Question

Is this a ‘real’ task, that can be written on any language ( C/C++, for example )

So, my task is ‘generate’ random number with length over 50 digits ( maximum = 200 )?

Then, i must check this number on primality test.

So, is this task ‘real’ and how many time/resources it will consume?

alternative way is to generate prime Mersenn numbers or other numbers from special class ( which class could be used? )

Answer 1

There are efficient probabilistic algorithms for primality testing like Miller-Rabin that are usually used for such purposes.

Picking a random number and testing for primality using a randomized algorithm is efficient since the density of primes guarantees you that for n-bit numbers you need to pick around n numbers to test.