2007 iTest Problems/Problem 1

Problem

A twin prime pair is a set of two primes $(p, q)$ such that $q$ is $2$ greater than $p$. What is the arithmetic mean of the two primes in the smallest twin prime pair?

Solution

We consider the first few primes. $(2,2+2)\equiv (2,4)$. $4$ isn't a prime, so this isn't a set of twin primes.

$(3,3+2)\equiv (3,5)$. $5$ is a prime, so the answer is $\frac{3+5}{2}=4$.

See Also

2007 iTest (Problems)
Preceded by:
First Question
Followed by:
Problem 2
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