Generating primes quickly of a given bit size has important applications in multiple fields. For example, RSA, the first public-key cryptosystem, generates 4000-bit primes to secure your data. There are multiple algorithms that rely on generating a random prime within a given bit length and then testing for primality with a strong pseudo-primality test. Currently, this algorithm is characterized by being inconsistent in the time it takes to compute. Our goal was to create a computationally consistent algorithm that could be used to find large prime numbers. Our algorithm was found to be 91% faster than the standard method when generating primes up to 730 bits with our Primorial Approach.
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An Algorithm presented at 2018 Algorithmic Number Theory Symposium that reduces the computational time of generating 4000-bit primes for cryptosystems.
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