# Fun with Numbers #8

Some numbers are amazing. Let’s look the number $113$.

$113$ backwards is $311$, when squared $113^2 = 12769$. The interesting part is that $12769$ backwards is $96721$ which is $311$ squared.

$113$ is a prime number which means it cannot be factored. It is a Sophie Germain prime which means that $2(113)+1 = 227$ which is also a prime number. A Chen prime which means that $113+2$ is a multiple of two prime numbers: $113+2= 23*5$. It is a permutable prime since $113$ backwards, $311$, is also a prime number.

$113$ can be found in geometry.  $355/113$ approximates PI to its sixth digit. Also with the numbers $15$ and $112$, these three form a Pythagorean triple, basically any group of three numbers that satisfies the Pythagorean theorem: $15^2 + 112^2 = 113^2$.

$113$ is without a doubt an amazing number.