library(gtools)

is.prime <- function(num) {
  if (num == 2) {
    TRUE
  } else if (any(num %% 2:(num-1) == 0)) {
    FALSE
  } else {
    TRUE
  }
}

primesLessThan <- function(limit) {
  # Get prime numbers less than or equal to limit.
  d <- seq(2:(limit - 1))

  # Get only those divisors that are prime.
  d[sapply(d, is.prime) == TRUE]
}

findSums <- function(nums, target) {
  # Returns the combinations of nums that sum to the target.
  result <- NA

  for (len in 1:5) {
    # Get all permutations of the numbers (repeat numbers allowed).
    sets <- permutations(length(nums), len, nums, repeats.allowed=T)

    # Calculate the sum of each set.
    totals <- apply(sets, 1, sum)

    # Find which set sums to our target.
    result <- sets[which(apply(sets, 1, sum) == target),]
    if (length(result) > 0) {
      break
    }
  }

  # Sort and filter the list to distinct numbers.
  unique(t(apply(result, 1, sort)))
}

goldbach <- function(target) {
  findSums(primesLessThan(target), target)
}