Math Problem Statement

The conjecture 'if n is a whole number, then 3n + 1 is a prime number' is disproved by which statement? Options: A) 3×2+1=7, B) 3×6+1=19, C) 3×4+1=13, D) 3×8+1=25

Solution

The question asks which statement disproves the conjecture that 3n+13n + 1 is a prime number when nn is a whole number. Let's analyze each option:

  1. Option A: 3×2+1=73 \times 2 + 1 = 7
    77 is a prime number. This does not disprove the conjecture.

  2. Option B: 3×6+1=193 \times 6 + 1 = 19
    1919 is a prime number. This does not disprove the conjecture.

  3. Option C: 3×4+1=133 \times 4 + 1 = 13
    1313 is a prime number. This does not disprove the conjecture.

  4. Option D: 3×8+1=253 \times 8 + 1 = 25
    2525 is not a prime number (it is divisible

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Math Problem Analysis

Mathematical Concepts

Prime Numbers
Algebra
Arithmetic Operations

Formulas

3n + 1

Theorems

Definition of Prime Numbers

Suitable Grade Level

Grades 6-8