Prime-pattern triple (choose the matching set): Given set: (23, 29, 37)

Difficulty: Medium

(13, 15, 23)
(17, 21, 29)
(31, 37, 49)
(41, 47, 53)
(19, 25, 31)

Correct Answer: (41, 47, 53)

Explanation:

Introduction / Context:
We are given a sequence of three primes and asked to select another triplet showing a similar structure.

Given Data / Assumptions:

Given: 23, 29, 37 (all primes).
Gaps: 29 − 23 = 6; 37 − 29 = 8 (small even increments typical of prime hops in moderate ranges).

Concept / Approach:
Look for another all-prime triplet with modest even gaps, preserving the “all are primes, reasonably spaced” character (exact differences need not be identical but should reflect a similar prime-run feel).

Step-by-Step Solution:

1) Eliminate any set containing a composite (e.g., 15, 21, 49). 2) (41, 47, 53) are all primes; gaps are +6 then +6 — a tight, clean prime progression. 3) Select (41, 47, 53).

Verification / Alternative check:
Confirm primality: 41, 47, 53 are prime; others listed contain composites.

Why Other Options Are Wrong:
They include non-primes (15, 21, 49, 25), breaking the “all-prime triplet” property.

Common Pitfalls:
Focusing only on constant differences without verifying primality of each member.

Prime-pattern triple (choose the matching set): Given set: (23, 29, 37)

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