Java Program for Legendre’s Conjecture
Last Updated :
16 Nov, 2022
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 incomplete 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
Java
class GFG {
static boolean isprime( int n)
{
for ( int i = 2 ; i * i <= n; i++)
if (n % i == 0 )
return false ;
return true ;
}
static void LegendreConjecture( int n)
{
System.out.println("Primes in the range "+n*n
+" and "+(n+ 1 )*(n+ 1 )
+" are:");
for ( int i = n*n; i <= ((n+ 1 )*(n+ 1 )); i++)
{
if (isprime(i))
System.out.println(i);
}
}
public static void main(String[] args)
{
int n = 50 ;
LegendreConjecture(n);
}
}
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Please refer complete article on Legendre’s Conjecture for more details!
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