Prime numbers 5 - Reasoning

Exploring the concept of prime numbers through reasoning, we delve into an interesting characteristic of certain numbers: their ability to be expressed as the sum of two prime numbers. For example, both the numbers 4 and 5 can be represented this way, with 4 being the sum of two 2s, and 5 as the sum of 2 and 3. This property prompts an intriguing question: how many numbers less than 20 are there that cannot be written as the sum of two prime numbers?

Upon investigation, it is found that there are 5 numbers under 20 that do not have the capability to be expressed as a sum of two prime numbers. These numbers are 1, 2, 3, 11, and 17. While numbers like 4 and 5 demonstrate the possibility of such a sum, these five numbers stand out as exceptions to the rule. Understanding these exceptions helps deepen our comprehension of the unique properties of prime numbers and their role within the realm of multiplication and division.