Question

I am a prime number less than 23 and greater than 5. If you multiply meby myself and then subtract 2 from the result, you will get a primenumber between 40 and 50. What number am I?

Answer 1

Let p be the prime number.

Then

$5

Also,

[tex]\begin{gathered} p^2-2\text{ is a prime such that} \\ 40

The first prime number in the interval (5,23) is 7.

Also,

[tex]\begin{gathered} 7^2=49 \\ \text{and 7}^2-2=49-2=47 \\ \text{Thus} \\ 40<7^2-2<50 \\ \end{gathered}$

Therefore the number is 7