Trial Division Primality in Python

from bisect import bisect_left

# Trial Division Primality in Python
#
# 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
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 1.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def is_prime(n: int) -> int:
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    if n < 2:
        return 0
    if n == 2:
        return 1
    if n % 2 == 0:
        return 0
    d: int = 3
    while d <= n // d:
        if n % d == 0:
            return 0
        d += 2
    return 1

n = 97
result = is_prime(n)
print(result)