Adding Jojo's Miller-Rabin code to the document and improving prime sieve.

1 files changed, 19 insertions, 0 deletions

diff --git a/math/millerRabin.cpp b/math/millerRabin.cpp
new file mode 100644
index 0000000..d41f33a
--- /dev/null
+++ b/math/millerRabin.cpp
@@ -0,0 +1,19 @@
+// Theoretisch: n < 318,665,857,834,031,151,167,461 (> 10^23)
+// Praktisch: n <= 10^18 (long long)
+// Laufzeit: O(log n)
+bool isPrime(ll n) {
+	if(n == 2) return true;
+	if(n < 2 || n % 2 == 0) return false;
+	ll d=n-1,j=0;
+	while(d % 2 == 0) d >>= 1, j++;
+	for(int a = 2; a <= min((ll)37, n-1); a++) {
+		ll v = pow_mod(a, d, n);
+		if(v == 1 || v == n-1) continue;
+		for(int i = 1;  i <= j; i++) {
+			v = mult_mod(v, v, n);
+			if(v == n-1 || v <= 1) break;
+		}
+		if(v != n-1) return false;
+	}
+	return true;
+}