Palindromic primes
Find and show all palindromic primes n, where n < 1000
- Task
AWK
<lang AWK>
- syntax: GAWK -f PALINDROMIC_PRIMES.AWK
BEGIN {
start = 1
stop = 999
for (i=start; i<=stop; i++) {
if (is_prime(i) && reverse(i) == i) {
printf("%d ",i)
count++
}
}
printf("\nPalindromic primes %d-%d: %d\n",start,stop,count)
exit(0)
} function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
} function reverse(str, i,rts) {
for (i=length(str); i>=1; i--) {
rts = rts substr(str,i,1)
}
return(rts)
} </lang>
- Output:
2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929 Palindromic primes 1-999: 20
Factor
Simple
A simple solution that suffices for the task:
<lang factor>USING: kernel math.primes present prettyprint sequences ;
1000 primes-upto [ present dup reverse = ] filter stack.</lang>
- Output:
2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
Fast
A much more efficient solution that generates palindromic numbers directly and filters primes from them:
<lang factor>USING: io kernel lists lists.lazy math math.functions math.primes math.ranges prettyprint sequences tools.memory.private ;
! Create a palindrome from its base natural number.
- create-palindrome ( n odd? -- m )
dupd [ 10 /i ] when swap [ over 0 > ] [ 10 * [ 10 /mod ] [ + ] bi* ] while nip ;
! Create an ordered infinite lazy list of palindromic numbers.
- lpalindromes ( -- l )
0 lfrom [
10 swap ^ dup 10 * [a,b)
[ [ t create-palindrome ] map ]
[ [ f create-palindrome ] map ] bi
[ sequence>list ] bi@ lappend
] lmap-lazy lconcat ;
- lpalindrome-primes ( -- list )
lpalindromes [ prime? ] lfilter ;
"10,000th palindromic prime:" print 9999 lpalindrome-primes lnth commas print nl
"Palindromic primes less than 1,000:" print lpalindrome-primes [ 1000 < ] lwhile [ . ] leach</lang>
- Output:
10,000th palindromic prime: 13,649,694,631 Palindromic primes less than 1,000: 2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
Go
<lang go>package main
import (
"fmt" "rcu"
)
func reversed(n int) int {
rev := 0
for n > 0 {
rev = rev*10 + n%10
n /= 10
}
return rev
}
func main() {
primes := rcu.Primes(99999)
var pals []int
for _, p := range primes {
if p == reversed(p) {
pals = append(pals, p)
}
}
fmt.Println("Palindromic primes under 1,000:")
var smallPals, bigPals []int
for _, p := range pals {
if p < 1000 {
smallPals = append(smallPals, p)
} else {
bigPals = append(bigPals, p)
}
}
rcu.PrintTable(smallPals, 10, 3, false)
fmt.Println()
fmt.Println(len(smallPals), "such primes found.")
fmt.Println("\nAdditional palindromic primes under 100,000:")
rcu.PrintTable(bigPals, 10, 6, true)
fmt.Println()
fmt.Println(len(bigPals), "such primes found,", len(pals), "in all")
}</lang>
- Output:
Same as Wren entry.
Haskell
<lang haskell>import Data.Numbers.Primes
palindromicPrimes :: [Integer] palindromicPrimes =
filter (((==) <*> reverse) . show) primes
main :: IO () main =
mapM_ print $
takeWhile
(1000 >)
palindromicPrimes</lang>
- Output:
2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
Julia
Generator method. <lang julia>using Primes
parray = [2, 3, 5, 7, 9, 11]
results = vcat(parray, filter(isprime, [100j + 10i + j for i in 0:9, j in 1:9]))
println(results)
</lang>
- Output:
[2, 3, 5, 7, 9, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929]
Phix
filter primes for palindromicness
function palindrome(string s) return s=reverse(s) end function for l=3 to 5 by 2 do integer limit = power(10,l) -- 1000 then 100000 sequence res = get_primes_le(limit) res = apply(true,sprintf,{{"%d"},res}) res = filter(res,palindrome) string s = join(shorten(res,"",5)) printf(1,"found %d < %,d: %s\n",{length(res),limit,s}) end for
- Output:
found 20 < 1,000: 2 3 5 7 11 ... 757 787 797 919 929 found 113 < 100,000: 2 3 5 7 11 ... 97379 97579 97879 98389 98689
filter palindromes for primality
sequence r = {} for l=2 to 3 do for i=1 to power(10,l) do string s = sprintf("%d",i) integer t = to_number(s&reverse(s[1..$-1])), u = to_number(s&reverse(s)) if is_prime(t) then r &= t end if if is_prime(u) then r &= u end if end for r = unique(r) string s = join(shorten(apply(true,sprintf,{{"%d"},r}),"",5)) printf(1,"found %d < %,d: %s\n",{length(r),power(10,l*2-1),s}) end for
Same output. Didn't actually test if this way was any faster, but expect it would be.
