Minimizing the Time of Detection of Large (Probably) Prime Numbers
This work addresses an incremental optimization in primality testing for cryptographic applications like RSA, aiming to improve computational efficiency.
The paper tackles the problem of optimizing the detection of large probable prime numbers by determining when to switch from trial division to the Miller-Rabin algorithm, and it incorporates Goldbach's conjecture to address related RSA cryptosystem questions without compromising security or time efficiency.
In this paper we present the experimental results that more clearly than any theory 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 numbers should be replaced by primality testing? As an innovation, the procedure above will be supplemented by considering the use of the well-known Goldbach's conjecture in the solving of this and some other important questions about the RSA cryptosystem, always guided by the motto "do not harm" - neither the security nor the time spent.