fermatsprime_eastwind.cpp

added prime check by Fermat's algorithm

Author: bad-eastwind

fermatsprime

@@ -0,0 +1,72 @@
+// C++ program to find the smallest twin in given range 
+#include <bits/stdc++.h> 
+using namespace std; 
+
+/* Iterative Function to calculate (a^n)%p in O(logy) */
+int power(int a, unsigned int n, int p) 
+{ 
+	int res = 1;	 // Initialize result 
+	a = a % p; // Update 'a' if 'a' >= p 
+
+	while (n > 0) 
+	{ 
+		// If n is odd, multiply 'a' with result 
+		if (n & 1) 
+			res = (res*a) % p; 
+
+		// n must be even now 
+		n = n>>1; // n = n/2 
+		a = (a*a) % p; 
+	} 
+	return res; 
+} 
+
+/*Recursive function to calculate gcd of 2 numbers*/
+int gcd(int a, int b) 
+{ 
+	if(a < b) 
+		return gcd(b, a); 
+	else if(a%b == 0) 
+		return b; 
+	else return gcd(b, a%b); 
+} 
+
+// If n is prime, then always returns true, If n is 
+// composite than returns false with high probability 
+// Higher value of k increases probability of correct 
+// result. 
+bool isPrime(unsigned int n, int k) 
+{ 
+// Corner cases 
+if (n <= 1 || n == 4) return false; 
+if (n <= 3) return true; 
+
+// Try k times 
+while (k>0) 
+{ 
+	// Pick a random number in [2..n-2]		 
+	// Above corner cases make sure that n > 4 
+	int a = 2 + rand()%(n-4); 
+
+	// Checking if a and n are co-prime 
+	if (gcd(n, a) != 1) 
+		return false; 
+
+	// Fermat's little theorem 
+	if (power(a, n-1, n) != 1) 
+		return false; 
+
+	k--; 
+	} 
+
+	return true; 
+} 
+
+// Driver Program to test above function 
+int main() 
+{ 
+	int k = 3; 
+	isPrime(11, k)? cout << " true\n": cout << " false\n"; 
+	isPrime(15, k)? cout << " true\n": cout << " false\n"; 
+	return 0; 
+}