Descending primes
You are encouraged to solve this task according to the task description, using any language you may know.
Generate and show all primes with strictly descending decimal digits.
- See also
- Related
11l
F is_prime(p)
I p < 2 | p % 2 == 0
R p == 2
L(i) (3 .. Int(sqrt(p))).step(2)
I p % i == 0
R 0B
R 1B
V c = 0
V ps = [1, 2, 3, 4, 5, 6, 7, 8, 9]
V nxt = [0] * 128
L
V nc = 0
L(a) ps
I is_prime(a)
c++
print(‘#8’.format(a), end' I c % 5 == 0 {"\n"} E ‘ ’)
V b = a * 10
V l = a % 10 + b
b++
L b < l
nxt[nc] = b
nc++
b++
I nc > 1
ps = nxt[0 .< nc]
E
L.break
print("\n"c‘ descending primes found’)- Output:
2 3 5 7 31
41 43 53 61 71
73 83 97 421 431
521 541 631 641 643
653 743 751 761 821
853 863 941 953 971
983 5431 6421 6521 7321
7541 7621 7643 8431 8521
8543 8641 8731 8741 8753
8761 9421 9431 9521 9631
9643 9721 9743 9851 9871
75431 76421 76541 76543 86531
87421 87541 87631 87641 87643
94321 96431 97651 98321 98543
98621 98641 98731 764321 865321
876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321
98764321 98765431
87 descending primes found
Alternative solution:
F is_prime(p)
I p < 2 | p % 2 == 0
R p == 2
L(i) (3 .. Int(sqrt(p))).step(2)
I p % i == 0
R 0B
R 1B
[Int] descending_primes
L(n) 1 .< 2 ^ 9
V s = ‘’
L(i) (8 .. 0).step(-1)
I n [&] (1 << i) != 0
s ‘’= String(i + 1)
I is_prime(Int(s))
descending_primes.append(Int(s))
L(n) sorted(descending_primes)
print(‘#8’.format(n), end' I (L.index + 1) % 5 == 0 {"\n"} E ‘ ’)
print("\n"descending_primes.len‘ descending primes found’)ALGOL 68
Almost identical to the Ascending_primes Algol 68 sample.
Note, the sources of primes.incl.a68 and sort.incl.a68 are on separate pages on Rosetta Code - see the above links.
BEGIN # find all primes with strictly decreasing digits #
PR read "primes.incl.a68" PR # include prime utilities #
PR read "sort.incl.a68" PR # include sort utilities #
[ 1 : 512 ]INT primes; # there will be at most 512 (2^9) primes #
INT p count := 0; # number of primes found so far #
FOR d1 FROM 0 TO 1 DO
INT n1 = IF d1 = 1 THEN 9 ELSE 0 FI;
FOR d2 FROM 0 TO 1 DO
INT n2 = IF d2 = 1 THEN ( n1 * 10 ) + 8 ELSE n1 FI;
FOR d3 FROM 0 TO 1 DO
INT n3 = IF d3 = 1 THEN ( n2 * 10 ) + 7 ELSE n2 FI;
FOR d4 FROM 0 TO 1 DO
INT n4 = IF d4 = 1 THEN ( n3 * 10 ) + 6 ELSE n3 FI;
FOR d5 FROM 0 TO 1 DO
INT n5 = IF d5 = 1 THEN ( n4 * 10 ) + 5 ELSE n4 FI;
FOR d6 FROM 0 TO 1 DO
INT n6 = IF d6 = 1 THEN ( n5 * 10 ) + 4 ELSE n5 FI;
FOR d7 FROM 0 TO 1 DO
INT n7 = IF d7 = 1 THEN ( n6 * 10 ) + 3 ELSE n6 FI;
FOR d8 FROM 0 TO 1 DO
INT n8 = IF d8 = 1 THEN ( n7 * 10 ) + 2 ELSE n7 FI;
FOR d9 FROM 0 TO 1 DO
INT n9 = IF d9 = 1 THEN ( n8 * 10 ) + 1 ELSE n8 FI;
IF n9 > 0 THEN
IF is probably prime( n9 ) THEN
# have a prime with strictly decreasing digits #
primes[ p count +:= 1 ] := n9
FI
FI
OD
OD
OD
OD
OD
OD
OD
OD
OD;
primes QUICKSORT ELEMENTS( 1, p count ); # sort the primes #
FOR i TO p count DO # display the primes #
print( ( " ", whole( primes[ i ], -8 ) ) );
IF i MOD 10 = 0 THEN print( ( newline ) ) FI
OD
END- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
ALGOL W
...and only a few characters different from the Algol W Ascending primes sample.
