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Instructions

Test suite

Solution

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

- take the next available unmarked number in your list (it is prime)
- mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes.

See this guide for instructions on how to setup your local R environment.

In each problem folder, there is a file named `<exercise_name>.R`

containing a function that returns a `NULL`

value. Place your implementation inside the body of the function.

Inside of RStudio, simply execute the `test_<exercise_name>.R`

script. This can be conveniently done with testthat's `auto_test`

function. Because exercism code and tests are in the same folder, use this same path for both `code_path`

and `test_path`

parameters. On the command-line, you can also run `Rscript test_<exercise_name>.R`

.

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
source("./sieve.R")
library(testthat)
context("sieve")
test_that("no primes under two", {
expect_equal(sieve(1), c())
})
test_that("find first prime", {
expect_equal(sieve(2), 2)
})
test_that("find primes up to 10", {
expect_equal(sieve(10), c(2, 3, 5, 7))
})
test_that("limit is prime", {
expect_equal(sieve(13), c(2, 3, 5, 7, 11, 13))
})
test_that("find primes up to 1000", {
expect_equal(sieve(1000),
c(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619,
631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787,
797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953,
967, 971, 977, 983, 991, 997))
})
message("All tests passed for exercise: sieve")
```

```
sieve <- function(limit) {
# catch edge case
if (limit == 1)
return()
# list candidates
candidates <- 2:limit
# walk through list, calculate multiples and eliminate
lapply(candidates, setdiff(candidates, candidates * c))
}
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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## Community comments

Argh! Error non-numeric argument to binary operator. I uploaded prematurely m-)