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A 512 bit composite is not a lot of entropy - it's about 45 bits of entropy, which isn't much. sqrt(512) * 2 (since each prime is approx the size of the sqrt of the number, and there are two of them).

A few months to crack a 45 bit encryption doesn't sound quick to me. Even a 64 bit encryption would take many centuries at that rate.

Each prime is approximately sqrt of the product, not of size that is sqrt of size of product, the size of primes is approximately half of the size of their product. As they are primes their entropy is slightly lower than their length, but not too much (there are approximately x/ln(x) primes smaller than x, which would lead to entropy of 256bit prime being 248.5bits)

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