jim <firstname.lastname@example.org> writes: > Is there any way to combine 2 primes to get a larger prime, either > guarantying the primality of the result or with a quick test for the > primality?
Kinda - there are ways to combine 2 primes to get a larger prime, on the assumption that you're permitted bounded iteration in the generation of the result.
If your known primes are p and q, then test k*p*q+1 for small even k (k < (pq)^2). Once you've found a probable prime, you can then use a N-1 test to quickly prove it to be prime.
So having 2 smaller primes (even 1 will do) gives you a quicker *proof* of the primality, but it won't have sped up the finding of the candidate. For this to be significant, you must understand and care about the difference between probable primes and proven primes.
Phil -- If "law-abiding citizens have nothing to fear" from privacy-invading technologies and policies, then law-abiding governments should have nothing to fear from whistleblowers.