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Python Program for Legendre\’s Conjecture
• Last Updated : 03 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

```
 `# 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!

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