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In this paper we present the experimental results that more clearly than anytheory suggest an answer to the question: when in detection of large (probably)prime numbers to apply, a very resource demanding, Miller-Rabin algorithm. Or,to put it another way, when the dividing by first several tens of prime numbersshould be replaced by primality testing? As an innovation, the procedure abovewill be supplemented by considering the use of the well-known Goldbach'sconjecture in the solving of this and some other important questions about theRSA cryptosystem, always guided by the motto "do not harm" - neither thesecurity nor the time spent.

Minimizing the Time of Detection of Large (Probably) Prime Numbers