# In how many ways can 24 be expressed as the sum of two prime numbers ?

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### 1 Answer

By definition, a prime number is a positive integer, excluding '1', that is divisible only by itself and '1'.

For purpose of explanation, allow me to paraphrase the question as:

**"Consider m and n being prime numbers. How many ways can the sum of m and n be equal to 24."**

The answer to this question can be derived systematically as follows by listing m (all prime numbers<24 or until it repeats in column for n), then the possibility of n being prime:

"m", "possible n", "is n a prime number?"

2, 22, no

3, 21, no

5, 19, yes

7, 17, yes

11, 13, yes

Any value of m beyond 11 would have been repeated as n previously.

Hence my answer to this question is:

**There are exactly 3 ways of expressing 24 as the sum of two prime numbers.**

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