> Eratosthenes = 2) { + sieve

> Eratosthenes <- function(n) {

+ # Print prime numbers up to n (based on the sieve of Eratosthenes)

+ if (n >= 2) {

+ sieve <- seq(2, n)

+ primes <- c()

+ while (length(sieve) > 0) {

+ p <- sieve[1]

+ primes <- c(primes, p)

+ sieve <- sieve[(sieve %% p) != 0]

+ }

+ return(primes)

+ } else {

+ stop("Input value of n should be at least 2.")

+ }

+ }

(b) Show that once p >= sqrt(n)all remaining entries in sieve are prime.

(c) Modify this function using break to take advantage of the above result.