Smarandache prime-digital sequence: Difference between revisions

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dup pprint "th smarandache prime: " write
dup pprint "th smarandache prime: " write
nth-smarandache
nth-smarandache
] each ;</lang>
] each ;

MAIN: smarandache-demo</lang>
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Revision as of 02:43, 1 June 2019

Smarandache prime-digital sequence is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The Smarandache prime-digital sequence (SPDS for brevity) is the sequence of primes whose digits are themselves prime.

For example 257 is an element of this sequence because it is prime itself and its digits: 2, 5 and 7 are also prime.

Task
  • Show the first 25 SPDS primes.
  • Show the hundredth SPDS prime.


See also



F#

This task uses Extensible Prime Generator (F#) <lang fsharp> // Generate Smarandache prime-digital sequence. Nigel Galloway: May 31st., 2019 let rec spds g=seq{yield! g; yield! (spds (Seq.collect(fun g->[g*10+2;g*10+3;g*10+5;g*10+7]) g))}|>Seq.filter(isPrime) spds [2;3;5;7] |> Seq.take 25 |> Seq.iter(printfn "%d") printfn "\n\n100th item of this sequence is %d" (spds [2;3;5;7] |> Seq.item 99) printfn "1000th item of this sequence is %d" (spds [2;3;5;7] |> Seq.item 999) </lang>

Output:
2
3
5
7
23
37
53
73
223
227
233
257
277
337
353
373
523
557
577
727
733
757
773
2237
2273


100th item of this sequence is 33223
1000th item of this sequence is 3273527

Factor

Naive

<lang factor>USING: combinators.short-circuit io lists lists.lazy math math.parser math.primes prettyprint sequences ; IN: rosetta-code.smarandache-naive

smarandache? ( n -- ? )
   {
       [ number>string string>digits [ prime? ] all? ]
       [ prime? ]
   } 1&& ;
smarandache ( -- list ) 1 lfrom [ smarandache? ] lfilter ;
smarandache-demo ( -- )
   "First 25:" print 25 smarandache ltake list>array .
   "100th: " write smarandache 99 [ cdr ] times car . ;

MAIN: smarandache-demo</lang>

Output:
First 25:
{
    2
    3
    5
    7
    23
    37
    53
    73
    223
    227
    233
    257
    277
    337
    353
    373
    523
    557
    577
    727
    733
    757
    773
    2237
    2273
}
100th: 33223

Optimized

<lang factor>USING: combinators generalizations io kernel math math.functions math.primes prettyprint sequences ; IN: rosetta-code.smarandache

! Observations: ! * For 2-digit numbers and higher, only 3 and 7 are viable in ! the ones place. ! * 2, 3, 5, and 7 are viable anywhere else. ! * It is possible to use this information to drastically ! reduce the amount of numbers to check for primality. ! * For instance, by these rules we can tell that the next ! potential smarandache prime after 777 is 2223.

next-one ( n -- n' ) 3 = 7 3 ? ; inline
next-ten ( n -- n' )
   { { 2 [ 3 ] } { 3 [ 5 ] } { 5 [ 7 ] } [ drop 2 ] } case ;
inc ( seq quot: ( n -- n' ) -- seq' )
   [ 0 ] 2dip [ change-nth ] curry keep ; inline
inc1 ( seq -- seq' ) [ next-one ] inc ;
inc10 ( seq -- seq' ) [ next-ten ] inc ;
inc-all ( seq -- seq' )
   inc1 [ zero? not [ next-ten ] when ] V{ } map-index-as ;
carry ( seq -- seq' )
   dup [ 7 = not ] find drop {
       { 0 [ inc1 ] }
       { f [ inc-all 2 suffix! ] }
       [ cut [ inc-all ] [ inc10 ] bi* append! ]
   } case ;
digits>integer ( seq -- n ) [ 10 swap ^ * ] map-index sum ;
next-smarandache ( seq -- seq' )
   [ digits>integer prime? ] [ carry dup ] do until ;
.sm ( seq -- ) <reversed> [ pprint ] each nl ;
first25 ( -- )
   2 3 5 7 [ . ] 4 napply V{ 7 } clone
   21 [ next-smarandache dup .sm ] times drop ;
nth-smarandache ( n -- )
   4 - V{ 7 } clone swap [ next-smarandache ] times .sm ;
smarandache-demo ( -- )
   "First 25 smarandache primes:" print first25 nl
   { 100 1000 10000 100000 } [
       dup pprint "th smarandache prime: " write
       nth-smarandache
   ] each ;