begin % find all primes with strictly descending digits - translation of Lua %
% quicksorts v, the bounds of v must be specified in lb and ub %
procedure quicksort ( integer array v( * )
; integer value lb, ub
) ;
if ub > lb then begin
% more than one element, so must sort %
integer left, right, pivot;
left := lb;
right := ub;
% choosing the middle element of the array as the pivot %
pivot := v( left + ( ( right + 1 ) - left ) div 2 );
while begin
while left <= ub and v( left ) < pivot do left := left + 1;
while right >= lb and v( right ) > pivot do right := right - 1;
left <= right
end do begin
integer swap;
swap := v( left );
v( left ) := v( right );
v( right ) := swap;
left := left + 1;
right := right - 1
end while_left_le_right ;
quicksort( v, lb, right );
quicksort( v, left, ub )
end quicksort ;
% returns true if n is prime, false otherwise %
logical procedure is_prime( integer value n ) ;
if n < 2 then false
else if n rem 2 = 0 then n = 2
else if n rem 3 = 0 then n = 3
else begin
logical prime; prime := true;
for f := 5 step 6 until entier( sqrt( n ) ) do begin
if n rem f = 0 or n rem ( f + 2 ) = 0 then begin
prime := false;
goto done
end if_n_rem_f_eq_0_or_n_rem_f_plus_2_eq_0
end for_f;
done: prime
end is_prime ;
% increments n and also returns its new value %
integer procedure inc ( integer value result n ) ; begin n := n + 1; n end;
% sets primes to the list of descending primes and lenPrimes to the %
% number of descending primes - primes must be big enough, e.g. have 511 %
% elements %
procedure descending_primes ( integer array primes ( * )
; integer result lenPrimes
) ;
begin
integer array digits ( 1 :: 9 );
integer array candidates ( 1 :: 6000 );
integer lenCandidates;
candidates( 1 ) := 0;
lenCandidates := 1;
lenPrimes := 0;
for i := 1 until 9 do digits( i ) := 10 - i;
for i := 1 until 9 do begin
for j := 1 until lenCandidates do begin
integer cValue; cValue := candidates( j ) * 10 + digits( i );
if is_prime( cValue ) then primes( inc( lenPrimes ) ) := cValue;
candidates( inc( lenCandidates ) ) := cValue
end for_j
end for_i ;
quickSort( primes, 1, lenPrimes );
end descending_primes ;
begin % find the descending primes and print them %
integer array primes ( 1 :: 512 );
integer lenPrimes;
descending_primes( primes, lenPrimes );
for i := 1 until lenPrimes do begin
writeon( i_w := 8, s_w := 0, " ", primes( i ) );
if i rem 10 = 0 then write()
end for_i
end
end.- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
Arturo
descending: @[
loop 1..9 'a [
loop 1..dec a 'b [
loop 1..dec b 'c [
loop 1..dec c 'd [
loop 1..dec d 'e [
loop 1..dec e 'f [
loop 1..dec f 'g [
loop 1..dec g 'h [
loop 1..dec h 'i -> @[a b c d e f g h i]
@[a b c d e f g h]]
@[a b c d e f g]]
@[a b c d e f]]
@[a b c d e]]
@[a b c d]]
@[a b c]]
@[a b]]
@[a]]
]
descending: filter descending 'd -> some? d 'n [not? positive? n]
descending: filter descending 'd -> d <> unique d
descending: sort map descending 'd -> to :integer join to [:string] d
loop split.every:10 select descending => prime? 'row [
print map to [:string] row 'item -> pad item 8
]
- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
AWK
# syntax: GAWK -f DESCENDING_PRIMES.AWK
BEGIN {
start = 1
stop = 99999999
for (i=start; i<=stop; i++) {
leng = length(i)
flag = 1
for (j=1; j<leng; j++) {
if (substr(i,j,1) <= substr(i,j+1,1)) {
flag = 0
break
}
}
if (flag) {
if (is_prime(i)) {
printf("%9d%1s",i,++count%10?"":"\n")
}
}
}
printf("\n%d-%d: %d descending primes\n",start,stop,count)
exit(0)
}
function is_prime(n, d) {
d = 5
if (n < 2) { return(0) }
if (n % 2 == 0) { return(n == 2) }
if (n % 3 == 0) { return(n == 3) }
while (d*d <= n) {
if (n % d == 0) { return(0) }
d += 2
if (n % d == 0) { return(0) }
d += 4
}
return(1)
}
- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
1-99999999: 87 descending primes
C
#include <stdio.h>
int ispr(unsigned int n) {
if ((n & 1) == 0 || n < 2) return n == 2;
for (unsigned int j = 3; j * j <= n; j += 2)
if (n % j == 0) return 0; return 1; }
int main() {
unsigned int c = 0, nc, pc = 9, i, a, b, l,
ps[128], nxt[128];
for (a = 0, b = 1; a < pc; a = b++) ps[a] = b;
while (1) {
nc = 0;
for (i = 0; i < pc; i++) {
if (ispr(a = ps[i]))
printf("%8d%s", a, ++c % 5 == 0 ? "\n" : " ");
for (b = a * 10, l = a % 10 + b++; b < l; b++)
nxt[nc++] = b;
}
if (nc > 1) for(i = 0, pc = nc; i < pc; i++) ps[i] = nxt[i];
else break;
}
printf("\n%d descending primes found", c);
}
- Output:
Same as C#
C#
This task can be accomplished without using nine nested loops, without external libraries, without dynamic arrays, without sorting, without string operations and without signed integers.
