2016 Update
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Tina Müller
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7965 changed files with 139854 additions and 31002 deletions
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A truncatable prime is a prime number that when you successively remove digits from one end of the prime, you are left with a new prime number; for example, the number 997 is called a ''left-truncatable prime'' as the numbers 997, 97, and 7 are all prime. The number 7393 is a ''right-truncatable prime'' as the numbers 7393, 739, 73, and 7 formed by removing digits from its right are also prime. No zeroes are allowed in truncatable primes.
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;Task:
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The task is to find the largest left-truncatable and right-truncatable primes less than one million (base 10 is implied).
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;C.f:
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* [[Find largest left truncatable prime in a given base]]
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* [[Sieve of Eratosthenes]]
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* [http://mathworld.wolfram.com/TruncatablePrime.html Truncatable Prime] from Mathworld.
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[[:Category:Prime_Numbers]]
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<br>
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[[:Category: Prime_Numbers]]
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<br><br>
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78
Task/Truncatable-primes/Elena/truncatable-primes.elena
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78
Task/Truncatable-primes/Elena/truncatable-primes.elena
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#import system.
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#import extensions.
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#symbol MAXN = 1000000.
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#class(extension)mathOp
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{
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#method is &prime
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[
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#var(type:int)n := self int.
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(n < 2) ? [ ^ false. ].
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(n < 4) ? [ ^ true. ].
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(n mod:2 == 0) ? [ ^ false. ].
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(n < 9) ? [ ^ true. ].
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(n mod:3 == 0) ? [ ^ false. ].
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#var(type:int)r := n sqrt.
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#var(type:int)f := 5.
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#loop (f <= r)?
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[
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((n mod:f == 0) || (n mod:(f + 2) == 0))
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? [ ^ false. ].
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f := f + 6.
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].
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^ true.
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]
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#method is &rightTruncatable
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[
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#var(type:int)n := self int.
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#loop (n != 0)?
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[
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(n is &prime)
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! [ ^ false. ].
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n := n / 10.
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].
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^ true.
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]
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#method is &leftTruncatable
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[
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#var(type:int)n := self int.
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#var(type:int)tens := 1.
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#loop (tens < n)
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? [ tens := tens * 10. ].
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#loop (n != 0)?
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[
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(n is &prime)
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! [ ^ false. ].
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tens := tens / 10.
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n := n - (n / tens * tens).
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].
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^ true.
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]
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}
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#symbol program =
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[
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#var n := MAXN.
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#var max_lt := 0.
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#var max_rt := 0.
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#loop ((max_lt == 0) || (max_rt == 0))?
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[
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(n literal indexOf:"0" == -1) ?
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[
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((max_lt == 0) and:[ n is &leftTruncatable ])
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? [ max_lt := n. ].
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((max_rt == 0) and:[ n is &rightTruncatable ])
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? [ max_rt := n. ].
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].
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n := n - 1.
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].
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console writeLine:"Largest truncable left is ":max_lt.
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console writeLine:"Largest truncable right is ":max_rt.
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].
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47
Task/Truncatable-primes/Elixir/truncatable-primes.elixir
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47
Task/Truncatable-primes/Elixir/truncatable-primes.elixir
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defmodule Prime do
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defp left_truncatable?(n, prime) do
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func = fn i when i<=9 -> 0
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i -> to_string(i) |> String.slice(1..-1) |> String.to_integer end
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truncatable?(n, prime, func)
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end
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defp right_truncatable?(n, prime) do
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truncatable?(n, prime, fn i -> div(i, 10) end)
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end
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defp truncatable?(n, prime, trunc_func) do
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if to_string(n) |> String.match?(~r/0/),
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do: false,
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else: trunc_loop(trunc_func.(n), prime, trunc_func)
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end
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defp trunc_loop(0, _prime, _trunc_func), do: true
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defp trunc_loop(n, prime, trunc_func) do
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if elem(prime,n), do: trunc_loop(trunc_func.(n), prime, trunc_func), else: false
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end
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def eratosthenes(limit) do # descending order
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Enum.to_list(2..limit) |> sieve(:math.sqrt(limit), [])
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end
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defp sieve([h|_]=list, max, sieved) when h>max, do: Enum.reverse(list, sieved)
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defp sieve([h | t], max, sieved) do
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list = for x <- t, rem(x,h)>0, do: x
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sieve(list, max, [h | sieved])
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end
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defp prime_table(_, [], list), do: [false, false | list]
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defp prime_table(n, [n|t], list), do: prime_table(n-1, t, [true|list])
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defp prime_table(n, prime, list), do: prime_table(n-1, prime, [false|list])
