Which of the following statements is not correct ?

The correct option is: All prime numbers are odd numbers.

Let us analyze each statement step-by-step to find the incorrect one:

1. Statement 1: "All prime numbers are odd numbers."
A prime number is a natural number greater than 1 that has exactly two positive factors: 1 and itself.
The smallest prime number is 2, which is an even number.
Since 2 is a prime number and it is even, the statement that "all prime numbers are odd numbers" is incorrect.

2. Statement 2: "There are infinitely many prime numbers."
This is a well-known theorem in mathematics (proved by Euclid). Prime numbers continue infinitely without bound. Thus, this statement is correct.

3. Statement 3: "A prime number has only two factors."
By definition, a prime number has exactly two factors: 1 and the number itself. Thus, this statement is correct.

4. Statement 4: "There are only four single digit prime numbers."
The single-digit prime numbers are 2, 3, 5, and 7. There are indeed exactly four single-digit prime numbers. Thus, this statement is correct.

Therefore, the statement that is not correct is "All prime numbers are odd numbers."