Project Euler 37

3797 is a prime. What is interesting about this prime, is that if we truncate it one digit at a time from left, ie:
3797, 797, 97, 7 every step is also prime. And if we do the same from the right, we see the same property:
3797, 379, 37, 3.

There are 11 primes with this property. What is the sum of them?

2, 3, 5 and 7 are not considered to be truncatable primes.

And that gives us a hint. The first digit of a truncatble prime must be either 2, 3, 5 or 7. And the last digit must be 3, 5 or 7.

Lets begin by loading the package numbers:

library(numbers)

That gives us couple of useful functions. isPrime(x) returns true if x is prime. And Primes(x,y) returns all primes between x and y.

I am going to need a couple of functions. One that repeatedly truncates a number from the left, and returns true if all the steps in the sequence are prime. And another that does the same, just from the rigth.

truncleft <- function(x){
  res <- TRUE
  while(x>9){
    x <- x %/% 10
    res <- isPrime(x)*res
  }
  return(as.logical(res))
}

truncright <- function(x){
  res <- TRUE
  while(x>9){
    x <- x - (x %/% 10**floor(log10(x)))*(10**floor(log10(x)))
    res <- isPrime(x)*res
  }
  return(as.logical(res))
}

Now I can determine if a given number is truncatable prime from both left and right. Next, finding all 11 primes with that property.

Lets take a chance, and see if not number 11 is found before we reach 1000000

library(purrr)
answer <- Primes(9,1000000) %>%
  keep(truncleft) %>%
  keep(truncright) %>%
  sum()

Yep. The difficult part is finding number 11. The first four primes with this property have two digits – you can find them manually. The next four are a bit more difficult. Number 10 is the example Project Euler provides.

Lessons learned

Well – purrr is pretty useful. But I already knew that.