An algorithm for getting $n$ primes Is there any way to get $n$ primes efficiently? That is, is there any polynomial algorithm for doing this? ($n$ is the cardinality.)

Re-phrasing the question:

1) Suppose that at the input level, we insert $n$. This is the number of primes we want to obtain. (any set) (So, for example, getting five number of prime. The example output would be 2,3,5,7,11)

2) Is there any algorithm that does this efficiently? What would be its complexity (based on $n$)?
Given $n$, let $M = 2n\log n$ (here $2$ is any constant larger than $1$). Put all numbers from $2$ to $M$ in a linked list. Now implement Eratosthenes sieve, by repeatedly running the following algorithm, until you get $n$ primes. Look for the first unmarked number $p$ (they all start unmarked; start looking at the previous prime), take it as a prime, and mark every integer in hops of length $p$. The running time is roughly $M + \sum_p M/p = \Theta(M\log\log M) = \Theta(n \log n \log\log n)$, where $p$ goes over the first $n$ primes. Since the $k$th prime $p_k$ is about $k\log k$, heuristically indeed
$$ \sum_{k=1}^n \frac{1}{p_k} \approx \sum_{k=2}^n \frac{1}{k\log k} \approx \int_2^n \frac{dk}{k\log k} \approx \log\log n.$$
This approximation can be proved rigorously, this is one of the results known as Mertens' theorem.

See Emil's comment below or the Wikipedia article for improvements on this algorithm.

Edit: Before Emil's comment, I suggested implementing the algorithm using a linked list, but that's a bad suggestion since you can't "hop" in a linked list, causing the runtime to be $\Omega(n^2)$.