Descending primes: Difference between revisions
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Line 157:
98621 98641 98731 764321 865321 876431 975421 986543 987541 987631
8764321 8765321 9754321 9875321 97654321 98764321 98765431
</pre>
=={{header|ALGOL W}}==
{{Trans|Lua}}
...and only a few characters different from the Algol W [[Ascending primes]] sample.
<syntaxhighlight lang="algolw">
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.
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
Line 421 ⟶ 521:
S:=S+Format('%12.0n', [I*1.0]);
Inc(Cnt);
if (Cnt mod
begin
Memo.Lines.Add(S);
Line 431 ⟶ 531:
Memo.Lines.Add('Descending Primes Found: '+IntToStr(Cnt));
end;
Line 437 ⟶ 536:
{{out}}
<pre>
2 3 5 7 31 41 43 53
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
</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang=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
.
</syntaxhighlight>
Line 462 ⟶ 593:
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
</pre>
=={{header|Factor}}==
{{works with|Factor|0.99 2021-06-02}}
Line 585 ⟶ 717:
</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="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
</syntaxhighlight>
{{output}}
<pre>
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
</pre>
=={{header|Go}}==
{{trans|Wren}}
Line 667 ⟶ 866:
=={{header|J}}==
Compare with [[Ascending_primes#J|Ascending primes]].
<syntaxhighlight lang="j"> 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</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="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;
}
}
</syntaxhighlight>
{{ out }}
<pre>
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.
</pre>
=={{header|jq}}==
Line 792 ⟶ 1,056:
<pre>{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}</pre>
=={{header|
<syntaxhighlight lang="
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()
</syntaxhighlight>
{{out}}
<pre> 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
</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<syntaxhighlight lang="perl">
use strict;
use warnings;
use ntheory
print join( '',
sort
map { sprintf '%9d', $_ }
grep /./ && is_prime $_,
glob join '', map "{$_,}", reverse 1..9
) =~ s/.{45}\K/\n/gr;
</syntaxhighlight>
{{out}}
<pre>
Line 911 ⟶ 1,236:
8764321 8765321 9754321 9875321 97654321 98764321 98765431
len = 87</pre>
=={{header|Prolog}}==
{{works with|swi-prolog}}© 2023<syntaxhighlight lang="prolog">
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).
</syntaxhighlight>
{{out}}
<pre>
?- 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.
</pre>
=={{header|Python}}==
Line 1,036 ⟶ 1,410:
8764321 8765321 9754321 9875321 97654321
98764321 98765431</pre>
=={{header|RPL}}==
{{trans|C#}}
{{works with|HP|49g}}
≪ { } → 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
≫ ≫ '<span style="color:blue">DPRIM</span>' STO
{{out}}
<pre>
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 }
</pre>
=={{header|Ruby}}==
Line 1,104 ⟶ 1,499:
{{libheader|Wren-perm}}
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./math" for Int
import "./seq" for Lst
Line 1,117 ⟶ 1,511:
.sort()
System.print("There are %(descPrimes.count) descending primes, namely:")
{{out}}
| |||