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Re:How hard can generating 1024-bit primes be? by glitchcomet on Friday May 03, 2024 @05:24PM (#40252549)
As the other comments have mentioned, by setting the first bit to one it looses a bit of entropy but ensures that the prime is large enough. Another thing to add is that in RSA two primes are multiplied together. If one of them is 1024 bits the other can be ~200 bits (if i remember correctly) and still reach the required number of entropy bits for the key. So, having both primes be 1024-bit adds a bit of wiggle room too.

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