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prime = function(n) { n = as.integer(n) if(n > 1e8) stop(“n too large”) primes = rep(TRUE, n) primes[1] = FALSE last.prime = 2L fsqr = floor(sqrt(n)) while (last.prime <= fsqr) { primes[seq.int(2L*last.prime, n, last.prime)] = FALSE sel = which(primes[(last.prime+1):(fsqr+1)]) if(any(sel)){ last.prime = last.prime + min(sel) }else last.prime = fsqr+1 } which(primes) }

To list out the primes within 100, simply type the command:

prime(100)

Now, question is

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

We simply accessing the elements of vector by using [ and ]

We first concatenate more than 10001 primes into prime2 variable by command prime(2000000). Then accessing the 10001st element of the vector and we get the 10001st prime number!