Descending primes: Difference between revisions
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=={{header|Arturo}}== |
=={{header|Arturo}}== |
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{{trans|ALGOL 68}} |
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<lang rebol>descending: @[ |
<lang rebol>descending: @[ |
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loop 1..9 'a [ |
loop 1..9 'a [ |
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Revision as of 14:34, 16 May 2022
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
ALGOL 68
Almost identical to the Ascending_primes Algol 68 sample.
<lang algol68>BEGIN # find all primes with strictly decreasing digits #
PR read "primes.incl.a68" PR # include prime utilities #
PR read "rows.incl.a68" PR # include array 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 descending digits #
primes[ p count +:= 1 ] := n9
FI
FI
OD
OD
OD
OD
OD
OD
OD
OD
OD;
QUICKSORT primes FROMELEMENT 1 TOELEMENT p count; # sort the primes #
# display the primes #
FOR i TO p count DO
print( ( " ", whole( primes[ i ], -8 ) ) );
IF i MOD 10 = 0 THEN print( ( newline ) ) FI
OD
END</lang>
- 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
<lang rebol>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
]</lang>
- 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
<lang 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)
} </lang>
- 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
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // 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 ""
</lang>
- 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
<lang 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.</lang>
- 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
Go
<lang 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()
}</lang>
- 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 (focusing on the computational details, rather than the presentation).
<lang J> extend=: {{ y;y,L:0(1+each i.1-{:y)}}
($~ q:@$)(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9 2 3 31 43 41 431 421 5 53 541 521 5431 61 653 643 641 631 6521 6421 7 73 71 761 751 743 7643 7621 7541 7321
76543 76541 76421 75431 764321 83 863 853 821 8761 8753 8741 8731 8641 8543 8521 8431 87643 87641 87631 87541 87421 86531 876431 865321 8765321 8764321 97 983
971 953 941 9871 9851 9743 9721 9643 9631 9521 9431 9421 98731 98641 98621 98543 98321 97651 96431 94321 987631 987541 986543 975421 9875321 9754321 98765431 98764321 97654321</lang>
Julia
<lang 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()))
</lang>
- 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
<lang perl>#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Descending_primes use warnings; use ntheory qw( is_prime );
print join(, sort map { sprintf "%9d", $_ } grep /./ && is_prime($_),
glob join , map "{$_,}", reverse 1 .. 9) =~ s/.{45}\K/\n/gr;</lang>
- 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.
Raku
Trivial variation of Ascending primes task.
<lang perl6>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;
}</lang>
- 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
<lang ring> load "stdlibcore.ring"
limit = 1000 row = 0
for n = 1 to limit
flag = 0
strn = string(n)
if isprime(n) = 1
for m = 1 to len(strn)-1
if number(substr(strn,m)) < number(substr(strn,m+1))
flag = 1
ok
next
if flag = 1
row++
see "" + n + " "
ok
if row % 10 = 0
see nl
ok
ok
next
</lang>
Output:
2 3 5 7 11 13 17 19 23 29
31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107 109 113
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733
739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863
877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997
Sidef
<lang ruby>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(' ')
})</lang>
- 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
<lang ecmascript>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:") for (chunk in Lst.chunks(descPrimes, 10)) Fmt.print("$8s", chunk)</lang>
- 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
<lang 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);
];
];
]</lang>
- 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