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def task(limit \\ 1000000) do
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prime = eratosthenes(limit)
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prime_tuple = prime_table(limit, prime, []) |> List.to_tuple
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left = Enum.find(prime, fn n -> left_truncatable?(n, prime_tuple) end)
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IO.puts "Largest left-truncatable prime : #{left}"
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right = Enum.find(prime, fn n -> right_truncatable?(n, prime_tuple) end)
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IO.puts "Largest right-truncatable prime: #{right}"
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end
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end
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Prime.task
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/*REXX pgm finds largest left- & right-truncatable primes ≤1m (or arg1).*/
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parse arg high .; if high=='' then high=1000000 /*assume 1 million.*/
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!.=0; Lp=0; Rp=0; w=length(high) /*placeholders for primes, Lp, Rp*/
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@.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17 /*some low primes. */
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!.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1 /*low prime flags. */
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#=7; s.#=@.#**2 /*number of primes so far, prime²*/
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/*───────────────────────────────────────generate more primes ≤ high. */
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do j=@.#+2 by 2 to high /*only find odd primes from here.*/
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if j//3 ==0 then iterate /*is J divisible by three? */
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if right(j,1)==5 then iterate /*is the right-most digit a "5" ?*/
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if j//7 ==0 then iterate /*is J divisible by seven? */
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if j//11 ==0 then iterate /*is J divisible by eleven? */
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if j//13 ==0 then iterate /*is J divisible by thirteen? */
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/*[↑] above five lines saves time*/
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do k=7 while s.k<=j /*divide by known odd primes. */
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if j//@.k==0 then iterate j /*Is J divisible by X? ¬ prime.*/
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/*REXX program finds largest left─ and right─truncatable primes ≤ 1m (or argument 1).*/
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parse arg high .; if high=='' then high=1000000 /*Not specified? Then use 1m*/
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!.=0; w=length(high) /*placeholders for primes; max width. */
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@.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17 /*define some low primes. */
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!.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1 /*set some low prime flags. */
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#=7; s.#=@.#**2 /*number of primes so far; prime². */
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/* [↓] generate more primes ≤ high.*/
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do j=@.#+2 by 2 to high /*only find odd primes from here on out*/
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if j// 3==0 then iterate /*is J divisible by three? */
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parse var j '' -1 _; if _==5 then iterate /* " " " " five? (right digit)*/
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if j// 7==0 then iterate /* " " " " seven? */
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if j//11==0 then iterate /* " " " " eleven? */
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if j//13==0 then iterate /* " " " " thirteen? */
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/* [↑] the above five lines saves time*/
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do k=7 while s.k<=j /* [↓] divide by the known odd primes.*/
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if j//@.k==0 then iterate j /*Is J divisible by X? Then not prime.*/
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end /*k*/
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#=#+1 /*bump number of primes found. */
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@.#=j; s.#=j*j /*assign to sparse array; prime².*/
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!.j=1 /*indicate that J is a prime.*/
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end /*j*/
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/*─────────────────────────────────────find largest left truncatable P. */
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do L=# by -1 for #; if pos(0,@.L)\==0 then iterate
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do k=1 for length(@.L)-1; _=right(@.L,k) /*L truncate #.*/
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if \!._ then iterate L /*Truncated # ¬prime? Skip it.*/
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end /*k*/
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leave /*leave the DO loop, we found one*/
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end /*L*/
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/*─────────────────────────────────────find largest right truncatable P.*/
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do R=# by -1 for #; if pos(0,@.R)\==0 then iterate
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do k=1 for length(@.R)-1; _=left(@.R,k) /*R truncate #.*/
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if \!._ then iterate R /*Truncated # ¬prime? Skip it.*/
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end /*k*/
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leave /*leave the DO loop, we found one*/
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end /*R*/
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/*───────────────────────────────────────show largest left/right trunc P*/
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say 'The last prime found is ' @.# " (there are" # 'primes ≤' high")."
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say copies('─',70) /*show a separator line. */
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say 'The largest left-truncatable prime ≤' high " is " right(@.L,w)
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say 'The largest right-truncatable prime ≤' high " is " right(@.R,w)
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/*stick a fork in it, we're done.*/
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#=#+1 /*bump the number of primes found. */
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@.#=j; s.#=j*j; !.j=1 /*assign next prime; prime²; prime #.*/
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end /*j*/
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/* [↓] find largest left truncatable P*/
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do L=# by -1 for #; digs=length(@.L) /*search from top end; get the length.*/
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do k=1 for digs; _=right(@.L, k) /*validate all left truncatable primes.*/
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if \!._ then iterate L /*Truncated number not prime? Skip it.*/
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end /*k*/
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leave /*egress, found left truncatable prime.*/
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end /*L*/
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/* [↓] find largest right truncated P.*/
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do R=# by -1 for #; digs=length(@.R) /*search from top end; get the length.*/
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do k=1 for digs; _=left(@.R, k) /*validate all right truncatable primes*/
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if \!._ then iterate R /*Truncated number not prime? Skip it.*/
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end /*k*/
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leave /*egress, found right truncatable prime*/
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end /*R*/
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/* [↓] show largest left/right trunc P*/
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say 'The last prime found is ' @.# " (there are" # 'primes ≤' high")."
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say copies('─', 70) /*show a separator line for the output.*/
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say 'The largest left─truncatable prime ≤' high " is " right(@.L, w)
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say 'The largest right─truncatable prime ≤' high " is " right(@.R, w)
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/*stick a fork in it, we're all done. */
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