To determine which list of numbers consists entirely of prime numbers, we need first to clearly understand what a prime number is. A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.
Let's analyze each list based on this definition:
- List (a): 1, 3, 5, 9
- 1: Not a prime number (only divisible by 1 itself).
- 3: Prime number (divisible only by 1 and 3).
- 5: Prime number (divisible only by 1 and 5).
- 9: Not a prime number (divisible by 1, 3, and 9).
Since this list contains 1 and 9, which are not prime numbers, list (a) is not entirely composed of prime numbers.
- List (b): 1, 3, 5, 7
- 1: Not a prime number (only divisible by 1 itself).
- 3: Prime number (divisible only by 1 and 3).
- 5: Prime number (divisible only by 1 and 5).
- 7: Prime number (divisible only by 1 and 7).
Since list (b) contains 1, which is not a prime number, this list is not entirely composed of prime numbers.
- List (c): 2, 4, 6, 8
- 2: Prime number (divisible only by 1 and 2).
- 4: Not a prime number (divisible by 1, 2, and 4).
- 6: Not a prime number (divisible by 1, 2, 3, and 6).
- 8: Not a prime number (divisible by 1, 2, 4, and 8).
Since list (c) contains 4, 6, and 8, which are not prime numbers, this list is not entirely composed of prime numbers.
- List (d): 1, 2, 3, 4
- 1: Not a prime number (only divisible by 1 itself).
- 2: Prime number (divisible only by 1 and 2).
- 3: Prime number (divisible only by 1 and 3).
- 4: Not a prime number (divisible by 1, 2, and 4).
Since list (d) contains 1 and 4, which are not prime numbers, this list is not entirely composed of prime numbers.
After reviewing all the lists, we can conclude that none of the provided lists contain only prime numbers. Therefore, the answer is:
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