Truncatable primes
You are encouraged to solve this task according to the task description, using any language you may know.
A truncatable prime is 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.
The task is to find the largest left-truncatable and right-truncatable primes less than one million.
C.f: Sieve of Eratosthenes; Truncatable Prime from Mathworld.
Ada
<lang Ada> with Ada.Text_IO; use Ada.Text_IO; with Ada.Containers.Ordered_Sets;
procedure Truncatable_Primes is
package Natural_Set is new Ada.Containers.Ordered_Sets (Natural); use Natural_Set;
Primes : Set;
function Is_Prime (N : Natural) return Boolean is
Position : Cursor := First (Primes);
begin
while Has_Element (Position) loop
if N mod Element (Position) = 0 then
return False;
end if;
Position := Next (Position);
end loop;
return True;
end Is_Prime;
function Is_Left_Trucatable_Prime (N : Positive) return Boolean is
M : Natural := 1;
begin
while Contains (Primes, N mod (M * 10)) and (N / M) mod 10 > 0 loop
M := M * 10;
if N <= M then
return True;
end if;
end loop;
return False;
end Is_Left_Trucatable_Prime;
function Is_Right_Trucatable_Prime (N : Positive) return Boolean is
M : Natural := N;
begin
while Contains (Primes, M) and M mod 10 > 0 loop
M := M / 10;
if M <= 1 then
return True;
end if;
end loop;
return False;
end Is_Right_Trucatable_Prime;
Position : Cursor;
begin
for N in 2..1_000_000 loop
if Is_Prime (N) then
Insert (Primes, N);
end if;
end loop;
Position := Last (Primes);
while Has_Element (Position) loop
if Is_Left_Trucatable_Prime (Element (Position)) then
Put_Line ("Largest LTP from 1..1000000:" & Integer'Image (Element (Position)));
exit;
end if;
Previous (Position);
end loop;
Position := Last (Primes);
while Has_Element (Position) loop
if Is_Right_Trucatable_Prime (Element (Position)) then
Put_Line ("Largest RTP from 1..1000000:" & Integer'Image (Element (Position)));
exit;
end if;
Previous (Position);
end loop;
end Truncatable_Primes; </lang> Sample output:
Largest LTP from 1..1000000: 998443 Largest RTP from 1..1000000: 739399
C
<lang C>#include<stdio.h>
- include<string.h>
- include<stdlib.h>
- include<math.h>
int isprime(int n){
int isprm[]={0,0,1,1,0,1,0,1,0,0};
int a=7,h;
if(n<10)return isprm[n];
if(!(n&1)||!(n%3))return 0;
h=sqrt(n)+3;
while(a<h){
if(!(n%a)||!(n%(a-2)))return 0;
a+=6;
}
return 1;
}
void leftTrunc(char*s,int l){
memmove(s,s+1,l);
}
void rightTrunc(char*s,int l){
s[l-1]=0;
}
int isTruncPrime(int n,void(*func)(char*,int)){
char s[32];
while(isprime(n)){
ltoa(n,s,10);
if(strchr(s,'0'))break;
func(s,strlen(s));
if(!(n=atol(s)))return 1;
}
return 0;
}
void getHiTruncPrime(int n,void(*func)(char*,int)){
while(n--){
if(isTruncPrime(n,func)){
printf("%d\n",n);
break;
}
}
}
int main(){
puts("Highest left- and right-truncatable primes under 1e6:");
getHiTruncPrime(1000000,leftTrunc);
getHiTruncPrime(1000000,rightTrunc);
puts("Press Enter");
getchar();
return 0;
}</lang> Output:
Highest left- and right-truncatable primes under 1e6: 998443 739399 Press Enter
C#
<lang csharp>using System; using System.Diagnostics;
namespace RosettaCode {
internal class Program
{
public static bool IsPrime(int n)
{
if (n<2) return false;
if (n<4) return true;
if (n%2==0) return false;
if (n<9) return true;
if (n%3==0) return false;
var r = (int) Math.Sqrt(n);
var f = 6-1;
while (f<=r)
{
if (n%f==0 ||n%(f+2)==0)
return false;
f += 6;
}
return true;
}
private static bool IsRightTruncatable(int n)
{
for (;;)
{
n /= 10;
if (n==0)
return true;
if (!IsPrime(n))
return false;
}
}
private static bool IsLeftTruncatable(int n)
{
string c = n.ToString();
if (c.Contains("0"))
return false;
for (int i = 1; i<c.Length; i++)
if (!IsPrime(Convert.ToInt32(c.Substring(i))))
return false;
return true;
}
private static void Main()
{
var sb = new Stopwatch();
sb.Start();
int lt = 0, rt = 0;
for (int i = 1000000; i>0; --i)
{
if (IsPrime(i))
{
if (rt==0 && IsRightTruncatable(i))
rt = i;
else if (lt==0 && IsLeftTruncatable(i))
lt = i;
if (lt!=0 && rt!=0)
break;
}
}
sb.Stop();
Console.WriteLine("Largest truncable left is={0} & right={1}, calculated in {2} msec.",
lt, rt, sb.ElapsedMilliseconds);
}
}
}</lang>
Largest truncable left is=998443 & right=739399, calculated in 16 msec.
