The 64 bit machine's biggest number can be 2^63 (9,223,372,036,854,775,807). So what kind of a monstrous machine can generate 100-400 digits prime number? I probably don't understand something, so that's why I am asking.
You can simply combine mathematical operations on 64 bit numbers to create mathematical operations on bigger numbers. Just like a computer can combine bit operations to create operations on bytes and - yes - 64 bit values. In the end it is all binary arithmetic, calculations in current computers are performed on values of just 0 and 1.