Python Program for Legendre\’s Conjecture

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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 n^2 to (n + 1)^2 where n is any natural number.

for examples-
2 and 3 are the primes in the range 1^2 to 2^2.

5 and 7 are the primes in the range 2^2 to 3^2.

11 and 13 are the primes in the range 3^2 to 4^2.

17 and 19 are the primes in the range 4^2 to 5^2.

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)
 

Output :

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

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