# Python 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 :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) ` ` ` `# ` |

**Output :**

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