# Java Program for 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

```

 `// 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 `

Please refer complete article on Legendre’s Conjecture for more details!

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