# Answer to Puzzle #18: Mean of Consecutive Primes

18. Can the mean of any two consecutive prime numbers ever be prime?

This is one is fairly simple if you can do it, and difficult if you can't too, there may be a mathematical proof but it's not necessary...

Before reading the answer can I interest you in a clue?

By definition of mean the result must be between the two source numbers.

By definition of consecutive there can't be a prime number in between two consecutive prime numbers.

N.B. There also can't be any apples in between two consecutive apples.

They both got this answer right and both struggled to explain it succinctly.

If you're curious what

If you're curious what

By definition of mean the result must be between the two source numbers.

By definition of consecutive there can't be a prime number in between two consecutive prime numbers.

N.B. There also can't be any apples in between two consecutive apples.

They both got this answer right and both struggled to explain it succinctly.

If you're curious what

**Bard**made of this puzzle...If you're curious what

**ChatGPT**made of this puzzle...© Nigel Coldwell 2004 - – The

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