Prime-pattern triple (choose the matching set): Given set: (23, 29, 37)
Correct Answer: (41, 47, 53)
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.
Final Answer:(41, 47, 53)