$n\ln n + n\ln\ln nān < p_n < n\ln n+n\ln\ln n \mbox{ for } n\geq 6$
This is the range where the $n$-th prime must lie. However sieving within this range generates a large number of primes. So if one is asked to, for example, find the 48574th prime, how does one go about it?
I was able to find the relevant prime by using an implementation of the sieve algorithm, checking only till the square root of the given number. However the method described above takes merely an instant to give a list of possible candidates and the correct answer also lies in them, but I am unable to pinpoint the primes as 'nth' or 'mth'.