Is the number theory a complete abstraction or are there real applications of it in the wold?

To answer your question in short: yes and yes.
To answer your question in long . . .
Philosophers have been arguing for literally millennia about whether or not mathematics (and by extension number theory) is merely an abstraction or whether numbers actually exist in a meaningful sense. So, right off the bat, there's that, and it makes it tricky to answer. That being said (and philosophy discussions aside), yes, most people would consider number theory a complete and total abstraction. It's arguably the most important subfield of pure mathematics, so by definition, it only deals in the abstract. It's free of any references to the "real" world, unlike statistics, or computer science, or game theory. Those fields are collectively referred to as applied mathematics. Number theory only deals with the study of integers: nothing more, nothing less.
However, that doesn't mean number theory or pure mathematics in general don't have very real applications. Number theory is extremely important in cryptography, which essentially a cornerstone of modern communication technologies. Further, it has wide-ranging interdisciplinary applications, from differential topology to mathematical physics. Also, while not an example of number theory, Boolean algebra, another branch of pure mathematics, is the basis for modern digital circuits. It was developed a full ninety-nine years before the first digital computer was built in 1946!
To make my point short here: just because a field or discourse is abstract doesn't mean it has no applications, and just because something seems useless doesn't mean it always will be. A nice rule of thumb for pure mathematics is "if there isn't a use for it now, there will be."
https://plato.stanford.edu/entries/platonism-mathematics/

https://uwaterloo.ca/pure-mathematics/about-pure-math/what-is-pure-math