Which is prime number ?

Options

A. 1001
B. 100001
C. 1027
D. 1009

Answer

To determine which number is a prime number from the given options, we need to understand what a prime number is. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has exactly two distinct positive divisors: 1 and itself.

Let's analyze the options step by step:

### Step 1: Identify the options
The options given are:
- Option A: 1001
- Option B: 10001
- Option C: 1027
- Option D: 1009

### Step 2: Check each option for primality

**Option A: 1001**
- Factors of 1001: 1, 7, 11, 13, 77, 91, 1001
- Since it has more than two factors, 1001 is **not a prime number**.

**Option B: 10001**
- Factors of 10001: 1, 73, 137, 10001
- Since it has more than two factors, 10001 is **not a prime number**.

**Option C: 1027**
- Factors of 1027: 1, 1027
- Since it has exactly two factors, 1027 is a **prime number**.

**Option D: 1009**
- Factors of 1009: 1, 1009
- Since it has exactly two factors, 1009 is also a **prime number**.

### Step 3: Conclusion
From our analysis:
- Option A (1001) is not prime.
- Option B (10001) is not prime.
- Option C (1027) is prime.
- Option D (1009) is also prime.

Thus, both Option C (1027) and Option D (1009) are prime numbers. However, if we are to select one, we can choose either based on the context of the question.

### Final Answer
The prime numbers from the options are **Option C: 1027** and **Option D: 1009**.

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