using System;
class Program {
static bool ispr(uint n) {
if ((n & 1) == 0 || n < 2) return n == 2;
for (uint j = 3; j * j <= n; j += 2)
if (n % j == 0) return false; return true; }
static void Main(string[] args) {
uint c = 0; int nc;
var ps = new uint[]{ 1, 2, 3, 4, 5, 6, 7, 8, 9 };
var nxt = new uint[128];
while (true) {
nc = 0;
foreach (var a in ps) {
if (ispr(a))
Console.Write("{0,8}{1}", a, ++c % 5 == 0 ? "\n" : " ");
for (uint b = a * 10, l = a % 10 + b++; b < l; b++)
nxt[nc++] = b;
}
if (nc > 1) {
Array.Resize (ref ps, nc); Array.Copy(nxt, ps, nc); }
else break;
}
Console.WriteLine("\n{0} descending primes found", c);
}
}
- Output:
2 3 5 7 31
41 43 53 61 71
73 83 97 421 431
521 541 631 641 643
653 743 751 761 821
853 863 941 953 971
983 5431 6421 6521 7321
7541 7621 7643 8431 8521
8543 8641 8731 8741 8753
8761 9421 9431 9521 9631
9643 9721 9743 9851 9871
75431 76421 76541 76543 86531
87421 87541 87631 87641 87643
94321 96431 97651 98321 98543
98621 98641 98731 764321 865321
876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321
98764321 98765431
87 descending primes found
C++
#include <iostream>
bool ispr(unsigned int n) {
if ((n & 1) == 0 || n < 2) return n == 2;
for (unsigned int j = 3; j * j <= n; j += 2)
if (n % j == 0) return false; return true; }
int main() {
unsigned int c = 0, nc, pc = 9, i, a, b, l,
ps[128]{ 1, 2, 3, 4, 5, 6, 7, 8, 9 }, nxt[128];
while (true) {
nc = 0;
for (i = 0; i < pc; i++) {
if (ispr(a = ps[i]))
printf("%8d%s", a, ++c % 5 == 0 ? "\n" : " ");
for (b = a * 10, l = a % 10 + b++; b < l; b++)
nxt[nc++] = b;
}
if (nc > 1) for(i = 0, pc = nc; i < pc; i++) ps[i] = nxt[i];
else break;
}
printf("\n%d descending primes found", c);
}
- Output:
Same as C#
Delphi
type TProgress = procedure(Percent: integer);
function IsPrime(N: integer): boolean;
{Optimised prime test - about 40% faster than the naive approach}
var I,Stop: integer;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (i + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
function IsDescending(N: integer): boolean;
{Determine if each digit is less than previous, left to right}
var S: string;
var I: integer;
begin
Result:=False;
S:=IntToStr(N);
for I:=1 to Length(S)-1 do
if S[I]<=S[I+1] then exit;
Result:=True;
end;
procedure ShowDescendingPrimes(Memo: TMemo; Prog: TProgress);
{Write Descending primes up to 123,456,789 }
{The Optional progress }
var I,Cnt: integer;
var S: string;
const Max = 123456789;
begin
if Assigned(Prog) then Prog(0);
S:='';
Cnt:=0;
for I:=2 to Max do
begin
if ((I mod 1000000)=0) and Assigned(Prog) then Prog(Trunc(100*(I/Max)));
if IsDescending(I) and IsPrime(I) then
begin
S:=S+Format('%12.0n', [I*1.0]);
Inc(Cnt);
if (Cnt mod 8)=0 then
begin
Memo.Lines.Add(S);
S:='';
end;
end;
end;
if S<>'' then Memo.Lines.Add(S);
Memo.Lines.Add('Descending Primes Found: '+IntToStr(Cnt));
end;
- Output:
2 3 5 7 31 41 43 53
61 71 73 83 97 421 431 521
541 631 641 643 653 743 751 761
821 853 863 941 953 971 983 5,431
6,421 6,521 7,321 7,541 7,621 7,643 8,431 8,521
8,543 8,641 8,731 8,741 8,753 8,761 9,421 9,431
9,521 9,631 9,643 9,721 9,743 9,851 9,871 75,431
76,421 76,541 76,543 86,531 87,421 87,541 87,631 87,641
87,643 94,321 96,431 97,651 98,321 98,543 98,621 98,641
98,731 764,321 865,321 876,431 975,421 986,543 987,541 987,631
8,764,321 8,765,321 9,754,321 9,875,321 97,654,321 98,764,321 98,765,431
Descending Primes Found: 87
EasyLang
func isprim num .
if num < 2
return 0
.
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
proc nextdesc n . .
if isprim n = 1
write n & " "
.
if n > 987654321
return
.
for d = n mod 10 - 1 downto 1
nextdesc n * 10 + d
.
.
for i = 9 downto 1
nextdesc i
.
F#
This task uses Extensible Prime Generator (F#)
// Descending primes. Nigel Galloway: April 19th., 2022
[2;3;5;7]::List.unfold(fun(n,i)->match n with []->None |_->let n=n|>List.map(fun(n,g)->[for n in n..9->(n+1,i*n+g)])|>List.concat in Some(n|>List.choose(fun(_,n)->if isPrime n then Some n else None),(n|>List.filter(fst>>(>)10),i*10)))([(4,3);(2,1);(8,7)],10)
|>List.concat|>List.sort|>List.iter(printf "%d "); printfn ""
- Output:
2 3 5 7 31 41 43 53 61 71 73 83 97 421 431 521 541 631 641 643 653 743 751 761 821 853 863 941 953 971 983 5431 6421 6521 7321 7541 7621 7643 8431 8521 8543 8641 8731 8741 8753 8761 9421 9431 9521 9631 9643 9721 9743 9851 9871 75431 76421 76541 76543 86531 87421 87541 87631 87641 87643 94321 96431 97651 98321 98543 98621 98641 98731 764321 865321 876431 975421 986543 987541 987631 8764321 8765321 9754321 9875321 97654321 98764321 98765431
Factor
USING: grouping grouping.extras math math.combinatorics
math.functions math.primes math.ranges prettyprint sequences
sequences.extras ;
9 1 [a,b] all-subsets [ reverse 0 [ 10^ * + ] reduce-index ]
[ prime? ] map-filter 10 "" pad-groups 10 group simple-table.
- Output:
7 5 3 2 97 83 73 71 61 53 43 41 31 983 971 953 941 863 853 821 761 751 743 653 643 641 631 541 521 431 421 9871 9851 9743 9721 9643 9631 9521 9431 9421 8761 8753 8741 8731 8641 8543 8521 8431 7643 7621 7541 7321 6521 6421 5431 98731 98641 98621 98543 98321 97651 96431 94321 87643 87641 87631 87541 87421 86531 76543 76541 76421 75431 987631 987541 986543 975421 876431 865321 764321 9875321 9754321 8765321 8764321 98765431 98764321 97654321
FreeBASIC
#include "isprime.bas"
#include "sort.bas"
Dim As Double t0 = Timer
Dim As Integer i, n, tmp, num, cant
Dim Shared As Integer matriz(512)
For i = 0 To 511
n = 0
tmp = i
num = 9
While tmp
If tmp And 1 Then n = n * 10 + num
tmp = tmp Shr 1
num -= 1
Wend
matriz(i) = n
Next i
Sort(matriz())
cant = 0
For i = 1 To Ubound(matriz)-1
n = matriz(i)
If IsPrime(n) Then
Print Using "#########"; n;
cant += 1
If cant Mod 10 = 0 Then Print
End If
Next i
Print Using !"\n\nThere are & descending primes."; cant
Sleep
- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
There are 87 descending primes.
