Trial Division Primality in Java

// Trial Division Primality in Java
//
// PURPOSE
// A composite integer has a factor no larger than its square root. Trial division checks
// only candidate divisors up to that bound.
//
// METHOD
// Reject values below two, handle two, and reject other even values. Test odd divisors until
// d exceeds n/d, which avoids computing d squared.
//
// COMPLEXITY
// O(sqrt(n)) time and O(1) auxiliary space.
//
// CONTRACT
// Returns 1 for prime, 0 otherwise. This is suitable for small integers, not large
// cryptographic candidates.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 1.
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int is_prime(int n) {
        if ((n < 2)) {
            return 0;
        }
        if ((n == 2)) {
            return 1;
        }
        if (((n % 2) == 0)) {
            return 0;
        }
        int d = 3;
        while ((d <= (n / d))) {
            if (((n % d) == 0)) {
                return 0;
            }
            d = Math.addExact(d, 2);
        }
        return 1;
    }

    public static void main(String[] args) {
        int n = 97;
        int result = is_prime(n);
        System.out.println(result);
    }
}