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RSA - bit-length p and q

I'm just trying to understand the main part of RSA, or rather, to choose primes and primes. Given a given bit length for the module, n, what range should I generate p and q in?

The module, n, is the product of p and q, where p and q are both primes. I read that p and q should be relatively close to each other, and somewhere around sqrt (n). If the target bit length is, for example, 32 bits (I realize very little), then does p and q have to be a random number with a maximum of 16 bits?

Thanks for any clarification.

Rob

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32- : p q , , 2^32 , p q. , , p q .

- , 1024- , , 512- p q : p q [2^511, 2^512]. " ", , - , , p q , p-1 q-1 , Pollard 'p-1. (GNFS, ECM). , , p q, .

: , .

, :

  • , 512- , 1023-, 1024- ; , , , , 1024- , p, q , , [1.5 * 2^511, 2^512], 1023- .

  • p q, : p q (, 10^10, ), pq . p q [2^511, 2^512], - .

  • , () [2^511, 2^512], , . , : , , , . , , (, , , , ).

  • , .

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