Is the random picking of big n-bits random numbers for primality test a time sensitive operation?
If so, would an heuristic for limiting the search space (about 5-10x) without missing out on any prime be an interesting addition?
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RSA keys are most often used for long-term 30 days or more) identification & authentication. The few hundred milliseconds it takes to generate an RSA key are inconsequential.
For short-term use Elliptic-Curve schemes like ECDH and EdDSA are common. Their keys take only a few microseconds to generate, thousands of times faster than RSA. They can also be used for long-term use. So speeding up RSA key generation isn't a particularly useful task, particularly if only small (10-1000x) speedups are achieved.