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In the context of RSA, when we say an "N bit prime", we mean that it's a prime in the range $[2^{n-1}, 2^n)$. In addition, when we say an RSA key is an "N bit key", we mean that it's in the range $[2^{n-1}, 2^n)$. What this means that if you pick two random $N/2$ bit primes, and multiply them together, you'll get an $N-1$ bit modulus about half the time. ...

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