# project euler-Problem 41

November 7, 2011
By

(This article was first published on YGC » R, and kindly contributed to R-bloggers)

```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.

?View Code RSPLUS
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ``` ```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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