Clojure
<lang Clojure>(use '[clojure.contrib.lazy-seqs :only [primes]])
(def prime?
(let [mem (ref #{})
primes (ref primes)]
(fn [n]
(dosync
(if (< n (first @primes))
(@mem n) (let [[mems ss] (split-with #(<= % n) @primes)] (ref-set primes ss) ((commute mem into mems) n)))))))
(defn drop-lefts [n]
(let [dropl #(if (< % 10) 0 (Integer. (subs (str %) 1)))] (->> (iterate dropl n)
(take-while pos? ,) next)))
(defn drop-rights [n]
(->> (iterate #(quot % 10) n)
next
(take-while pos? ,)))
(defn truncatable-left? [n]
(every? prime? (drop-lefts n)))
(defn truncatable-right? [n]
(every? prime? (drop-rights n)))
user> (->> (for [p primes :while (< p 1000000) :when (not-any? #{\0} (str p)) :let [l? (if (truncatable-left? p) p 0) r? (if (truncatable-right? p) p 0)] :when (or l? r?)]
[l? r?])
((juxt #(apply max-key first %) #(apply max-key second %)) ,)
((juxt ffirst (comp second second)) ,)
(map vector ["left truncatable: " "right truncatable: "] ,))
(["left truncatable: " 998443] ["right truncatable: " 739399])</lang>
D
<lang d>import std.stdio, std.math, std.string, std.conv;
bool isPrime(int n) {
if (n <= 1)
return false;
foreach (i; 2 .. cast(int)sqrt(cast(real)n) + 1)
if (!(n % i))
return false;
return true;
}
bool isTruncatablePrime(bool left)(int n) {
string s = to!string(n);
if (indexOf(s, '0') != -1)
return false;
foreach (i; 0 .. s.length)
static if (left) {
if (!isPrime(to!int(s[i .. $])))
return false;
} else {
if (!isPrime(to!int(s[0 .. i+1])))
return false;
}
return true;
}
void main() {
enum int n = 1_000_000;
foreach_reverse (i; 2 .. n)
if (isTruncatablePrime!true(i)) {
writeln("Largest left-truncatable prime in 2 .. ", n, ": ", i);
break;
}
foreach_reverse (i; 2 .. n)
if (isTruncatablePrime!false(i)) {
writeln("Largest right-truncatable prime in 2 .. ", n, ": ", i);
break;
}
}</lang> Output:
Largest left-truncatable prime in 2 .. 1000000: 998443 Largest right-truncatable prime in 2 .. 1000000: 739399
Fortran
<lang fortran>module primes_mod
implicit none logical, allocatable :: primes(:)
contains
subroutine Genprimes(parr)
logical, intent(in out) :: parr(:) integer :: i
! Prime sieve
parr = .true. parr (1) = .false. parr (4 : size(parr) : 2) = .false. do i = 3, int (sqrt (real (size(parr)))), 2 if (parr(i)) parr(i * i : size(parr) : i) = .false. end do
end subroutine
function is_rtp(candidate)
logical :: is_rtp integer, intent(in) :: candidate integer :: n
is_rtp = .true.
