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Why Do We Say “It is probably prime”? Surely it is, or it isn’t!

Prime numbers are at the core of your online security. Without them, an intruder could listen to your secret communications, or pretend to be a server that you connect to. They are at the core of our key exchange (with ECDH) and in digital signatures (such as ECDSA). And so we might generate a random prime number, such as for our key exchange method. But the result can tell if we…