MAIN: smarandache-demo</lang>

Output:
First 25 smarandache primes:
2
3
5
7
23
37
53
73
223
227
233
257
277
337
353
373
523
557
577
727
733
757
773
2237
2273

100th smarandache prime: 33223
1000th smarandache prime: 3273527
10000th smarandache prime: 273322727
100000th smarandache prime: 23325232253

Go

As this task doesn't involve large numbers, a simple prime test routine is adequate. <lang go>package main

import "fmt"

func isPrime(n int) bool { 

   if n < 2 {
       return false
   }
   if n%2 == 0 {
       return n == 2
   }
   if n%3 == 0 {
       return n == 3
   }
   d := 5
   for d*d <= n {
       if n%d == 0 {
           return false
       }
       d += 2
       if n%d == 0 {
           return false
       }
       d += 4
   }
   return true

}

func isSPDSPrime(n int) bool { 

   if !isPrime(n) {
       return false
   }
   for n > 0 {
       r := n % 10
       if r != 2 && r != 3 && r != 5 && r != 7 {
           return false
       }
       n /= 10
   }
   return true

}

func listSPDSPrimes(startFrom, countFrom, countTo int, printOne bool) int { 

   count := countFrom
   for n := startFrom; ; n += 2 {
       if isSPDSPrime(n) {
           count++
           if !printOne {
               fmt.Printf("%2d. %d\n", count, n)
           }
           if count == countTo {
               if printOne {
                   fmt.Printf("%2d. %d\n", count, n)
               }
               return n
           }
       }
   }

}

func main() { 

   fmt.Println("The first 25 terms of the Smarandache prime-digital sequence are:")
   fmt.Println(" 1. 2")
   n := listSPDSPrimes(3, 1, 25, false)
   fmt.Println("\nThe hundredth term of the sequence is:")
   listSPDSPrimes(n+2, 25, 100, true)

}</lang>

Output:
The first 25 terms of the Smarandache prime-digital sequence are:
 1. 2
 2. 3
 3. 5
 4. 7
 5. 23
 6. 37
 7. 53
 8. 73
 9. 223
10. 227
11. 233
12. 257
13. 277
14. 337
15. 353
16. 373
17. 523
18. 557
19. 577
20. 727
21. 733
22. 757
23. 773
24. 2237
25. 2273

The hundredth term of the sequence is:
100. 33223

Perl 6

<lang perl6>use Lingua::EN::Numbers::Cardinal; sub comma { $^i.flip.comb(3).join(',').flip }

  1. Implemented as a lazy, extendable list

my $spds = flat 2,3,5,7, (1..*).map: { grep { .is-prime }, [X~] |((2,3,5,7) xx $_), (3,7) };

say 'Smarandache prime-digitals:'; printf "%15s: %s\n", ordinal(1+$_).tclc, comma $spds[$_] for flat ^25, 99, 999, 9999;</lang>

Output:
Smarandache prime-digitals:
          First: 2
         Second: 3
          Third: 5
         Fourth: 7
          Fifth: 23
          Sixth: 37
        Seventh: 53
         Eighth: 73
          Ninth: 223
          Tenth: 227
       Eleventh: 233
        Twelfth: 257
     Thirteenth: 277
     Fourteenth: 337
      Fifteenth: 353
      Sixteenth: 373
    Seventeenth: 523
     Eighteenth: 557
     Nineteenth: 577
      Twentieth: 727
   Twenty-first: 733
  Twenty-second: 757
   Twenty-third: 773
  Twenty-fourth: 2,237
   Twenty-fifth: 2,273
  One hundredth: 33,223
 One thousandth: 3,273,527
 Ten thousandth: 273,322,727

REXX

The prime number generator has been simplified and very little optimization was included. <lang rexx>/*REXX program lists a sequence of SPDS (Smarandache prime-digital sequence) primes.*/ parse arg n q /*get optional number of primes to find*/ if n== | n=="," then n= 25 /*Not specified? Then use the default.*/ if q= then q= 100 /* " " " " " " */ say '═══listing the first' n "SPDS primes═══" call spds n 

            do i=1  for words(q)+1;     y=word(q, i);    if y== | y==","   then iterate
            say
            say '═══listing the last of '    y     "SPDS primes═══"
            call spds -y
            end   /*i*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ spds: parse arg x 1 ox; x= abs(x) /*obtain the limit to be used for list.*/ 

