Consider the following expression.

$1631310734315390891207403279946696528907777175176794464896666909137684785971138$ $2649033004075188224$ This is a $98$ decimal digit number. This can be represented as $424^{37}$ which has just 5 digits.

or consider this number:

$1690735149233357049107817709433863585132662626950821430178417760728661153414605$ $2484795771275896190661372675631981127803129649521785142469703500691286617000071$ $8058938908895318046488014239482587502405094704563355293891175819575253800433524$ $5277559791129790156439596789351751130805731546751249418933225268643093524912185$ $5914917866181252548011072665616976069886958296149475308550144566145651839224313$ $3318400757678300223742779393224526956540729201436933362390428757552466287676706$ $382965998179063631507434507871764226500558776264$

This $200$ decimal digit number can be simply expressed as $\log_e 56$ when we discard first $6$ numbers and then consider first $200$ digits.

Now the question is, is it possible to represent any and every huge random number using very few characters as possible, theoretically.

...Also, is there any standard way to reduce it mathematically?