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

**Explanation**: Here 4^{2} = 16 and 5^{2} = 25

Hence, prime numbers between 16 and 25 are 17, 19 and 23.

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

`# 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` |

**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!