Python
A non-finite generator of palindromic primes – one of many approaches to solving this problem in Python. <lang python>Palindromic primes
from itertools import takewhile
- palindromicPrimes :: Generator [Int]
def palindromicPrimes():
An infinite stream of palindromic primes
def p(n):
s = str(n)
return s == s[::-1]
return (n for n in primes() if p(n))
- ------------------------- TEST -------------------------
def main():
Palindromic primes below 1000
print('\n'.join(
str(x) for x in takewhile(
lambda n: 1000 > n,
palindromicPrimes()
)
))
- ----------------------- GENERIC ------------------------
- primes :: [Int]
def primes():
Non finite sequence of prime numbers.
n = 2
dct = {}
while True:
if n in dct:
for p in dct[n]:
dct.setdefault(n + p, []).append(p)
del dct[n]
else:
yield n
dct[n * n] = [n]
n = 1 + n
- MAIN ---
if __name__ == '__main__':
main()
</lang>
- Output:
2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
Raku
<lang perl6>say "{+$_} 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 < 100,000 ───────┼─────────────────────────────────────────────────────────────────────────────────────────── 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 < 100,000
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl see "Palindromic primes are:" + nl row = 0 limit1 = 1000 limit2 = 100000
palindromicPrimes(limit1)
see "Found " + row + " palindromic primes" + nl + nl see "palindromic primes that are < 100,000" + nl
palindromicPrimes(limit2)
see nl + "Found " + row + " palindromic primes that are < 100,000" + nl see "done..." + nl
func palindromicPrimes(limit)
row = 0
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
</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 palindromic primes that are < 100,000 2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929 10301 10501 10601 11311 11411 12421 12721 12821 13331 13831 13931 14341 14741 15451 15551 16061 16361 16561 16661 17471 17971 18181 18481 19391 19891 19991 30103 30203 30403 30703 30803 31013 31513 32323 32423 33533 34543 34843 35053 35153 35353 35753 36263 36563 37273 37573 38083 38183 38783 39293 70207 70507 70607 71317 71917 72227 72727 73037 73237 73637 74047 74747 75557 76367 76667 77377 77477 77977 78487 78787 78887 79397 79697 79997 90709 91019 93139 93239 93739 94049 94349 94649 94849 94949 95959 96269 96469 96769 97379 97579 97879 98389 98689 Found 113 palindromic primes that are < 100,000 done...
Wren
<lang ecmascript>import "/math" for Int import "/fmt" for Fmt import "/seq" for Lst
var reversed = Fn.new { |n|
var rev = 0
while (n > 0) {
rev = rev * 10 + n % 10
n = (n/10).floor
}
return rev
}
var primes = Int.primeSieve(99999) var pals = [] for (p in primes) {
if (p == reversed.call(p)) pals.add(p)
} System.print("Palindromic primes under 1,000:") var smallPals = pals.where { |p| p < 1000 }.toList for (chunk in Lst.chunks(smallPals, 10)) Fmt.print("$3d", chunk) System.print("\n%(smallPals.count) such primes found.")
System.print("\nAdditional palindromic primes under 100,000:") var bigPals = pals.where { |p| p >= 1000 }.toList for (chunk in Lst.chunks(bigPals, 10)) Fmt.print("$,6d", chunk) System.print("\n%(bigPals.count) such primes found, %(pals.count) in all.")</lang>
- Output:
Palindromic primes under 1,000: 2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929 20 such primes found. Additional palindromic primes under 100,000: 10,301 10,501 10,601 11,311 11,411 12,421 12,721 12,821 13,331 13,831 13,931 14,341 14,741 15,451 15,551 16,061 16,361 16,561 16,661 17,471 17,971 18,181 18,481 19,391 19,891 19,991 30,103 30,203 30,403 30,703 30,803 31,013 31,513 32,323 32,423 33,533 34,543 34,843 35,053 35,153 35,353 35,753 36,263 36,563 37,273 37,573 38,083 38,183 38,783 39,293 70,207 70,507 70,607 71,317 71,917 72,227 72,727 73,037 73,237 73,637 74,047 74,747 75,557 76,367 76,667 77,377 77,477 77,977 78,487 78,787 78,887 79,397 79,697 79,997 90,709 91,019 93,139 93,239 93,739 94,049 94,349 94,649 94,849 94,949 95,959 96,269 96,469 96,769 97,379 97,579 97,879 98,389 98,689 93 such primes found, 113 in all.