Nice primes: Difference between revisions

{{Draft task|Prime Numbers}}

::#   Take an positive integer   '''n'''

::#   '''sumn'''   is the sum of the decimal digits of   '''n'''

::*   The OEIS article:   [http://oeis.org/A78403 A78403 Primes such that digital root is prime].

<br><br>

 

=={{header|ALGOL W}}==

% returns the digital root of n in base 10 %

integer procedure digitalRoot( integer value n ) ;

end

end.

{{out}}

<pre>

33:997 dr(7)

</pre>

=={{header|AWK}}==

# syntax: GAWK -f NICE_PRIMES.AWK

BEGIN {

return(sum)

}

{{out}}

<pre>

</pre>

 

 

 

 

 

{{out}}

547

563

977

983

</pre>

 

({{math|<var>n</var> &#61; 0}} may not need to be special-cased depending on the behavior of your language's modulo operator.)

 

 

: digital-root ( m -- n ) 1 - 9 mod 1 + ;

 

{{out}}

<pre style="height:10em">

{{trans|Factor}}

{{works with|Gforth}}

: notprime! ( n -- ) here + 1 swap c! ;

 

 

: print_nice_primes ( m n -- )

over prime_sieve

do

i prime? if

i digital_root prime? if

then

then

 

1000 500 print_nice_primes

 

{{out}}

<pre>

</pre>

 

=={{header|Go}}==

{{trans|Wren}}

 

import "fmt"

}

}

 

{{out}}

</pre>

 

 

=={{header|J}}==

(#~ (2 3 5 7 e.~ digital_root&>)) p: 95 + i. 168 - 95

509 547 563 569 587 599 601 617 619 641 653 659 673 677 691 709 727 743 761 797 821 839 853 857 887 907 911 929 941 947 977 983 997

</pre>

 

=={{header|Julia}}==

See [[Strange_numbers#Julia]] for the filter_open_interval function.

 

isnice(n, base=10) = isprime(n) && (mod1(n - 1, base - 1) + 1) in [2, 3, 5, 7, 11, 13, 17, 19]

 

filter_open_interval(500, 1000, isnice)

<pre>

Finding numbers matching isnice for open interval (500, 1000):

The total found was 33

</pre>

 

=={{header|Perl}}==

{{libheader|ntheory}}

use warnings;

 

$cnt = @nice_primes;

print "Nice primes between $low and $high (total of $cnt):\n" .

{{out}}

<pre>Nice primes between 500 and 1000 (total of 33):

=={{header|Phix}}==

{{trans|Factor}}

{{out}}

<pre>

659 673 677 691 709 727 743 761 797 821 839

853 857 887 907 911 929 941 947 977 983 997

</pre>

 

=={{header|Raku}}==

my @is-nice = lazy (0..*).map: { .&is-prime && .&digroot.&is-prime ?? $_ !! False };

{{out}}

<pre> 509 547 563 569 587 599 601 617 619 641 653

659 673 677 691 709 727 743 761 797 821 839

853 857 887 907 911 929 941 947 977 983 997</pre>

 

=={{header|REXX}}==

parse arg lo hi cols . /*obtain optional argument from the CL.*/

if lo=='' | lo=="," then lo= 500 /*Not specified? Then use the default.*/

call genP /*build array of semaphores for primes.*/

w= 10 /*width of a number in any column. */

if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')

$= /*a list of nice primes (so far). */

do j=lo+1 to hi-1; if \!.j then iterate /*search for nice primes within range*/

digRoot= 1 + (j - 1) // 9 /*obtain the digital root of J. */

if \!.digRoot then iterate /*Is digRoot prime? No, then skip it.*/

c= commas(j) /*maybe add commas to the number. */

$= $ right(c, max(w, length(c) ) ) /*add a nice prime ──► list, allow big#*/

say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */

idx= idx + cols /*bump the index count for the output*/

 

if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/

say

exit 0 /*stick a fork in it, we're all done. */

/*──────────────────────────────────────────────────────────────────────────────────────*/

commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?

/*──────────────────────────────────────────────────────────────────────────────────────*/

do j=@.#+2 by 2 to hi /*find odd primes from here on. */

parse var j '' -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/

end /*k*/ /* [↑] only process numbers ≤ √ J */

#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */

{{out|output|text=&nbsp; when using the default inputs:}}

<pre>

index │ nice primes that are between 500 and 1,000 (not inclusive)

───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────

 

</pre>

 

=={{header|Ring}}==

load "stdlib.ring"

 

 

see "done..." + nl

{{out}}

<pre>

33: 997 > Σ = 7

done...

</pre>

 

=={{header|Rust}}==

{{trans|Factor}}

// primal = "0.3"

 

fn main() {

nice_primes(500, 1000);

 

{{out}}

983

997

</pre>

 

=={{header|Wren}}==

{{libheader|Wren-math}}

{{libheader|Wren-fmt}}

 

var sumDigits = Fn.new { |n|

}

}

 

{{out}}

32: 983 -> Σ = 2

33: 997 -> Σ = 7

</pre>