勒让德猜想的Java程序

它说在任何两个连续的自然数（n = 1, 2, 3, 4, 5, ...）平方之间总是有一个素数。这称为勒让德猜想。
猜想：猜想是基于不完整信息的命题或结论，尚未找到任何证据，即没有被证明或证伪。

Mathematically,
there is always one prime p in the range $n^2$ to $(n + 1)^2$ where n is any natural number.

for examples-
2 and 3 are the primes in the range $1^2$ to $2^2$.

5 and 7 are the primes in the range $2^2$ to $3^2$.

11 and 13 are the primes in the range $3^2$ to $4^2$.

17 and 19 are the primes in the range $4^2$ to $5^2$.

例子：

Input : 4 
output: Primes in the range 16 and 25 are:
        17
        19
        23

解释：这里 4 ² = 16 和 5 ² = 25
因此，16 到 25 之间的素数是 17、19 和 23。

Input : 10
Output: Primes in the range 100 and 121 are:
        101
        103
        107
        109
        113

// Java program to verify Legendre\'s Conjecture
// for a given n.
class GFG {
  
  // prime checking
  static boolean isprime(int n)
  { 
     for (int i = 2; i * i <= n; i++)
        if (n % i == 0)
            return false;
     return true;
  }
  
  static void LegendreConjecture(int n)
  {
     System.out.println("Primes in the range "+n*n
        +" and "+(n+1)*(n+1)
        +" are:");
      
     for (int i = n*n; i <= ((n+1)*(n+1)); i++)
     {
       // searching for primes
       if (isprime(i))
         System.out.println(i);
     }
  }
  
  // Driver program
  public static void main(String[] args)
  {
     int n = 50;
     LegendreConjecture(n);
  }
}
//This code is contributed by
//Smitha Dinesh Semwal

详情请参阅勒让德猜想的完整文章！