Add Goldbach's Conjecture algorithm (#6127)

Author: BILLSARAN

src/main/java/com/thealgorithms/maths/GoldbachConjecture.java

@@ -0,0 +1,30 @@
+package com.thealgorithms.maths;
+
+import static com.thealgorithms.maths.PrimeCheck.isPrime;
+
+/**
+ * This is a representation of the unsolved problem of Goldbach's Projection, according to which every
+ * even natural number greater than 2 can be written as the sum of 2 prime numbers
+ * More info: https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
+ * @author Vasilis Sarantidis (https://github.com/BILLSARAN)
+ */
+
+public final class GoldbachConjecture {
+    private GoldbachConjecture() {
+    }
+    public record Result(int number1, int number2) {
+    }
+
+    public static Result getPrimeSum(int number) {
+        if (number <= 2 || number % 2 != 0) {
+            throw new IllegalArgumentException("Number must be even and greater than 2.");
+        }
+
+        for (int i = 0; i <= number / 2; i++) {
+            if (isPrime(i) && isPrime(number - i)) {
+                return new Result(i, number - i);
+            }
+        }
+        throw new IllegalStateException("No valid prime sum found."); // Should not occur
+    }
+}

src/test/java/com/thealgorithms/maths/GoldbachConjectureTest.java

@@ -0,0 +1,29 @@
+package com.thealgorithms.maths;
+
+import static com.thealgorithms.maths.GoldbachConjecture.getPrimeSum;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+public class GoldbachConjectureTest {
+    @Test
+    void testValidEvenNumbers() {
+        assertEquals(new GoldbachConjecture.Result(3, 7), getPrimeSum(10)); // 10 = 3 + 7
+        assertEquals(new GoldbachConjecture.Result(5, 7), getPrimeSum(12)); // 12 = 5 + 7
+        assertEquals(new GoldbachConjecture.Result(3, 11), getPrimeSum(14)); // 14 = 3 + 11
+        assertEquals(new GoldbachConjecture.Result(5, 13), getPrimeSum(18)); // 18 = 5 + 13
+    }
+    @Test
+    void testInvalidOddNumbers() {
+        assertThrows(IllegalArgumentException.class, () -> getPrimeSum(7));
+        assertThrows(IllegalArgumentException.class, () -> getPrimeSum(15));
+    }
+    @Test
+    void testLesserThanTwo() {
+        assertThrows(IllegalArgumentException.class, () -> getPrimeSum(1));
+        assertThrows(IllegalArgumentException.class, () -> getPrimeSum(2));
+        assertThrows(IllegalArgumentException.class, () -> getPrimeSum(-5));
+        assertThrows(IllegalArgumentException.class, () -> getPrimeSum(-26));
+    }
+}