Check n^2 – m^2 is prime or not
Given two integers n and m. Check n^2 – m^2 is prime or not. n and m can be very large.
Examples:
Input : n = 6, m = 5 Output : YES Input : n = 16, m = 13 Output : NO
A simple solution is to fist compute n^2 – m^2, then check if it is prime or not. n^2 – m^2 might be very large – it might not even fit into 64-bit integer. Checking primality for it certainly cannot be performed naively.
A better solution is to express n^2 – m^2 as (n-m)(n+m). This is prime if and only if n-m = 1 and n+m is a prime.
C++
// CPP program to find n^2 - m^2 // is prime or not. #include <bits/stdc++.h> using namespace std; // Check a number is prime or not bool isprime(int x) { // run a loop upto square of given number for (int i = 2; i * i <= x; i++) if (x % i == 0) return false; return true; } // Check if n^2 - m^2 is prime bool isNSqMinusnMSqPrime(int m, int n) { if (n - m == 1 and isprime(m + n)) return true; else return false; } // Driver code int main() { int m = 13, n = 16; if (isNSqMinusnMSqPrime(m, n)) cout << "YES"; else cout << "NO"; return 0; } |
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Java
// Java program to find n^2 - m^2 // is prime or not. class GFG { // Check if a number is prime or not static boolean isprime(int x) { // run a loop upto square of given number for (int i = 2; i * i <= x; i++) if (x % i == 0) return false; return true; } // Check if n^2 - m^2 is prime static boolean isNSqMinusnMSqPrime(int m, int n) { if (n - m == 1 && isprime(m + n)) return true; else return false; } // Driver code public static void main(String [] args) { int m = 13, n = 16; if (isNSqMinusnMSqPrime(m, n)) System.out.println("YES"); else System.out.println("NO"); } } // This code is contributed // by ihritik |
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Python3
# Python program to find n^2 - m^2 # is prime or not. # Check a number is prime or not def isprime(x): # run a loop upto square # of given number for i in range(2, math.sqrt(x)): if (x % i == 0) : return False; return True; # Check if n^2 - m^2 is prime def isNSqMinusnMSqPrime( m, n): if (n - m == 1 and isprime(m + n)): return True; else: return False; # Driver code m = 13; n = 16; if (isNSqMinusnMSqPrime(m, n)) : print ( "YES"); else: print ("NO"); # This code is contributed # by Shivi_Aggarwal |
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C#
// C# program to find n^2 - m^2 // is prime or not. using System; class GFG { // Check if a number is prime or not static bool isprime(int x) { // run a loop upto square // of given number for (int i = 2; i * i <= x; i++) if (x % i == 0) return false; return true; } // Check if n^2 - m^2 is prime static bool isNSqMinusnMSqPrime(int m, int n) { if (n - m == 1 && isprime(m + n)) return true; else return false; } // Driver code public static void Main() { int m = 13, n = 16; if (isNSqMinusnMSqPrime(m, n)) Console.Write("YES"); else Console.Write("NO"); } } // This code is contributed // by Smitha |
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PHP
<?php //PHP program to find n^2 - m^2 // is prime or not. // Check a number is prime or not function isprime($x) { // run a loop upto square // of given number for ( $i = 2; $i * $i <= $x; $i++) if ($x % i == 0) return false; return true; } // Check if n^2 - m^2 is prime function isNSqMinusnMSqPrime($m, $n) { if ($n - $m == 1 and isprime($m + $n)) return true; else return false; } // Driver code $m = 13; $n = 16; if (isNSqMinusnMSqPrime($m, $n)) echo "YES"; else echo "NO"; // This code is contributed // by inder_verma ?> |
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Output:
NO
Time Complexity: O(sqrt(n+m))
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