     c= 0                                       /*C  number of SPDS primes found so far*/
     #= 0                                       /*#  number of      primes found so far*/
           do j=1  by 2  while  c<x;    z= j    /*start: 1st even prime, then use odd. */
           if z==1  then z= 2                   /*handle the even prime (special case) */
                                                /* [↓]  divide by the primes.   ___    */
                   do k=2  to #  while  k*k<=z  /*divide  Z  with all primes ≤ √ Z     */
                   if z//@.k==0  then iterate j /*÷ by prev. prime?  ¬prime     ___    */
                   end   /*j*/                  /* [↑]   only divide up to     √ Z     */
           #= # + 1;             @.#= z         /*bump the prime count;  assign prime #*/
           if verify(z, 2357)>0  then iterate j /*Digits ¬prime?  Then skip this prime.*/
           c= c + 1                             /*bump the number of SPDS primes found.*/
           if ox<0  then iterate                /*don't display it, display the last #.*/
           say right(z, 21)                     /*maybe display this prime ──► terminal*/
           end   /*j*/                          /* [↑]  only display N number of primes*/
     if ox<0  then say right(z, 21)             /*display one  (the last)  SPDS prime. */
     return</lang>
output   when using the default inputs:
═══listing the first 25 SPDS primes═══
                    2
                    3
                    5
                    7
                   23
                   37
                   53
                   73
                  223
                  227
                  233
                  257
                  277
                  337
                  353
                  373
                  523
                  557
                  577
                  727
                  733
                  757
                  773
                 2237
                 2273

═══listing the last of  100 SPDS primes═══
                33223

═══listing the last of  1000 SPDS primes═══
              3273527

Ring

<lang ring>

  1. Project: Calmo primes

load "stdlib.ring" limit = 25 max = 300000 num = 0 see "working..." + nl see "wait for done..." + nl see "First 25 Calmo primes are:" + nl for n = 1 to max 

   if isprime(n)
      res = calmo(n)
      if res = 1
         num = num + 1
         if num < limit + 1
            see "" + num + ". " + n + nl
         ok
         if num = 100
            see "The hundredth Calmo prime is:" + nl
            see "" + num + ". " + n + nl
            exit
         ok
      ok
   ok

next see "done..." + nl

func calmo(p) 

    sp = string(p)
    for n = 1 to len(sp)
        if not isprime(sp[n])
           return 0
        ok
    next
    return 1

</lang>

Output:
working...
wait for done...
First 25 Calmo primes are:
1. 2
2. 3
3. 5
4. 7
5. 23
6. 37
7. 53
8. 73
9. 223
10. 227
11. 233
12. 257
13. 277
14. 337
15. 353
16. 373
17. 523
18. 557
19. 577
20. 727
21. 733
22. 757
23. 773
24. 2237
25. 2273
The hundredth Calmo prime is:
100. 33223
done...

zkl

Library: GMP

GNU Multiple Precision Arithmetic Library

Using GMP ( probabilistic primes), because it is easy and fast to generate primes.

Extensible prime generator#zkl could be used instead. <lang zkl>var [const] BI=Import("zklBigNum"); // libGMP

spds:=Walker.zero().tweak(fcn(ps){ 

  var [const] nps=T(0,0,1,1,0,1,0,1,0,0);  // 2,3,5,7
  p:=ps.nextPrime().toInt();
  if(p.split().filter( fcn(n){ 0==nps[n] }) ) return(Void.Skip);
  p   //  733 --> (7,3,3) --> () --> good,       29 --> (2,9) --> (9) --> bad

}.fp(BI(1)));</lang> Or <lang zkl>spds:=Walker.zero().tweak(fcn(ps){ 

  var [const] nps="014689".inCommon;
  p:=ps.nextPrime().toInt();
  if(nps(p.toString())) return(Void.Skip);
  p   //  733 --> "" --> good,       29 --> "9" --> bad

}.fp(BI(1)));</lang> <lang zkl>println("The first 25 terms of the Smarandache prime-digital sequence are:"); spds.walk(25).concat(",").println();

println("The hundredth term of the sequence is: ",spds.drop(100-25).value); println("1000th item of this sequence is : ",spds.drop(1_000-spds.n).value);</lang>

Output:
The first 25 terms of the Smarandache prime-digital sequence are:
2,3,5,7,23,37,53,73,223,227,233,257,277,337,353,373,523,557,577,727,733,757,773,2237,2273
The hundredth term of the sequence is: 33223
1000th item of this sequence is : 3273527
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