Function to calculate whether a vector is prime.

isPrime.R

# This function will calculate whether a vector is prime. It is not completely efficient, but it's not too bad
isPrime <- function(n){
  # Check inputs are integers, and coerce
  if(any(n %% 1 >0)) stop("Input must be all integers")
  n2 <- as.integer(n)
  
  # Create default output
  out <- rep(NA,length(n2))
  
  # Check for already discovered primes & return early if possible
  out[n2 %in% p_list] <- TRUE
  if(all(!is.na(out))) return(out)
  
  # Check for already discovered non-Primes & return early if possible
  out[is.na(out) & n2 <= MaxChecked] <- FALSE
  if(all(!is.na(out))) return(out)
  
  # Check for divisibility by current prime list
  n3 <- n2[is.na(out)]
  
  # Create a divisibility matrix, and sum for any non-zero modulos
  is_divisible <- rowSums(
    !(
      matrix(rep(n3,length(p_list)),nrow=length(n3)) %%
        matrix(rep(p_list,each=length(n3)),nrow=length(n3))
      )
    ) > 0
  
  # Any that are divisble by a previously found Prime, are non-Prime
  out[is.na(out)][is_divisible] <- FALSE
  if(all(!is.na(out))) return(out)
  
  
  # Create a sequence from the previous maximum to the new current maximum
  NewMax <- max(n2)+1
  new_checks <- seq(MaxChecked+1,NewMax)
  
  # Check values in this new sequence, adding new primes when found
  for(c_new in new_checks){
    if(all(c_new %% p_list)){
      # Current checked value is prime, add to list and output
      out[n2 == c_new] <- TRUE
      out[is.na(out) & (n2 %% c_new == 0)] <- FALSE
      p_list <- c(p_list,c_new)
      
      # If all results have now been found, break early
      if(all(!is.na(out))) break
    }
  }
  
  # Re-cache the variables
  e <- parent.env(environment())
  e$MaxChecked <- c_new
  e$p_list <- p_list
  
  # Any that aren't marked as TRUE or FALSE must be non-Prime
  out[is.na(out)] <- FALSE
  
  return(out)
}

# Create a cache in the function's environment
environment(isPrime) <- list2env(list(
  # The L here forces the values to be integers (more efficient than numeric)
  p_list = c(2L,3L,5L),
  MaxChecked = 5L
))

# First run is slow!
start_timer <- Sys.time()
isPrime(300007)
print(Sys.time() - start_timer)

# Second run is fast because of caching
start_timer <- Sys.time()
isPrime(300007)
print(Sys.time() - start_timer)