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# C Program for Legendre\’s Conjecture

• Last Updated : 06 Dec, 2018

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

```
 `// 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 "` `<< n * n``         ``<< ``" and "` `<< (n + 1) * (n + 1)``         ``<< ``" are:"` `<< endl;`` ` `    ``for` `(``int` `i = n * n; i <= ((n + 1) * (n + 1)); i++)`` ` `        ``// searching for primes``        ``if` `(isprime(i))``            ``cout << i << endl;``}`` ` `// Driver program``int` `main()``{``    ``int` `n = 50;``    ``LegendreConjecture(n);``    ``return` `0;``}`
Output:
```Primes in the range 2500 and 2601 are:
2503
2521
2531
2539
2543
2549
2551
2557
2579
2591
2593
```

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

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