Find the nearest prime number given a random number?

The only way is by searching, but yuo can limit your search range by applying Bertrand's postulate :
for every n > 1 there is always at least one prime p such that n < p < 2n

Then you can search the range of [n/2, 2n] and find the prime out.

Another way to limit search is by approximation . From PNT, we have
nth prime number ~ nln(n)
then you can find k such that (k-1)ln(k) < n

2007-04-06 12:46:36 補充：
The last sentence is:then you can find k such that n within [ (k-1)ln(k), kln(k) ] and search the prime out

no you can not. it's because it's not an easy/fast way to find out the nth prime number.

if you know computer programming. you can use computer to find it out.