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What should I do to generate big prime numbers for RSA?
As you know, we need to big prime numbers to make private and public keys for RSA encryption algorithm.
If I want to do it by any sieve algorithms,it take lot of time.
What is the best way?
You’re better off using a library for crypto routines. There are several, and they are fraught with subtle problems hopefully most of which are fixed in the existing implementations, and yet to be fixed in a new implementation.
However, I’ve played around with generating primes using Python and GMP:
http://stromberg.dnsalias.org/svn/huge-prime/trunk/
In short, trial division is best for small numbers, Miller-Rabin is good as a quick filter/test for a little larger numbers but you sometimes still end up using trial division to get guaranteed primes.