n = candidate / 10
do while(n > 0)
if(.not. primes(n)) then
is_rtp = .false.
return
end if
n = n / 10
end do
end function
function is_ltp(candidate)
logical :: is_ltp integer, intent(in) :: candidate integer :: i, n character(10) :: nstr
write(nstr, "(i10)") candidate
is_ltp = .true.
do i = len_trim(nstr)-1, 1, -1
n = mod(candidate, 10**i)
if(.not. primes(n)) then
is_ltp = .false.
return
end if
end do
end function
end module primes_mod
program Truncatable_Primes
use primes_mod implicit none integer, parameter :: limit = 999999 integer :: i character(10) :: nstr
! Generate an array of prime flags up to limit of search
allocate(primes(limit)) call Genprimes(primes)
! Find left truncatable prime
do i = limit, 1, -1
write(nstr, "(i10)") i
if(index(trim(nstr), "0") /= 0) cycle ! check for 0 in number
if(is_ltp(i)) then
write(*, "(a, i0)") "Largest left truncatable prime below 1000000 is ", i
exit
end if
end do
! Find right truncatable prime
do i = limit, 1, -1
write(nstr, "(i10)") i
if(index(trim(nstr), "0") /= 0) cycle ! check for 0 in number
if(is_rtp(i)) then
write(*, "(a, i0)") "Largest right truncatable prime below 1000000 is ", i
exit
end if
end do
end program</lang> Output
Largest left truncatable prime below 1000000 is 998443 Largest right truncatable prime below 1000000 is 739399
Haskell
Using
from HackageDB
<lang haskell>import Data.Numbers.Primes(primes, isPrime) import Data.List import Control.Arrow
primes1e6 = reverse. filter (notElem '0'. show) $ takeWhile(<=1000000) primes
rightT, leftT :: Int -> Bool rightT = all isPrime. takeWhile(>0). drop 1. iterate (`div`10) leftT x = all isPrime. takeWhile(<x).map (x`mod`) $ iterate (*10) 10
main = do
let (ltp, rtp) = (head. filter leftT &&& head. filter rightT) primes1e6 putStrLn $ "Left truncatable " ++ show ltp putStrLn $ "Right truncatable " ++ show rtp</lang>
Output: <lang haskell>*Main> main Left truncatable 998443 Right truncatable 739399</lang>
Interpretation of the J contribution: <lang haskell>digits = [1..9] :: [Integer] smallPrimes = filter isPrime digits pow10 = iterate (*10) 1 mul10 = (pow10!!). length. show righT = (+) . (10 *) lefT = liftM2 (.) (+) ((*) . mul10)
primesTruncatable f = iterate (concatMap (filter isPrime.flip map digits. f)) smallPrimes</lang> Output: <lang haskell>*Main> maximum $ primesTruncatable righT !! 5 739399
- Main> maximum $ primesTruncatable lefT !! 5
998443</lang>
Icon and Unicon
Icon
<lang Icon>procedure main(arglist)
N := 0 < integer(\arglist[1]) | 1000000 # primes to generator 1 to ... (1M or 1st arglist)
D := (0 < integer(\arglist[2]) | 10) / 2 # primes to display (10 or 2nd arglist)
P := sieve(N) # from sieve task (modified)
write("There are ",*P," prime numbers in the range 1 to ",N)
if *P <= 2*D then
every writes( "Primes: "|!sort(P)||" "|"\n" )
else
every writes( "Primes: "|(L := sort(P))[1 to D]||" "|"... "|L[*L-D+1 to *L]||" "|"\n" )
largesttruncateable(P)
end
procedure largesttruncateable(P) #: find the largest left and right trucatable numbers in P local ltp,rtp
every x := sort(P)[*P to 1 by -1] do # largest to smallest
if not find('0',x) then {
/ltp := islefttrunc(P,x)
/rtp := isrighttrunc(P,x)
if \ltp & \rtp then break # until both found
}
write("Largest left truncatable prime = ", ltp)
write("Largest right truncatable prime = ", rtp)
return
end
procedure isrighttrunc(P,x) #: return integer x if x and all right truncations of x are in P or fails if x = 0 | (member(P,x) & isrighttrunc(P,x / 10)) then return x end
procedure islefttrunc(P,x) #: return integer x if x and all left truncations of x are in P or fails if *x = 0 | ( (x := integer(x)) & member(P,x) & islefttrunc(P,x[2:0]) ) then return x end</lang>
Sample output:
There are 78498 prime numbers in the range 1 to 1000000 Primes: 2 3 5 7 11 ... 999953 999959 999961 999979 999983 Largest left truncatable prime = 998443 Largest right truncatable prime = 739399
Unicon
The Icon solution works in Unicon.
