driver code
if __name__ == '__main__':
 
    n = 13
 
    if(isWeakPrime(n)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by Shivam Singh

C#

// C# program to check if a given number is weak prime
using System;
class GFG {
 
    // Utility function to check
    // if a number is prime or not
    static bool isPrime(int 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 || n % 3 == 0)
            return false;
 
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
 
        return true;
    }
 
    // Function that returns true
    // if n is a weak prime
    static bool isWeakPrime(int n)
    {
        // If n is not a prime number or
        // n is the first prime then return false
        if (!isPrime(n) || n == 2)
            return false;
 
        // Initialize previous_prime to n - 1
        // and next_prime to n + 1
        int previous_prime = n - 1;
        int next_prime = n + 1;
 
        // Find next prime number
        while (!isPrime(next_prime))
            next_prime++;
 
        // Find previous prime number
        while (!isPrime(previous_prime))
            previous_prime--;
 
        // Arithmetic mean
        int mean = (previous_prime
                    + next_prime)
                   / 2;
 
        // If n is a weak prime
        if (n < mean)
            return true;
        else
            return false;
    }
 
    // Driver code
    public static void Main()
    {
        int n = 13;
 
        if (isWeakPrime(n))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}

Javascript

    // Javascript program to check 
    // if a given number is weak prime 
     
    // Utility function to check 
    // if a number is prime or not 
    function 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 || n % 3 == 0) 
            return false; 
 
        for(let i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
 
        return true; 
    } 
 
    // Function that returns true 
    // if n is a weak prime 
    function isWeakPrime(n) 
    { 
 
        // If n is not a prime number or 
        // n is the first prime then return false 
        if (!isPrime(n) || n == 2) 
            return false; 
 
        // Initialize previous_prime to n - 1 
        // and next_prime to n + 1 
        let previous_prime = n - 1; 
        let next_prime = n + 1; 
 
        // Find next prime number 
        while (!isPrime(next_prime)) 
            next_prime++; 
 
        // Find previous prime number 
        while (!isPrime(previous_prime)) 
            previous_prime--; 
 
        // Arithmetic mean 
        let mean = (previous_prime + 
                    next_prime) / 2; 
 
        // If n is a weak prime 
        if (n < mean) 
            return true; 
        else
            return false; 
    } 
     
    let n = 13; 
   
    if (isWeakPrime(n)) 
        document.write("Yes"); 
    else
        document.write("No"); 
 
// This code is contributed by divyesh072019.

输出：

Yes