Forth
Tested on vfxforth and GForth.
: is-prime? \ n -- f ; \ Fast enough for this application
DUP 1 AND IF \ n is odd
DUP 3 DO
DUP I DUP * < IF DROP -1 LEAVE THEN \ Leave loop if I**2 > n
DUP I MOD 0= IF DROP 0 LEAVE THEN \ Leave loop if n%I is zero
2 +LOOP \ iterate over odd I only
ELSE \ n is even
2 = \ Returns true if n == 2.
THEN ;
: 1digit \ -- ; \ Select and print one digit numbers which are prime
10 2 ?DO
I is-prime? IF I 9 .r THEN
LOOP ;
: 2digit \ n-bfwd digit -- ;
\ Generate and print primes where least significant digit < digit
\ n-bfwd is the base number bought foward from calls to `digits` below.
SWAP 10 * SWAP 1 ?DO
DUP I + is-prime? IF DUP I + 9 .r THEN
2 I 3 = 2* - +LOOP DROP ; \ This generates the I sequence 1 3 7 9
: digits \ #digits n-bfwd max-digit -- ;
\ Print descendimg primes with #digits digits.
2 PICK 9 > IF ." #digits must be less than 10." 2DROP DROP EXIT THEN
2 PICK 1 = IF 2DROP DROP 1digit EXIT THEN \ One digit is special simple case
2 PICK 2 = IF \ Two digit special and
SWAP 10 * SWAP 2 DO \ I is 2 .. max-digit-1
DUP I + I 2digit
LOOP 2DROP
ELSE
SWAP 10 * SWAP 2 PICK ?DO \ I is #digits .. max-digit-1
DUP I + 2 PICK 1- SWAP I RECURSE \ Recurse with #digits reduced by 1.
LOOP 2DROP
THEN ;
: descending-primes
\ Print the descending primes. Call digits with increasing #digits
CR 9 1 DO I 0 10 digits LOOP ;
descending-primes
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431 ok
FutureBasic
local fn IsPrime( n as NSUInteger ) as BOOL
BOOL isPrime = YES
NSUInteger i
if n < 2 then exit fn = NO
if n = 2 then exit fn = YES
if n mod 2 == 0 then exit fn = NO
for i = 3 to int(n^.5) step 2
if n mod i == 0 then exit fn = NO
next
end fn = isPrime
void local fn DesecendingPrimes( limit as long )
long i, n, mask, num, count = 0
for i = 0 to limit -1
n = 0 : mask = i : num = 9
while ( mask )
if mask & 1 then n = n * 10 + num
mask = mask >> 1
num--
wend
mda(i) = n
next
mda_sort @"compare:"
for i = 1 to mda_count (0) - 1
n = mda_integer(i)
if ( fn IsPrime( n ) )
printf @"%10ld\b", n
count++
if count mod 10 == 0 then print
end if
next
printf @"\n\n\tThere are %ld descending primes.", count
end fn
window 1, @"Desecending Primes", ( 0, 0, 780, 230 )
print
CFTimeInterval t
t = fn CACurrentMediaTime
fn DesecendingPrimes( 512 )
printf @"\n\tCompute time: %.3f ms\n",(fn CACurrentMediaTime-t)*1000
HandleEvents- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
There are 87 descending primes.
Compute time: 8.976 ms
Go
package main
import (
"fmt"
"rcu"
"sort"
"strconv"
)
func combinations(a []int, k int) [][]int {
n := len(a)
c := make([]int, k)
var combs [][]int
var combine func(start, end, index int)
combine = func(start, end, index int) {
if index == k {
t := make([]int, len(c))
copy(t, c)
combs = append(combs, t)
return
}
for i := start; i <= end && end-i+1 >= k-index; i++ {
c[index] = a[i]
combine(i+1, end, index+1)
}
}
combine(0, n-1, 0)
return combs
}
func powerset(a []int) (res [][]int) {
if len(a) == 0 {
return
}
for i := 1; i <= len(a); i++ {
res = append(res, combinations(a, i)...)
}
return
}
func main() {
ps := powerset([]int{9, 8, 7, 6, 5, 4, 3, 2, 1})
var descPrimes []int
for i := 1; i < len(ps); i++ {
s := ""
for _, e := range ps[i] {
s += string(e + '0')
}
p, _ := strconv.Atoi(s)
if rcu.IsPrime(p) {
descPrimes = append(descPrimes, p)
}
}
sort.Ints(descPrimes)
fmt.Println("There are", len(descPrimes), "descending primes, namely:")
for i := 0; i < len(descPrimes); i++ {
fmt.Printf("%8d ", descPrimes[i])
if (i+1)%10 == 0 {
fmt.Println()
}
}
fmt.Println()
}
- Output:
There are 87 descending primes, namely:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
J
Compare with Ascending primes.
