Which of the following statements is not correct?

Question

Accepted Answer

Option 1 is the correct answer because it states that "All prime numbers are odd numbers," which is not true. The definition of a prime number is a number greater than 1 that has no divisors other than 1 and itself. While most prime numbers are indeed odd, there is one notable exception: the number 2. The number 2 is a prime number because it can only be divided evenly by 1 and 2. However, it is not odd; it is even. Therefore, the statement that all prime numbers are odd is incorrect.

Now, let's examine why the other options are correct and thus not the answer to the question:

2. "Prime numbers are infinitely many." This statement is correct. There are infinitely many prime numbers, a fact that was proven by the ancient Greek mathematician Euclid. He demonstrated that no matter how many prime numbers you list, you can always find another one not on the list, proving their infinitude.

3. "Prime numbers have only two factors." This statement is also correct. By definition, a prime number has exactly two distinct positive divisors: 1 and itself. This is the fundamental property that distinguishes prime numbers from composite numbers, which have more than two factors.

4. "There are only four single digit prime numbers." This statement is correct as well. The single-digit prime numbers are 2, 3, 5, and 7. These are the only prime numbers that are less than 10, confirming that there are indeed only four single-digit prime numbers.

In summary, Option 1 is the correct answer because it incorrectly claims that all prime numbers are odd, overlooking the fact that 2 is an even prime number. The other options are correct statements about prime numbers.