Merge pull request #166 from NarenCK11/eulerpseudoprime

Added Euler Pseudoprime Problem in Java

Author: admirerr

Java/maths/EulerPseudoprime.java

@@ -0,0 +1,98 @@
+import java.math.BigInteger;
+import java.util.Random;
+
+public final class EulerPseudoprime {
+
+    private EulerPseudoprime() {}
+
+    private static final Random RANDOM = new Random();
+
+    public static boolean isProbablePrime(BigInteger n, int trials) {
+        if (n.compareTo(BigInteger.TWO) < 0) {
+            return false;
+        }
+        if (n.equals(BigInteger.TWO) || n.equals(BigInteger.valueOf(3))) {
+            return true;
+        }
+        if (n.mod(BigInteger.TWO).equals(BigInteger.ZERO)) {
+            return false;
+        }
+
+        for (int i = 0; i < trials; i++) {
+            BigInteger a = uniformRandom(BigInteger.TWO, n.subtract(BigInteger.TWO));
+            BigInteger jacobi = BigInteger.valueOf(jacobiSymbol(a, n));
+
+            if (jacobi.equals(BigInteger.ZERO)) {
+                return false;
+            }
+
+            BigInteger exp = n.subtract(BigInteger.ONE).divide(BigInteger.TWO);
+            BigInteger modExp = a.modPow(exp, n);
+
+            if (!modExp.equals(jacobi.mod(n))) {
+                return false;
+            }
+        }
+        return true;
+    }
+
+    public static int jacobiSymbol(BigInteger a, BigInteger n) {
+        if (n.signum() <= 0 || n.mod(BigInteger.TWO).equals(BigInteger.ZERO)) {
+            throw new IllegalArgumentException("n must be a positive odd integer.");
+        }
+
+        int result = 1;
+        a = a.mod(n);
+
+        while (a.compareTo(BigInteger.ZERO) != 0) {
+            while (a.mod(BigInteger.TWO).equals(BigInteger.ZERO)) {
+                a = a.divide(BigInteger.TWO);
+                BigInteger nMod8 = n.mod(BigInteger.valueOf(8));
+                if (nMod8.equals(BigInteger.valueOf(3)) || nMod8.equals(BigInteger.valueOf(5))) {
+                    result = -result;
+                }
+            }
+
+            BigInteger temp = a;
+            a = n;
+            n = temp;
+
+            if (a.mod(BigInteger.valueOf(4)).equals(BigInteger.valueOf(3)) && n.mod(BigInteger.valueOf(4)).equals(BigInteger.valueOf(3))) {
+                result = -result;
+            }
+            a = a.mod(n);
+        }
+        return n.equals(BigInteger.ONE) ? result : 0;
+    }
+
+    private static BigInteger uniformRandom(BigInteger min, BigInteger max) {
+        BigInteger result;
+        do {
+            result = new BigInteger(max.bitLength(), RANDOM);
+        } while (result.compareTo(min) < 0 || result.compareTo(max) > 0);
+        return result;
+    }
+
+    public static void main(String[] args) {
+        // Define the numbers to test and the number of trials for the test.
+        int trials = 20;
+        String[] testNumbers = {
+            "7",       // Small prime
+            "10",      // Small even composite
+            "91",      // Small odd composite
+            "563",     // A known prime number
+            "1105",    // An Euler pseudoprime to base 2
+            "294409",  // A larger prime number
+            "294411"   // A larger composite number
+        };
+
+        System.out.printf("Running Euler Primality Test with %d trials...%n%n", trials);
+
+        for (String numStr : testNumbers) {
+            BigInteger n = new BigInteger(numStr);
+            boolean isPrime = isProbablePrime(n, trials);
+            String result = isPrime ? "Probably Prime" : "Composite";
+            System.out.printf("Is %s prime? --> %s%n", n, result);
+        }
+    }
+}