Logic may help

Number Theory Level 1

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

No Yes

Dinesh Nath Goswami by Dinesh Nath Goswami , 20, India

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2 solutions

The mean of any two different numbers always lies between the numbers.

And since the primes are consecutive, so no other prime can lie between them.

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Pablo Ruiz
Jan 1, 2016

The mean of a set of numbers is the "central" value of the set of numbers.

A mean of two numbers is (by definition) between the two numbers.

By having CONSECUTIVE primes we know that there is no other prime between this two primes.

Thus, the mean of whatever two consecutive primes will never be prime.

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