J
Truncatable primes may be constructed by starting with a set of one digit prime numbers and then repeatedly adding a non-zero digit (using the cartesian product of digit sequences) and, at each step, selecting the prime numbers which result.
In other words, given:
<lang j>selPrime=: #~ 1&p: seed=: selPrime digits=: 1+i.9 step=: selPrime@,@:(,&.":/&>)@{@;</lang>
The largest truncatable primes less than a million can be obtained by adding five digits to the prime seeds, then finding the largest value from the result:
<lang j> >./ digits&step^:5 seed NB. left truncatable 998443
>./ step&digits^:5 seed NB. right truncatable
739399</lang>
Java
<lang Java> import java.util.BitSet;
public class Main {
public static void main(String[] args){
final int MAX = 1000000;
//Sieve of Eratosthenes (using BitSet only for odd numbers) BitSet primeList = new BitSet(MAX>>1); primeList.set(0,primeList.size(),true);
int sqroot = (int) Math.sqrt(MAX); primeList.clear(0); for(int num = 3; num <= sqroot; num+=2) { if( primeList.get(num >> 1) ) { int inc = num << 1; for(int factor = num * num; factor < MAX; factor += inc) { //if( ((factor) & 1) == 1) //{ primeList.clear(factor >> 1); //} } } } //Sieve ends...
//Find Largest Truncatable Prime. (so we start from 1000000 - 1 int rightTrunc = -1, leftTrunc = -1; for(int prime = (MAX - 1) | 1; prime >= 3; prime -= 2) { if(primeList.get(prime>>1)) { //Already found Right Truncatable Prime? if(rightTrunc == -1) { int right = prime; while(right > 0 && primeList.get(right >> 1)) right /= 10; if(right == 0) rightTrunc = prime; }
//Already found Left Truncatable Prime? if(leftTrunc == -1 ) { //Left Truncation String left = Integer.toString(prime); if(!left.contains("0")) { while( left.length() > 0 ){ int iLeft = Integer.parseInt(left); if(!primeList.get( iLeft >> 1)) break; left = left.substring(1); } if(left.length() == 0) leftTrunc = prime; } } if(leftTrunc != -1 && rightTrunc != -1) //Found both? then Stop loop { break; } } } System.out.println("Left Truncatable : " + leftTrunc); System.out.println("Right Truncatable : " + rightTrunc); } } </lang> Output :
Left Truncatable : 998443 Right Truncatable : 796339
Lua
<lang lua>max_number = 1000000
numbers = {} for i = 2, max_number do
numbers[i] = i;
end
for i = 2, max_number do
for j = i+1, max_number do
if numbers[j] ~= 0 and j % i == 0 then numbers[j] = 0 end
end
end
max_prime_left, max_prime_right = 2, 2 for i = 2, max_number do
if numbers[i] ~= 0 then
local is_prime = true
local l = math.floor( i / 10 )
while l > 1 do
if numbers[l] == 0 then
is_prime = false
break
end
l = math.floor( l / 10 )
end
if is_prime then
max_prime_left = i
end
is_prime = true
local n = 10;
while math.floor( i % 10 ) ~= 0 and n < max_number do
if numbers[ math.floor( i % 10 ) ] ~= 0 then
is_prime = false
break
end
n = n * 10
end
if is_prime then
max_prime_right = i
end
end
end
print( "max_prime_left = ", max_prime_left ) print( "max_prime_right = ", max_prime_right )</lang>
PARI/GP
This version builds the truncatable primes with up to k digits in a straightforward fashion. Run time is about 15 milliseconds, almost all of which is I/O. <lang>left(n)={ my(v=[2,3,5,7],u,t=1,out=0); for(i=1,n, t*=10; u=[]; for(j=1,#v, forstep(a=t,t*9,t, if(isprime(a+v[j]),u=concat(u,a+v[j])) ) ); out=v[#v]; v=vecsort(u) ); out }; right(n)={ my(v=[2,3,5,7],u,out=0); for(i=1,n, u=[]; for(j=1,#v, forstep(a=1,9,[2,4], if(isprime(10*v[j]+a),u=concat(u,10*v[j]+a)) ) ); out=v[#v]; v=u ); out }; [left(6),right(6)]</lang>
Perl 6
This uses a fairly naive isprime routine. It works but is slow.
