Prime sums

Number Theory Level 2

$a$ , $b$ , and $c$ are distinct positive integers.

$a+b$ is prime
$b+c$ is prime
$a+c$ is prime

What is the lowest possible value for $a+b+c$ ?

If you think there are no answers, give your answer as 0.

The answer is 0.

1 solution

Geoff Pilling
Nov 17, 2016

At least two of $a$ , $b$ , and $c$ must be even or two must be odd. Either way, those two add up to an even number greater than $2$ , which will be a composite number.

So, there are $\boxed{0}$ solutions.

Prime sums

The answer is 0.

1 solution

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