Smarandache prime-digital sequence: Difference between revisions
No edit summary |
(Tidied and expanded task description a little plus added a Go solution.) |
||
Line 1: | Line 1: | ||
{{draft task|Calmo primes}} |
{{draft task|Calmo primes}} |
||
A prime p is defined to be a Calmo prime if each of its digits is also prime. |
|||
For example 257 is a Calmo prime because it is prime itself and its digits: 2, 5 and 7 are also prime. |
|||
;Task: |
|||
(Note: as there doesn't appear to be a generally accepted term for such primes, the author has named them after himself). |
|||
Show first 25 Calmo primes. |
|||
;Task |
|||
Show hundrest Calmo prime. |
|||
* Show the first 25 Calmo primes. |
|||
* Show the hundredth Calmo prime. |
|||
=={{header|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 isCalmoPrime(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 listCalmoPrimes(startFrom, countFrom, countTo int, printOne bool) int { |
|||
count := countFrom |
|||
for n := startFrom; ; n += 2 { |
|||
if isCalmoPrime(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 Calmo primes are:") |
|||
fmt.Println(" 1. 2") |
|||
n := listCalmoPrimes(3, 1, 25, false) |
|||
fmt.Println("\nThe hundredth Calmo prime is:") |
|||
listCalmoPrimes(n+2, 25, 100, true) |
|||
}</lang> |
|||
{{out}} |
|||
<pre> |
|||
The 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 |
|||
</pre> |
|||
=={{header|Ring}}== |
=={{header|Ring}}== |
Revision as of 10:13, 31 May 2019
A prime p is defined to be a Calmo prime if each of its digits is also prime.
For example 257 is a Calmo prime because it is prime itself and its digits: 2, 5 and 7 are also prime.
(Note: as there doesn't appear to be a generally accepted term for such primes, the author has named them after himself).
- Task
- Show the first 25 Calmo primes.
- Show the hundredth Calmo prime.
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 isCalmoPrime(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 listCalmoPrimes(startFrom, countFrom, countTo int, printOne bool) int {
count := countFrom for n := startFrom; ; n += 2 { if isCalmoPrime(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 Calmo primes are:") fmt.Println(" 1. 2") n := listCalmoPrimes(3, 1, 25, false) fmt.Println("\nThe hundredth Calmo prime is:") listCalmoPrimes(n+2, 25, 100, true)
}</lang>
- Output:
The 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
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 hundrest 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 hundrest Calmo prime is: 100. 33223 done...