<lang perl6> use v6; my %cache = <2 3 5 7 11 13 17 19 23> >>=>>> 1;
sub isprime ($test) {
return %cache{$test} if defined %cache{$test};
return (%cache{$test} = 0) if $test <= 25;
my $r = floor($test ** .5);
return (%cache{$test} = 0) unless $test % $_ for (2, 3, * + 2 ... * >= $r);
return (%cache{$test} = 1);
}
sub trunc_prime ($type, $limit is copy) {
$limit += ($limit % 2 ?? 0 !! 1);
for ($limit, * - 2 ... * < 2 ) -> $loop {
next if $loop ~~ /0/; # No zeros allowed
my $this = $loop;
while $this.&isprime {
$this.=subst($type, );
return $loop unless $this;
}
}
}
say "Largest Left Truncatable Prime < 1000000: ",trunc_prime(rx/^\d/, 1000000); say "Largest Right Truncatable Prime < 1000000: ",trunc_prime(rx/\d$/, 1000000); </lang> Output:
Largest Left Truncatable Prime < 1000000: 998443 Largest Right Truncatable Prime < 1000000: 739339
PicoLisp
<lang PicoLisp>(load "@lib/rsa.l") # Use the 'prime?' function from RSA package
(de truncatablePrime? (N Fun)
(for (L (chop N) L (Fun L))
(T (= "0" (car L)))
(NIL (prime? (format L)))
T ) )
(let (Left 1000000 Right 1000000)
(until (truncatablePrime? (dec 'Left) cdr)) (until (truncatablePrime? (dec 'Right) '((L) (cdr (rot L))))) (cons Left Right) )</lang>
Output:
-> (998443 . 739399)
PowerShell
<lang PowerShell>function IsPrime ( [int] $num ) {
$isprime = @{}
2..[math]::sqrt($num) | Where-Object {
$isprime[$_] -eq $null } | ForEach-Object {
$_
$isprime[$_] = $true
for ( $i=$_*$_ ; $i -le $num; $i += $_ )
{ $isprime[$i] = $false }
}
2..$num | Where-Object { $isprime[$_] -eq $null }
}
function Truncatable ( [int] $num ) {
$declen = [math]::abs($num).ToString().Length
$primes = @()
$ltprimes = @{}
$rtprimes = @{}
1..$declen | ForEach-Object { $ltprimes[$_]=@{}; $rtprimes[$_]=@{} }
IsPrime $num | ForEach-Object {
$lastltprime = 2
$lastrtprime = 2
} {
$curprim = $_
$curdeclen = $curprim.ToString().Length
$primes += $curprim
if( $curdeclen -eq 1 ) {
$ltprimes[1][$curprim] = $true
$rtprimes[1][$curprim] = $true
$lastltprime = $curprim
$lastrtprime = $curprim
} else {
$curmod = $curprim % [math]::pow(10,$curdeclen - 1)
$curdiv = [math]::floor($curprim / 10)
if( $ltprimes[$curdeclen - 1][[int]$curmod] ) {
$ltprimes[$curdeclen][$curprim] = $true
$lastltprime = $curprim
}
if( $rtprimes[$curdeclen - 1][[int]$curdiv] ) {
$rtprimes[$curdeclen][$curprim] = $true
$lastrtprime = $curprim
}
}
if( ( $ltprimes[$curdeclen - 2].Keys.count -gt 0 ) -and ( $ltprimes[$curdeclen - 1].Keys.count -gt 0 ) ) { $ltprimes[$curdeclen -2] = @{} }
if( ( $rtprimes[$curdeclen - 2].Keys.count -gt 0 ) -and ( $rtprimes[$curdeclen - 1].Keys.count -gt 0 ) ) { $rtprimes[$curdeclen -2] = @{} }
} {
"Largest Left Truncatable Prime: $lastltprime"
"Largest Right Truncatable Prime: $lastrtprime"
}
}</lang>
PureBasic
<lang PureBasic>#MaxLim = 999999
Procedure is_Prime(n)
If n<=1 : ProcedureReturn #False
ElseIf n<4 : ProcedureReturn #True
ElseIf n%2=0: ProcedureReturn #False
ElseIf n<9 : ProcedureReturn #True
