Maximus Prime

Number Theory Level pending

$a$ , $b$ , and $c$ are distinct non-negative integers.

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

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

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

If you think the answer is infinite, give your answer as 99999.

The answer is 99999.

1 solution

Geoff Pilling
Nov 18, 2016

At least two of the numbers need to be both odd or both even. If they are both odd, then they will add up to an even number greater than $2$ which will be composite. Therefore at least two must be even. But the only even prime is two, so they must add up to two, so two of the numbers must be $0$ and $2$ .

The third number, $n$ , must be prime, as well as $n+2$ . In other words their prime gap must be $2$ . Since there are infinitely many such prime gaps. The sum can go infinitely high. So, the answer is $\boxed{99999}$

Maximus Prime

The answer is 99999.

1 solution

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