An emirp (prime spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed.[1] This definition excludes the related palindromic primes.
Source: https://en.wikipedia.org/wiki/Emirp

By that definition you should expect to find some functions that express the main idea of a backward prime and by that I mean a way to know if a number is a palindrome, to reverse a number and if it's prime and therefore backward_prime should somehow call them.
It's a good practice to express in your code a language that show the main ideas of the people that bring you the problem.
I advice you to read a little about TDD.

Good solution but can get hard to read.

is_not_palindrome
Is not a good practice to use negatives in your signatures. is_palindrome could be better.

Execution Timed Out (12000 ms) in Rust and it surely did not run for 12000ms.

explain further since you aren't making any sense.