Spot the distinct pair: Choose the pair in which both numbers are prime, while in the other pairs at least one number is composite.

Introduction / Context:
Prime detection is a common theme in classification. Here you must identify the pair in which both numbers are prime. The distractors include at least one composite number per pair, making them unlike the target pair.

Given Data / Assumptions:

• Pairs: 547–563, 71–55, 517–523, 248–231.
• We treat 1 as neither prime nor composite (not present here).
• Primality checks rely on standard divisibility reasoning.

Concept / Approach:
Test each number for primality. A composite detection in any pair disqualifies it. The surviving pair must have two primes.

Step-by-Step Solution:

Verification / Alternative check:
Quick filters: even numbers > 2 are composite; numbers ending with 5 and greater than 5 are composite; sums of digits divisible by 3 indicate divisibility by 3. These filters immediately flag 55, 231, and 248 as composite. 517’s factor 11 emerges from divisibility by 11 test patterns.

Why Other Options Are Wrong:
Each contains at least one composite number, hence not both-prime pairs.

Common Pitfalls:
Assuming that closeness (like 517–523) implies similar primality; or overlooking basic composite cues (even endings, multiple-of-5 endings, digit-sum rules). Always test both numbers.

Final Answer:
547 - 563 is the only pair where both numbers are prime.