algo(2025-10-28): 10 001st Prime

notes: Primes go wild!
Ref.: https://projecteuler.net/problem=7
language: Java

Author: josimar-silva

algorithms/project-euler/java/src/main/java/com/josimarsilva/projecteuler/java/TenThousandFirstPrime.java

@@ -0,0 +1,46 @@
+package com.josimarsilva.projecteuler.java;
+
+/**
+ * By listing the first six prime numbers: 2,3,5,7, 11, and 13, we can see that the 6th prime is 13.
+ *
+ * What is the 10001st prime number?
+ *
+ * Ref.: <a href="https://projecteuler.net/problem=7">Reference</a>
+ *
+ */
+record TenThousandFirstPrime(long position) {
+
+    static TenThousandFirstPrime at(long position) {
+        return new TenThousandFirstPrime(position);
+    }
+
+    private boolean isPrime(long number) {
+        if (number == 0 || number == 1) return false;
+        if (number == 2) return true;
+        if (number % 2 == 0) return false;
+
+        final var squareOfN = (long) Math.sqrt((double) number);
+        for (long x = 3L; x <= squareOfN; x += 2) {
+            if (number % x == 0) return false;
+        }
+        return true;
+    }
+
+    //Time: O(N ^ 3/2 (log N) ^ 3/2) / Space: O(1)
+    long calculate() {
+        var primeCount = 0L;
+        var lastKnownPrime = 0L;
+        var number = 2L;
+
+        while (primeCount != position) {
+            if (isPrime(number)) {
+                lastKnownPrime = number;
+                primeCount++;
+            }
+            number++;
+        }
+
+        return lastKnownPrime;
+    }
+
+}

algorithms/project-euler/java/src/test/java/com/josimarsilva/projecteuler/java/TenThousandFirstPrimeTest.java

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+package com.josimarsilva.projecteuler.java;
+
+import org.junit.jupiter.api.TestInstance;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+import java.util.stream.Stream;
+
+import static org.assertj.core.api.Assertions.assertThat;
+
+@TestInstance(TestInstance.Lifecycle.PER_CLASS)
+public class TenThousandFirstPrimeTest {
+
+    @ParameterizedTest
+    @MethodSource("samples")
+    public void shouldReturnThePrimeNumberAtGivenPosition(long position, long expectedPrime) {
+        assertThat(TenThousandFirstPrime.at(position).calculate()).isEqualTo(expectedPrime);
+    }
+
+    private Stream<Arguments> samples() {
+        return Stream.of(
+                Arguments.of(6L, 13L),
+                Arguments.of(10L, 29L),
+                Arguments.of(10_001L, 104743L)
+        );
+    }
+
+}