The RSA values that state require factoring of two primes, does this mean that "the RSA number" can only have two prime factors but may have other factors that are not prime as well?
Is the fastest known algorithm to determine if a int1024 value is Prime slow or quick?
Factoring primes is quite easy. The modulus used in RSA is the product of precisely two large primes, so has four factors: 1, each prime, and itself. Checking a given number for being prime is rather quick, particularly if you use just the probabilistic tests. You can easily test an RSA modulus, too. The test will tell you it is composite. It just won't tell you the factors-the factoring is what is hard.
There are versions of RSA with more than two primes, see e.g. https://crypto.stackexchange.com/questions/5416/are-there-any-standards-of-multi-prime-rsa-key-generation
Determining if a 1024 bit number is prime is fast.
Besides being a serious security risk (assuming quantum computers can solve it fast) what is the practical use of determining what factors a numnber has? Is there anything useful that can be achieved?
– Derek James Nov 29 '13 at 19:41