NB. increase maximum output line length
9!:37 (512) 1} 9!:36 ''
(#~ 1&p:) (#: }. i. 512) 10&#.@# >: i. _9
2 3 31 41 421 43 431 5 521 53 541 5431 61 631 641 6421 643 6521 653 7 71 73 7321 743 751 7541 75431 761 7621 76421 7643 764321 76541 76543 821 83 8431 8521 853 8543 863 8641 86531 865321 8731 8741 87421 8753 87541 8761 87631 87641 87643 876431 8764321 8765321 941 9421 9431 94321 9521 953 9631 9643 96431 97 971 9721 9743 975421 9754321 97651 97654321 983 98321 9851 98543 98621 98641 986543 9871 98731 9875321 987541 987631 98764321 98765431
Java
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
public final class DescendingPrimes {
public static void main(String[] aArgs) {
List<Integer> allNumbersStrictlyDescendingDigits = new ArrayList<Integer>(512);
for ( int i = 0; i < 512; i++ ) {
int number = 0;
int temp = i;
int digit = 9;
while ( temp > 0 ) {
if ( temp % 2 == 1 ) {
number = number * 10 + digit;
}
temp >>= 1;
digit -= 1;
}
allNumbersStrictlyDescendingDigits.add(number);
}
Collections.sort(allNumbersStrictlyDescendingDigits);
int count = 0;
for ( int number : allNumbersStrictlyDescendingDigits ) {
if ( isPrime(number) ) {
System.out.print(String.format("%9d%s", number, ( ++count % 10 == 0 ? "\n" : " " )));
}
}
System.out.println(System.lineSeparator());
System.out.println("There are " + count + " descending primes.");
}
private static boolean isPrime(int aNumber) {
if ( aNumber < 2 || ( aNumber % 2 ) == 0 ) {
return aNumber == 2;
}
for ( int divisor = 3; divisor * divisor <= aNumber; divisor += 2 ) {
if ( aNumber % divisor == 0 ) {
return false;
}
}
return true;
}
}
- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
There are 87 descending primes.
jq
Also works with gojq and fq provided _nwise/1 is defined as in jq.
Preliminaries
# Output: a stream of the powersets of the input array
def powersets:
if length == 0 then .
else .[-1] as $x
| .[:-1] | powersets
| ., . + [$x]
end;
def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else 23
| until( (. * .) > $n or ($n % . == 0); .+2)
| . * . > $n
end;
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;Descending primes
[range(9;0;-1)]
| [powersets
| map(tostring)
| join("")
| select(length > 0)
| tonumber
| select(is_prime)]
| sort
| _nwise(10)
| map(lpad(9))
| join(" ")- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
Julia
using Combinatorics
using Primes
function descendingprimes()
return sort!(filter(isprime, [evalpoly(10, x)
for x in powerset([1, 2, 3, 4, 5, 6, 7, 8, 9]) if !isempty(x)]))
end
foreach(p -> print(rpad(p[2], 10), p[1] % 10 == 0 ? "\n" : ""), enumerate(descendingprimes()))
- Output:
2 3 5 7 31 41 43 53 61 71 73 83 97 421 431 521 541 631 641 643 653 743 751 761 821 853 863 941 953 971 983 5431 6421 6521 7321 7541 7621 7643 8431 8521 8543 8641 8731 8741 8753 8761 9421 9431 9521 9631 9643 9721 9743 9851 9871 75431 76421 76541 76543 86531 87421 87541 87631 87641 87643 94321 96431 97651 98321 98543 98621 98641 98731 764321 865321 876431 975421 986543 987541 987631 8764321 8765321 9754321 9875321 97654321 98764321 98765431
Lua
Identical to Ascending_primes#Lua except for the order of digits list.
local function is_prime(n)
if n < 2 then return false end
if n % 2 == 0 then return n==2 end
if n % 3 == 0 then return n==3 end
for f = 5, n^0.5, 6 do
if n%f==0 or n%(f+2)==0 then return false end
end
return true
end
local function descending_primes()
local digits, candidates, primes = {9,8,7,6,5,4,3,2,1}, {0}, {}
for i = 1, #digits do
for j = 1, #candidates do
local value = candidates[j] * 10 + digits[i]
if is_prime(value) then primes[#primes+1] = value end
candidates[#candidates+1] = value
end
end
table.sort(primes)
return primes
end
print(table.concat(descending_primes(), ", "))
- Output:
2, 3, 5, 7, 31, 41, 43, 53, 61, 71, 73, 83, 97, 421, 431, 521, 541, 631, 641, 643, 653, 743, 751, 761, 821, 853, 863, 941, 953, 971, 983, 5431, 6421, 6521, 7321, 7541, 7621, 7643, 8431, 8521, 8543, 8641, 8731, 8741, 8753, 8761, 9421, 9431, 9521, 9631, 9643, 9721, 9743, 9851, 9871, 75431, 76421, 76541, 76543, 86531, 87421, 87541, 87631, 87641, 87643, 94321, 96431, 97651, 98321, 98543, 98621, 98641, 98731, 764321, 865321, 876431, 975421, 986543, 987541, 987631, 8764321, 8765321, 9754321, 9875321, 97654321, 98764321, 98765431
Mathematica /Wolfram Language
Sort[Select[FromDigits/@Subsets[Range[9,1,-1],{1,\[Infinity]}],PrimeQ]]
- Output:
{2, 3, 5, 7, 31, 41, 43, 53, 61, 71, 73, 83, 97, 421, 431, 521, 541, 631, 641, 643, 653, 743, 751, 761, 821, 853, 863, 941, 953, 971, 983, 5431, 6421, 6521, 7321, 7541, 7621, 7643, 8431, 8521, 8543, 8641, 8731, 8741, 8753, 8761, 9421, 9431, 9521, 9631, 9643, 9721, 9743, 9851, 9871, 75431, 76421, 76541, 76543, 86531, 87421, 87541, 87631, 87641, 87643, 94321, 96431, 97651, 98321, 98543, 98621, 98641, 98731, 764321, 865321, 876431, 975421, 986543, 987541, 987631, 8764321, 8765321, 9754321, 9875321, 97654321, 98764321, 98765431}
Nim
import std/[strutils, sugar]
proc isPrime(n: int): bool =
assert n > 7
if n mod 2 == 0 or n mod 3 == 0: return false
var d = 5
var step = 2
while d * d <= n:
if n mod d == 0:
