Smarandache prime-digital sequence
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
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
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 var [const] primeBitMap=Data(100_000).fill(0);
spds:=Walker.zero().tweak(fcn(ps){
primeBitMap[ p:=ps.nextPrime().toInt() ]=1; if(p.split().filter( fcn(n){ 0==primeBitMap[n] }) ) return(Void.Skip); p // 733 --> (7,3,3) --> () --> good, 29 --> (2,9) --> (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