Is it practical to find actual very large prime numbers (such as those up to 100 digits)? I just asked How to find extremely large BigInt prime numbers exactly in JavaScript? and was explained that all I ever can hope for is a "probable" prime, not an exact/actual prime if they are that large (up to 100 digits). To me, the reason for that would be because it takes too long to compute the possible factors of the potential prime (which is what my JS code was saying to me). Is this true? Is there no way to find an exact/actual (i.e. non- "probable") prime number that is 70 to 100 digits long? If it is possible, how is it done (at least at a high, non-software/non-code level)? If it is possible, can we go to larger integers like up to 65536 digits? If not, why can't it be done/calculated with certainty, is there no possible way?

Not quite $70$ digits ("only" $61$) but the integer
$$p=2~000~000~000~000~000~000~030~000~000~000~000~000~000~500~000~000~000~000~000~007$$
Is prime. And, as per the request in your other question, it is also very clear that
$$\operatorname{mod}(p,4)=3$$