return false
inc d, step
step = 6 - step
result = true
iterator descendingPrimes(): int =
# Yield one digit primes.
for n in [2, 3, 5, 7]:
yield n
# Yield other primes by increasing length and in ascending order.
type Item = tuple[val, lastDigit: int]
var items: seq[Item] = collect(for n in 1..9: (n, n))
for ndigits in 2..9:
var nextItems: seq[Item]
for item in items:
for newDigit in 0..(item.lastDigit - 1):
let newVal = 10 * item.val + newDigit
nextItems.add (val: newVal, lastDigit: newDigit)
if newVal.isPrime():
yield newVal
items = move(nextItems)
var rank = 0
for prime in descendingPrimes():
inc rank
stdout.write ($prime).align(8)
stdout.write if rank mod 8 == 0: '\n' else: ' '
echo()
- Output:
2 3 5 7 31 41 43 53
61 71 73 83 97 421 431 521
541 631 641 643 653 743 751 761
821 853 863 941 953 971 983 5431
6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431
9521 9631 9643 9721 9743 9851 9871 75431
76421 76541 76543 86531 87421 87541 87631 87641
87643 94321 96431 97651 98321 98543 98621 98641
98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
PascalABC.NET
##
uses School;
function DescendingSeq(n: integer): sequence of integer;
begin
if n = 0 then
for var x := 9 downto 1 do
yield sequence DescendingSeq(x) + x
else for var x := n*10 + n mod 10 - 1 downto n*10 + 1 do
yield sequence DescendingSeq(x) + x;
end;
DescendingSeq(0).Order.Where(n -> n.IsPrime).Print;
- Output:
2 3 5 7 31 41 43 53 61 71 73 83 97 421 431 521 541 631 641 643 653 743 751 761 821 853 863 941 953 971 983 5431 6421 6521 7321 7541 7621 7643 8431 8521 8543 8641 8731 8741 8753 8761 9421 9431 9521 9631 9643 9721 9743 9851 9871 75431 76421 76541 76543 86531 87421 87541 87631 87641 87643 94321 96431 97651 98321 98543 98621 98641 98731 764321 865321 876431 975421 986543 987541 987631 8764321 8765321 9754321 9875321 97654321 98764321 98765431
Perl
use strict;
use warnings;
use ntheory 'is_prime';
print join( '',
sort
map { sprintf '%9d', $_ }
grep /./ && is_prime $_,
glob join '', map "{$_,}", reverse 1..9
) =~ s/.{45}\K/\n/gr;
- Output:
2 3 5 7 31
41 43 53 61 71
73 83 97 421 431
521 541 631 641 643
653 743 751 761 821
853 863 941 953 971
983 5431 6421 6521 7321
7541 7621 7643 8431 8521
8543 8641 8731 8741 8753
8761 9421 9431 9521 9631
9643 9721 9743 9851 9871
75431 76421 76541 76543 86531
87421 87541 87631 87641 87643
94321 96431 97651 98321 98543
98621 98641 98731 764321 865321
876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321
98764321 98765431
Phix
with javascript_semantics function descending_primes(sequence res, atom p=0, max_digit=9) for d=1 to max_digit do atom np = p*10+d if odd(d) and is_prime(np) then res &= np end if res = descending_primes(res,np,d-1) end for return res end function sequence r = sort(descending_primes({2})), --sequence r = descending_primes({2}), j = join_by(r,1,11," ","\n","%8d") printf(1,"There are %,d descending primes:\n%s\n",{length(r),j})
- Output:
There are 87 descending primes:
2 3 5 7 31 41 43 53 61 71 73
83 97 421 431 521 541 631 641 643 653 743
751 761 821 853 863 941 953 971 983 5431 6421
6521 7321 7541 7621 7643 8431 8521 8543 8641 8731 8741
8753 8761 9421 9431 9521 9631 9643 9721 9743 9851 9871
75431 76421 76541 76543 86531 87421 87541 87631 87641 87643 94321
96431 97651 98321 98543 98621 98641 98731 764321 865321 876431 975421
986543 987541 987631 8764321 8765321 9754321 9875321 97654321 98764321 98765431
Unsorted, ie in the order in which they are generated:
There are 87 descending primes:
2 3 31 41 421 43 431 5 521 53 541
5431 61 631 641 6421 643 6521 653 7 71 73
7321 743 751 7541 75431 761 7621 76421 7643 764321 76541
76543 821 83 8431 8521 853 8543 863 8641 86531 865321
8731 8741 87421 8753 87541 8761 87631 87641 87643 876431 8764321
8765321 941 9421 9431 94321 9521 953 9631 9643 96431 97
971 9721 9743 975421 9754321 97651 97654321 983 98321 9851 98543
98621 98641 986543 9871 98731 9875321 987541 987631 98764321 98765431
powerset
with javascript_semantics function descending_primes() sequence powerset = tagset(9), res = {} while length(powerset) do res &= filter(powerset,is_prime) sequence next = {} for i=1 to length(powerset) do for d=1 to remainder(powerset[i],10)-1 do next &= powerset[i]*10+d end for end for powerset = next end while return res end function sequence r = descending_primes(), j = join_by(r,1,11," ","\n","%8d") printf(1,"There are %,d descending primes:\n%s\n",{length(r),j})
Output same as the sorted output above, without requiring a sort.