ElseIf n%3=0: ProcedureReturn #False
Else
Protected r=Round(Sqr(n),#PB_Round_Down)
Protected f=5
While f<=r
If n%f=0 Or n%(f+2)=0
ProcedureReturn #False
EndIf
f+6
Wend
EndIf
ProcedureReturn #True
EndProcedure
Procedure TruncateLeft(n)
Protected s.s=Str(n), l=Len(s)-1
If Not FindString(s,"0",1)
While l>0
s=Right(s,l)
If Not is_Prime(Val(s))
ProcedureReturn #False
EndIf
l-1
Wend
ProcedureReturn #True
EndIf
EndProcedure
Procedure TruncateRight(a)
Repeat
a/10
If Not a
Break
ElseIf Not is_Prime(a) Or a%10=0
ProcedureReturn #False
EndIf
ForEver
ProcedureReturn #True
EndProcedure
i=#MaxLim Repeat
If is_Prime(i)
If Not truncateleft And TruncateLeft(i)
truncateleft=i
EndIf
If Not truncateright And TruncateRight(i)
truncateright=i
EndIf
EndIf
If truncateleft And truncateright
Break
Else
i-2
EndIf
Until i<=0
x.s="Largest TruncateLeft= "+Str(truncateleft) y.s="Largest TruncateRight= "+Str(truncateright)
MessageRequester("Truncatable primes",x+#CRLF$+y)</lang>
Python
<lang python>maxprime = 1000000
def primes(n):
multiples = set()
prime = []
for i in range(2, n+1):
if i not in multiples:
prime.append(i)
multiples.update(set(range(i*i, n+1, i)))
return prime
def truncatableprime(n):
'Return a longest left and right truncatable primes below n'
primelist = [str(x) for x in primes(n)[::-1]]
primeset = set(primelist)
for n in primelist:
# n = 'abc'; [n[i:] for i in range(len(n))] -> ['abc', 'bc', 'c']
alltruncs = set(n[i:] for i in range(len(n)))
if alltruncs.issubset(primeset):
truncateleft = int(n)
break
for n in primelist:
# n = 'abc'; [n[:i+1] for i in range(len(n))] -> ['a', 'ab', 'abc']
alltruncs = set([n[:i+1] for i in range(len(n))])
if alltruncs.issubset(primeset):
truncateright = int(n)
break
return truncateleft, truncateright
print(truncatableprime(maxprime))</lang>
Sample Output
(998443, 739399)
REXX
<lang REXX> /*find largest left- & right-truncatable primes < 1 million.*/ x.=0 /*placeholders for primes. */ p.=999 /*default value for P.n */ p.1= 2; x.2=1 /*1st prime: two. */ p.2= 3; x.3=1 /*2nd prime: three. */ p.3= 5; x.5=1 /*3rd prime: five. */ p.4= 7; x.7=1 /*4th prime: seven. */ p.5=11; x.11=1 /*5th prime: eleven. */ n=5 /*number of primes so far. */
do j=p.n+2 by 2 to 1000000 /*find all primes <1000000. */
if j//3 ==0 then iterate /*divisible by three? */
if right(j,1)==5 then iterate /*right-most digit a five? */
if j//7 ==0 then iterate /*divisible by seven? */
if j//11 ==0 then iterate /*divisible by eleven? */
/*the above 4 lines saves time*/
do k=6 /*divide by known odd primes. */
if p.k**2>j then leave /*only go up to sqrt(J). */
if j//p.k==0 then iterate j /*divisible by X? Not prime. */
end
n=n+1 /*bump number of primes found.*/ p.n=j /*assign to sparse array. */ x.j=1 /*indicate that J is a prime. */ end
say 'The last prime is' p.n "("n 'primes under one million).' say copies('-',66) /*show a separator. */ lp=0
do j=1 for n /*find left-trunc. primes. */ y=p.j; g=y if pos(0,y)\==0 then iterate /*if prime contains a 0, nope.*/
