Smarandache prime-digital sequence: Difference between revisions
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{{draft task|Primes whose digits are primes}} |
{{draft task|Primes whose digits are primes}} |
Revision as of 19:24, 31 May 2019
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
- OEIS A019546: Primes whose digits are primes.
- https://www.scribd.com/document/214851583/On-the-Smarandache-prime-digital-subsequence-sequences
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># Implemented as a lazy, extendable list
my @spds = lazy flat 2,3,5,7, (1..*).map: { grep { .is-prime }, flat ( [X] |((2,3,5,7) xx $_), (3,7) )».join };
say 'Smarandache prime-digitals:';
printf "%4d: %s\n", 1+$_, @spds[$_] for flat ^25, 99;</lang>
- Output:
Smarandache prime-digitals: 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 100: 33223
REXX
<lang rexx>/*REXX program lists a sequence of SPDS (Smarancache prime-digital sequence). */ parse arg n m . /*get optional number of primes to find*/ if n== | n=="," then n= 25 /*Not specified? Then use the default.*/ if m== | m=="," then m= 100 /* " " " " " " */ say '═══listing the first' n "SPDS primes═══" call spds n say say '═══listing the last of ' m "SPDS primes═══" call spds -m 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 is number of prime listed (so far)*/ #= 0 /*# is number of primes found (so far)*/ do j=1 by 2 while c<x; z= j /*start with the first odd prime. */ if z==1 then z= 2 /*handle the even prime (special case) */ /* [↓] divide by the primes. ___ */ do k=2 to # while !.k<=z /*divide J with all primes ≤ √ Z */ if z//@.k==0 then iterate j /*÷ by prev. prime? ¬prime ___ */ end /*j*/ /* [↑] only divide up to √ Z */ #= # + 1 /*bump the count of number of primes. */ @.#= z; !.#= z*z /*define this prime; define its square.*/ if verify(z, 2357)>0 then iterate j /*Digits ¬prime? Then skip this prime.*/ c= c + 1 /*bump the number of SPDS primes shown.*/ 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
Ring
<lang ring>
- 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
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);</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