A Prime... B Prime!

Number Theory Level 1

The sum of two prime numbers $a$ and $b$ is equal to 42.

$\large{a+b=42}$

Which one of these numbers cannot be $\mathbf{a}$ or $\mathbf{b}$ ?

13 37 29 17 23 5

2 solutions

Hans Gabriel Daduya
Apr 25, 2018

A prime number is a number that is only divisible by $1$ and itself.

e.g. $(2,3,5,7,...)$

By substituting $17$ as $A$ or $B$ , we get

$17+25 = 42$

$25=5\times5$

$\implies 25$ is not prime.

$\therefore 17$ is the answer since its pair number $25$ is not prime.

. .
Feb 13, 2021

If $a$ or $b$ is $17$ , then $b$ or $a$ must be $25$ , but $25$ is not a prime number, so the answer is $\boxed{17}$ .