Picat
import util.
main =>
DP = [N : S in power_set("987654321"), S != [], N = S.to_int, prime(N)].sort,
foreach({P,I} in zip(DP,1..DP.len))
printf("%9d%s",P,cond(I mod 10 == 0,"\n",""))
end,
nl,
println(len=DP.len).- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
len = 87
Prolog
© 2023
isPrime(2).
isPrime(N):-
between(3, inf, N),
N /\ 1 > 0, % odd
M is floor(sqrt(N)) - 1, % reverse 2*I+1
Max is M div 2,
forall(between(1, Max, I), N mod (2*I+1) > 0).
combi(0, _, []).
combi(N, [_|T], Comb):-
N > 0,
combi(N, T, Comb).
combi(N, [X|T], [X|Comb]):-
N > 0,
N1 is N - 1,
combi(N1, T, Comb).
descPrimes(Num):-
between(1, 9, N),
combi(N, [9, 8, 7, 6, 5, 4, 3, 2, 1], CList),
atomic_list_concat(CList, Tmp), % swi specific
atom_number(Tmp, Num), % int_list_to_number
isPrime(Num).
showList(List):-
findnsols(10, DPrim, (member(DPrim, List), writef('%9r', [DPrim])), _),
nl,
fail.
showList(_).
do:-findall(DPrim, descPrimes(DPrim), DList),
showList(DList).
- Output:
?- do.
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
true.
Python
from sympy import isprime
def descending(xs=range(10)):
for x in xs:
yield x
yield from descending(x*10 + d for d in range(x%10))
for i, p in enumerate(sorted(filter(isprime, descending()))):
print(f'{p:9d}', end=' ' if (1 + i)%8 else '\n')
print()
- Output:
2 3 5 7 31 41 43 53
61 71 73 83 97 421 431 521
541 631 641 643 653 743 751 761
821 853 863 941 953 971 983 5431
6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431
9521 9631 9643 9721 9743 9851 9871 75431
76421 76541 76543 86531 87421 87541 87631 87641
87643 94321 96431 97651 98321 98543 98621 98641
98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
Quackery
powerset is defined at Power set#Quackery, and isprime is defined at Primality by trial division#Quackery.
[ 0 swap witheach
[ swap 10 * + ] ] is digits->n ( [ --> n )
[]
' [ 9 8 7 6 5 4 3 2 1 ] powerset
witheach
[ digits->n dup isprime
iff join else drop ]
sort echo- Output:
[ 2 3 5 7 31 41 43 53 61 71 73 83 97 421 431 521 541 631 641 643 653 743 751 761 821 853 863 941 953 971 983 5431 6421 6521 7321 7541 7621 7643 8431 8521 8543 8641 8731 8741 8753 8761 9421 9431 9521 9631 9643 9721 9743 9851 9871 75431 76421 76541 76543 86531 87421 87541 87631 87641 87643 94321 96431 97651 98321 98543 98621 98641 98731 764321 865321 876431 975421 986543 987541 987631 8764321 8765321 9754321 9875321 97654321 98764321 98765431 ]
Raku
Trivial variation of Ascending primes task.
put (flat 2, 3, 5, 7, sort +*, gather (3..9).map: &recurse ).batch(10)».fmt("%8d").join: "\n";
sub recurse ($str) {
.take for ($str X~ (1, 3, 7)).grep: { .is-prime && [>] .comb };
recurse $str × 10 + $_ for 2 ..^ $str % 10;
}
- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
Ring
show("decending primes", sort(cending_primes(seq(9, 1))))
func show(title, itm)
l = len(itm); ? "" + l + " " + title + ":"
for i = 1 to l
see fmt(itm[i], 9)
if i % 5 = 0 and i < l? "" ok
next : ? ""
func seq(b, e)
res = []; d = e - b
s = d / fabs(d)
for i = b to e step s add(res, i) next
return res
func ispr(n)
if n < 2 return 0 ok
if n & 1 = 0 return n = 2 ok
if n % 3 = 0 return n = 3 ok
l = sqrt(n)
for f = 5 to l
if n % f = 0 or n % (f + 2) = 0 return false ok
next : return 1
func cending_primes(digs)
cand = [0]
pr = []
for i in digs
lcand = cand
for j in lcand
v = j * 10 + i
if ispr(v) add(pr, v) ok
add(cand, v)
next
next
return pr
func fmt(x, l)
res = " " + x
return right(res, l)- Output:
87 decending primes:
2 3 5 7 31
41 43 53 61 71
73 83 97 421 431
521 541 631 641 643
653 743 751 761 821
853 863 941 953 971
983 5431 6421 6521 7321
7541 7621 7643 8431 8521
8543 8641 8731 8741 8753
8761 9421 9431 9521 9631
9643 9721 9743 9851 9871
75431 76421 76541 76543 86531
87421 87541 87631 87641 87643
94321 96431 97651 98321 98543
98621 98641 98731 764321 865321
876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321
98764321 98765431
RPL
≪ { } → dprimes
≪ { 1 2 3 4 5 6 7 8 9 } DUP
DO
SWAP DROP { }
1 3 PICK SIZE FOR j
OVER j GET
IF DUP ISPRIME? THEN 'dprimes' OVER STO+ END
10 * LASTARG MOD OVER + → b l
≪ WHILE 'b' INCR l < REPEAT b + END ≫
NEXT
UNTIL DUP SIZE 1 ≤ END
DROP2 dprimes
≫ ≫ 'DPRIM' STO
- Output:
1: { 2 3 5 7 31 41 43 53 61 71 73 83 97 421 431 521 541 631 641 643 653 743 751 761 821 853 863 941 953 971 983 5431 6421 6521 7321 7541 7621 7643 8431 8521 8543 8641 8731 8741 8753 8761 9421 9431 9521 9631 9643 9721 9743 9851 9871 75431 76421 76541 76543 86531 87421 87541 87631 87641 87643 94321 96431 97651 98321 98543 98621 98641 98731 764321 865321 876431 975421 986543 987541 987631 8764321 8765321 9754321 9875321 97654321 98764321 98765431 }
Ruby
require 'prime'
digits = [9,8,7,6,5,4,3,2,1].to_a
res = 1.upto(digits.size).flat_map do |n|
digits.combination(n).filter_map do |set|
candidate = set.join.to_i
candidate if candidate.prime?
