# Legendre’s Conjecture

It says that there is always one prime number between any two consecutive natural number’s(n = 1, 2, 3, 4, 5, …) square. This is called Legendre’s Conjecture.
Conjecture: A conjecture is a proposition or conclusion based upon incompleate information to which no proof has been found i.e it has not been proved or disproved.

Mathematically,
there is always one prime p in the range to where n is any natural number.

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

5 and 7 are the primes in the range to .

11 and 13 are the primes in the range to .

17 and 19 are the primes in the range to .

Examples:

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

Explanation: Here 42 = 16 and 52 = 25
Hence, prime numbers between 16 and 25 are 17, 19 and 23.

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

## C++

 // CPP program to verify Legendre's Conjecture // for a given n. #include using namespace std;    // prime checking bool isprime(int n) {     for (int i = 2; i * i <= n; i++)         if (n % i == 0)             return false;     return true; }    void LegendreConjecture(int n) {    cout << "Primes in the range "<

## Java

 // 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

## Python3

 # Python program to verify Legendre's Conjecture # for a given n    import math     def isprime( n ):            i = 2     for i in range (2, int((math.sqrt(n)+1))):         if n%i == 0:             return False     return True        def LegendreConjecture( n ):     print ( "Primes in the range ", n*n             , " and ", (n+1)*(n+1)             , " are:" )                           for i in range (n*n, (((n+1)*(n+1))+1)):         if(isprime(i)):             print (i)                n = 50 LegendreConjecture(n)    # Contributed by _omg

## C#

 // C# program to verify Legendre's // Conjecture for a given n. using System;    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)     {         Console.WriteLine("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))                 Console.WriteLine(i);         }     }            // Driver program     public static void Main(String[] args)     {         int n = 50;                    LegendreConjecture(n);     } }    // This code is contributed by parashar.

## PHP



Output :
Primes in the range 2500 and 2601 are:
2503
2521
2531
2539
2543
2549
2551
2557
2579
2591
2593

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