Palindromic primes
- Task
Find and show all palindromic primes n, where n < 1000
Raku
<lang perl6>say "{+$_} matching numbers:\n{.batch(10)».fmt('%3d').join: "\n"}"
given (^1000).grep: { .is-prime and $_ eq .flip };</lang>
- Output:
20 matching numbers: 2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
REXX
<lang rexx>/*REXX program finds and displays palindromic primes for all N < 1000. */ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 1000 /*Not specified? Then use the default.*/ if cols== | cols=="," then cols= 10 /* " " " " " " */ call genP /*build array of semaphores for primes.*/ w= max(8, length( commas(hi) ) ) /*max width of a number in any column. */
@pal= ' palindromic primes that are < ' commas(hi)
if cols>0 then say ' index │'center(@pal, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') pals= 0; idx= 1 /*define # of palindromic primes & idx.*/ $= /*a list of palindromic primes so far).*/
do j=1 for # /*search for palindromic primes. */
if @.j\==reverse(@.j) then iterate /*Not a palindromic prime? Then skip. */
pals= pals + 1 /*bump the number of palindromic primes*/
if cols==0 then iterate /*Build the list (to be shown later)? */
$= $ right( commas(@.j), w) /*add a palindromic prime ──► $ list.*/
if pals//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') say say 'Found ' commas(pals) @pal 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 ? /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: !.= 0; hprime= copies(9, length(hi) ) /*placeholders for primes (semaphores).*/
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */
#=5; s.#= @.# **2 /*number of primes so far; prime². */
/* [↓] generate more primes ≤ high.*/
do j=@.#+2 by 2 to hprime /*find odd primes from here on. */
parse var j -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
/* [↑] the above 3 lines saves time.*/
do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</lang>
- output when using the default inputs:
index │ palindromic primes that are < 1,000 ───────┼─────────────────────────────────────────────────────────────────────────────────────────── 1 │ 2 3 5 7 11 101 131 151 181 191 11 │ 313 353 373 383 727 757 787 797 919 929 ───────┴─────────────────────────────────────────────────────────────────────────────────────────── Found 20 palindromic primes that are < 1,000
- output when using the input of: 100000
index │ palindromic primes that are < 10,000 ───────┼─────────────────────────────────────────────────────────────────────────────────────────── 1 │ 2 3 5 7 11 101 131 151 181 191 11 │ 313 353 373 383 727 757 787 797 919 929 21 │ 10,301 10,501 10,601 11,311 11,411 12,421 12,721 12,821 13,331 13,831 31 │ 13,931 14,341 14,741 15,451 15,551 16,061 16,361 16,561 16,661 17,471 41 │ 17,971 18,181 18,481 19,391 19,891 19,991 30,103 30,203 30,403 30,703 51 │ 30,803 31,013 31,513 32,323 32,423 33,533 34,543 34,843 35,053 35,153 61 │ 35,353 35,753 36,263 36,563 37,273 37,573 38,083 38,183 38,783 39,293 71 │ 70,207 70,507 70,607 71,317 71,917 72,227 72,727 73,037 73,237 73,637 81 │ 74,047 74,747 75,557 76,367 76,667 77,377 77,477 77,977 78,487 78,787 91 │ 78,887 79,397 79,697 79,997 90,709 91,019 93,139 93,239 93,739 94,049 101 │ 94,349 94,649 94,849 94,949 95,959 96,269 96,469 96,769 97,379 97,579 111 │ 97,879 98,389 98,689 ───────┴─────────────────────────────────────────────────────────────────────────────────────────── Found 113 palindromic primes that are < 10,000
Ring
<lang ring> load "stdlib.ring"
decimals(0) see "working..." + nl see "Palindromic primes are:" + nl
row = 0 limit = 1000
for n = 1 to limit
strn = string(n)
if ispalindrome(strn) and isprime(n)
row = row + 1
see "" + n + " "
if row%5 = 0
see nl
ok
ok
next
see "Found " + row + " palindromic primes" + nl see "done..." + nl </lang>
- Output:
working... Palindromic primes are: 2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929 Found 20 palindromic primes done...