do k=1 for length(y)-1 /*test for prime, skip whole #*/ g=right(y,k); if \x.g then iterate j end
lp=max(lp,y) /*choose the maximum so far. */ end
rp=0
do j=1 for n /*find left-trunc. primes. */ y=p.j; g=y if pos(0,y)\==0 then iterate /*if prime contains a 0, nope.*/
do k=1 for length(y)-1 /*test for prime, skip whole #*/ g=left(y,k); if \x.g then iterate j end
rp=max(rp,y) /*choose the maximum so far. */ end
say 'The largest left-truncatable prime is' lp '(under one million).' say 'The largest right-truncatable prime is' rp '(under one million).'
</lang> Output:
The last prime is 999983 (78498 primes under one million). ------------------------------------------------------------------ The largest left-truncatable prime is 998443 (under one million). The largest right-truncatable prime is 739399 (under one million).
Ruby
<lang ruby>def left_truncatable?(n)
return truncatable?(n, $left_truncate)
end
$left_truncate = proc do |n|
begin n = Integer(String(n)[1..-1]) rescue ArgumentError n = 0 end n
end
def right_truncatable?(n)
return truncatable?(n, $right_truncate)
end
$right_truncate = proc {|n| n/10}
def truncatable?(n, trunc_func)
return false if String(n).include? "0" loop do n = trunc_func.call(n) return true if n == 0 return false if not Prime.prime?(n) end
end
require 'prime' primes = Prime.each(1_000_000).to_a.reverse
p primes.detect {|p| left_truncatable? p} p primes.detect {|p| right_truncatable? p}</lang>
returns
998443 739399
Tcl
<lang tcl>package require Tcl 8.5
- Optimized version of the Sieve-of-Eratosthenes task solution
proc sieve n {
set primes [list]
if {$n < 2} {return $primes}
set nums [dict create]
for {set i 2} {$i <= $n} {incr i} {
dict set nums $i ""
}
set next 2
set limit [expr {sqrt($n)}]
while {$next <= $limit} {
for {set i $next} {$i <= $n} {incr i $next} {dict unset nums $i}
lappend primes $next
dict for {next -} $nums break
} return [concat $primes [dict keys $nums]]
}
proc isLeftTruncatable n {
global isPrime
while {[string length $n] > 0} {
if {![info exist isPrime($n)]} { return false } set n [string range $n 1 end]
} return true
} proc isRightTruncatable n {
global isPrime
while {[string length $n] > 0} {
if {![info exist isPrime($n)]} { return false } set n [string range $n 0 end-1]
} return true
}
- Demo code
set limit 1000000 puts "calculating primes up to $limit" set primes [sieve $limit] puts "search space contains [llength $primes] members" foreach p $primes {
set isPrime($p) "yes"
} set primes [lreverse $primes]
puts "searching for largest left-truncatable prime" foreach p $primes {
if {[isLeftTruncatable $p]} {
puts FOUND:$p break
}
}
puts "searching for largest right-truncatable prime" foreach p $primes {
if {[isRightTruncatable $p]} {
puts FOUND:$p break
}
}</lang> Output:
calculating primes up to 1000000 search space contains 78498 members searching for largest left-truncatable prime FOUND:998443 searching for largest right-truncatable prime FOUND:739399