Choose the odd number: In 143, 257, 195, and 15, three are composite, while one is prime. Identify the prime number.

Introduction / Context:
Prime vs composite classification: factor quickly to isolate the prime.

Given Data / Assumptions:

• 143 = 11 * 13.
• 195 = 3 * 5 * 13.
• 15 = 3 * 5.
• 257 = ?

Concept / Approach:
Test divisibility for 257 by small primes up to sqrt(257) ≈ 16 (i.e., 2, 3, 5, 7, 11, 13).

Step-by-Step Solution:

Verification / Alternative check:
Nearby products show no 257 = p * q with small primes; hence prime.

Why Other Options Are Wrong:
Each factors non-trivially (11*13, 3*5*13, 3*5).

Common Pitfalls:
Assuming a number near a square (16^2=256) must be composite; 257 is prime.

Final Answer:
257 is the odd number (prime).