A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

R Language Code

The Prime Function

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!

prime2 = prime(200000)
prime2[10001]

Result

Enjoy ^^