A riddle question number 20

Probability Level 1

An integer $n$ is between two primes if both $n-1$ and $n+1$ are prime numbers.

What is the closest integer to 50 that is also between two primes?

Example: The closest number to 100 between two primes is 102.

38 48 42 None of above 40

1 solution

Tom Engelsman
Dec 25, 2020

Breaking each answer choice down:

$37 < 38 < 39 \Rightarrow 39$ is composite,

$47 < 48 < 49 \Rightarrow 49$ is composite,

$41 < 42 < 43 \Rightarrow 41, 43$ are both prime,

$39 < 40 < 41 \Rightarrow 39$ is composite.

Hence, $\boxed{42}$ satisfies the above conditions.