end.reverse
end
puts res.join(",")
- Output:
2,3,5,7,31,41,43,53,61,71,73,83,97,421,431,521,541,631,641,643,653,743,751,761,821,853,863,941,953,971,983,5431,6421,6521,7321,7541,7621,7643,8431,8521,8543,8641,8731,8741,8753,8761,9421,9431,9521,9631,9643,9721,9743,9851,9871,75431,76421,76541,76543,86531,87421,87541,87631,87641,87643,94321,96431,97651,98321,98543,98621,98641,98731,764321,865321,876431,975421,986543,987541,987631,8764321,8765321,9754321,9875321,97654321,98764321,98765431
Scala
def isPrime(n: Long): Boolean = {
@annotation.tailrec
def hasDivisor(f: Long): Boolean =
if (f * f > n) false
else if (n % f == 0 || n % (f + 2) == 0) true
else hasDivisor(f + 6)
if (n < 2) false
else if (n == 2 || n == 3) true
else if (n % 2 == 0 || n % 3 == 0) false
else {
!hasDivisor(5)
}
}
def descendingPrimes(): Seq[Int] = {
val digits = Seq(9, 8, 7, 6, 5, 4, 3, 2, 1)
val (_, primes) = digits.foldLeft((Seq(0), Seq.empty[Int])) { case ((candidates, primes), digit) =>
val newCandidates = candidates.map(_ * 10 + digit)
val newPrimes = primes ++ newCandidates.filter(isPrime)
(candidates ++ newCandidates, newPrimes)
}
primes.sorted
}
@main def main(): Unit = {
def test(): Unit = {
val primes = descendingPrimes()
val maxDigits = primes.map(_.toString.length).max
val columnsPerLine = 8
val groupedPrimes = primes.grouped(columnsPerLine)
groupedPrimes.foreach { group =>
val formattedGroup = group.map(p => String.format(s"%${maxDigits}d", Int.box(p))).mkString(" ")
println(formattedGroup)
}
}
test()
}
- Output:
2 3 5 7 31 41 43 53
61 71 73 83 97 421 431 521
541 631 641 643 653 743 751 761
821 853 863 941 953 971 983 5431
6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431
9521 9631 9643 9721 9743 9851 9871 75431
76421 76541 76543 86531 87421 87541 87631 87641
87643 94321 96431 97651 98321 98543 98621 98641
98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
Sidef
func primes_with_descending_digits(base = 10) {
var list = []
var digits = @(1..^base)
var end_digits = digits.grep { .is_coprime(base) }
list << digits.grep { .is_prime && !.is_coprime(base) }...
for k in (0 .. digits.end) {
digits.combinations(k, {|*a|
var v = a.digits2num(base)
end_digits.each {|d|
var n = (v*base + d)
next if ((n >= base) && (a[0] <= d))
list << n if n.is_prime
}
})
}
list.sort
}
var base = 10
var arr = primes_with_descending_digits(base)
say "There are #{arr.len} descending primes in base #{base}.\n"
arr.each_slice(8, {|*a|
say a.map { '%9s' % _ }.join(' ')
})
- Output:
There are 87 descending primes in base 10.
2 3 5 7 31 41 43 53
61 71 73 83 97 421 431 521
541 631 641 643 653 743 751 761
821 853 863 941 953 971 983 5431
6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431
9521 9631 9643 9721 9743 9851 9871 75431
76421 76541 76543 86531 87421 87541 87631 87641
87643 94321 96431 97651 98321 98543 98621 98641
98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
Wren
import "./perm" for Powerset
import "./math" for Int
import "./seq" for Lst
import "./fmt" for Fmt
var ps = Powerset.list((9..1).toList)
var descPrimes = ps.skip(1).map { |s| Num.fromString(s.join()) }
.where { |p| Int.isPrime(p) }
.toList
.sort()
System.print("There are %(descPrimes.count) descending primes, namely:")
Fmt.tprint("$8s", descPrimes, 10)
- Output:
There are 87 descending primes, namely:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
XPL0
include xpllib; \provides IsPrime and Sort
int I, N, Mask, Digit, A(512), Cnt;
[for I:= 0 to 511 do
[N:= 0; Mask:= I; Digit:= 9;
while Mask do
[if Mask&1 then
N:= N*10 + Digit;
Mask:= Mask>>1;
Digit:= Digit-1;
];
A(I):= N;
];
Sort(A, 512);
Cnt:= 0;
Format(9, 0);
for I:= 1 to 511 do \skip empty set
[N:= A(I);
if IsPrime(N) then
[RlOut(0, float(N));
Cnt:= Cnt+1;
if rem(Cnt/10) = 0 then CrLf(0);
];
];
]- Output:
2 3 5 7 31 41 43 53 61 71
73 83 97 421 431 521 541 631 641 643
653 743 751 761 821 853 863 941 953 971
983 5431 6421 6521 7321 7541 7621 7643 8431 8521
8543 8641 8731 8741 8753 8761 9421 9431 9521 9631
9643 9721 9743 9851 9871 75431 76421 76541 76543 86531
87421 87541 87631 87641 87643 94321 96431 97651 98321 98543
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
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