Yan Cui

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#### Problem

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

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

#### Solution

let hasDivisor(n:bigint) = let upperBound = bigint(sqrt(double(n))) [2I..upperBound] |> Seq.exists (fun x -> n % x = 0I) let isPrime(n:bigint) = if n = 1I then false else not(hasDivisor(n)) let primeSequence = Seq.unfold (fun state -> Some(state, (state+1I))) 1I |> Seq.filter isPrime let rec recTruncatable (predicate:bigint -> bool) (next:bigint -> bigint) (n:bigint) = if predicate(n) then let len = n.ToString().Length if len = 1 then true else recTruncatable predicate next (next n) else false let leftTruncatable = recTruncatable isPrime (fun x -> bigint.Parse(x.ToString().Substring(1))) let rightTruncatable = recTruncatable isPrime (fun x -> bigint.Parse(x.ToString().Substring(0, x.ToString().Length-1))) let sum = primeSequence |> Seq.filter (fun n -> n > 7I) |> Seq.filter (fun n -> leftTruncatable n && rightTruncatable n) |> Seq.take 11 |> Seq.sum

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