We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?

using gmp and permute package, this problem is very straightforward, and easy to solve.

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require(gmp)
require(permute)
maxP <- 0
 
vec2num <- function(vec) {
    m <- length(vec)
    n <-  sum(10^(m:1-1) * vec)
    return(n)
}
 
for (j in 9:4) {
    p <- allPerms(j, max=prod(1:j)*j)
    pn <- sapply(1:nrow(p), function(i) vec2num(p[i,]))
    idx <- isprime(pn) !=0
    if ( any(idx) ) {
        maxP <- max(pn[idx])
    }
    if (maxP != 0) {
        cat("The larget n-digit pandigital prime is ", maxP, "\n")
        break
    }
}

> system.time(source("problem41.R"))
The larget n-digit pandigital prime is  7652413 
   user  system elapsed 
  20.95    0.03   20.99 

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