How do I generate a 160 bit prime number in java?

Question

I want to generate a 160-bit prime number in java. I know that I'll have to loop through all the 160-bit numbers and for any number n, I'll have to check if they are divisible by any primes less than sqroot(n) or by any primality test like Miller-Rabin test. My questions are:

1. Is there any specific library which does this?

2. Is there any other (better) way to do this?

Answer 1

BigInteger.probablePrime(160, new Random()) generates a BigInteger that is almost certainly prime -- the probability that it is not a prime is less than the probability that you will get struck by lightning. In general, BigInteger already has heavily tested and optimized primality testing operations built in.

For what it's worth, the reason this won't take forever is that by the prime number theorem, a randomly chosen n-bit number has probability proportional to 1/n of being prime, so on average you only need to try O(n) different random n-bit numbers before you'll find one that's prime.