Ascending primes: Difference between revisions
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Revision as of 17:04, 3 August 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 ascending decimal digits.
Aside: Try solving without peeking at existing solutions. I had a weird idea for generating a prime sieve faster, which needless to say didn't pan out. The solution may be p(r)etty trivial but generating them quickly is at least mildly interesting. Tip: filtering all 7,027,260 primes below 123,456,789 probably won't kill you, but there is at least one significantly better and much faster way, needing a mere 511 odd/prime tests.
- See also
- Related
- Primes with digits in nondecreasing order (infinite series allowing duplicate digits, whereas this isn't and doesn't)
- Pandigital prime (whereas this is the smallest, with gaps in the used digits being permitted)
ALGOL 68
Uses Pete's hint to enumerate the 512 possible numbers.
The numbers are generated in order of the first digit, so we have to sort them.
As there are only 512 possible numbers to consider, it doesn't attempt the optimisation that the final digit can't be 4, 6 or 8 and can only be 2 or 5 if it is the only digit (also, I always forget that can't be even thing...).
<lang algol68>BEGIN # find all primes with strictly increasing 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 = d1;
FOR d2 FROM 0 TO 1 DO
INT n2 = IF d2 = 1 THEN ( n1 * 10 ) + 2 ELSE n1 FI;
FOR d3 FROM 0 TO 1 DO
INT n3 = IF d3 = 1 THEN ( n2 * 10 ) + 3 ELSE n2 FI;
FOR d4 FROM 0 TO 1 DO
INT n4 = IF d4 = 1 THEN ( n3 * 10 ) + 4 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 ) + 6 ELSE n5 FI;
FOR d7 FROM 0 TO 1 DO
INT n7 = IF d7 = 1 THEN ( n6 * 10 ) + 7 ELSE n6 FI;
FOR d8 FROM 0 TO 1 DO
INT n8 = IF d8 = 1 THEN ( n7 * 10 ) + 8 ELSE n7 FI;
FOR d9 FROM 0 TO 1 DO
INT n9 = IF d9 = 1 THEN ( n8 * 10 ) + 9 ELSE n8 FI;
IF n9 > 0 THEN
IF is probably prime( n9 ) THEN
# have a prime with strictly ascending 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 #
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</lang>
- Output:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Arturo
<lang rebol>ascending?: function [x][
initial: digits x and? [equal? sort initial initial][equal? size initial size unique initial]
]
candidates: select (1..1456789) ++ [
12345678, 12345679, 12345689, 12345789, 12346789, 12356789, 12456789, 13456789, 23456789, 123456789
] => prime?
ascendingNums: select candidates => ascending?
loop split.every:10 ascendingNums 'nums [
print map nums 'num -> pad to :string num 10
]</lang>
- Output:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
AWK
<lang AWK>
- syntax: GAWK -f ASCENDING_PRIMES.AWK
BEGIN {
start = 1
stop = 23456789
for (i=start; i<=stop; i++) {
if (is_prime(i)) {
primes++
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) {
printf("%9d%1s",i,++count%10?"":"\n")
}
}
}
printf("\n%d-%d: %d primes, %d ascending primes\n",start,stop,primes,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 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
1-23456789: 1475171 primes, 100 ascending primes
C
<lang C>/*
* Ascending primes * * Generate and show all primes with strictly ascending decimal digits. * * * Solution * * We only consider positive numbers in the range 1 to 123456789. We would * get 7027260 primes, because there are so many primes smaller than 123456789 * (see also Wolfram Alpha).On the other hand, there are only 511 distinct * nonzero positive integers having their digits arranged in ascending order. * Therefore, it is better to start with numbers that have properly arranged * digitsand then check if they are prime numbers.The method of generating * a sequence of such numbers is not indifferent.We want this sequence to be * monotonically increasing, because then additional sorting of results will * be unnecessary. It turns out that by using a queue we can easily get the * desired effect. Additionally, the algorithm then does not use recursion * (although the program probably does not have to comply with the MISRA * standard). The problem to be solved is the queue size, the a priori * assumption that 1000 is good enough, but a bit magical. */
- include <stdio.h>
- include <stdlib.h>
- include <stdbool.h>
- include <math.h>
- if UINT_MAX < 123456789
- error "we need at least 9 decimal digits (32-bit integers)"
- endif
- define MAXSIZE 1000
unsigned queue[MAXSIZE]; unsigned primes[MAXSIZE];
unsigned begin = 0; unsigned end = 0; unsigned n = 0;
bool isPrime(unsigned n)
{
if (n == 2)
{
return true;
}
if (n == 1 || n % 2 == 0)
{
return false;
}
unsigned root = sqrt(n);
for (unsigned k = 3; k <= root; k += 2)
{
if (n % k == 0)
{
return false;
}
}
return true;
}
int main(int argc, char argv[])
{
for (int k = 1; k <= 9; k++)
{
queue[end++] = k;
}
while (begin < end)
{
int value = queue[begin++];
if (isPrime(value))
{
primes[n++] = value;
}
for (int k = value % 10 + 1; k <= 9; k++)
{
queue[end++] = value * 10 + k;
}
}
for (int k = 0; k < n; k++)
{
printf("%u ", primes[k]);
}
return EXIT_SUCCESS;
}</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
C++
<lang Cpp>/*
* Ascending primes * * Generate and show all primes with strictly ascending decimal digits. * * * Solution * * We only consider positive numbers in the range 1 to 123456789. We would * get 7027260 primes, because there are so many primes smaller than 123456789 * (see also Wolfram Alpha).On the other hand, there are only 511 distinct * nonzero positive integers having their digits arranged in ascending order. * Therefore, it is better to start with numbers that have properly arranged * digitsand then check if they are prime numbers.The method of generating * a sequence of such numbers is not indifferent.We want this sequence to be * monotonically increasing, because then additional sorting of results will * be unnecessary. It turns out that by using a queue we can easily get the * desired effect. Additionally, the algorithm then does not use recursion * (although the program probably does not have to comply with the MISRA * standard). The problem to be solved is the queue size, the a priori * assumption that 1000 is good enough, but a bit magical. */
- include <cmath>
- include <iostream>
- include <queue>
- include <vector>
using namespace std;
queue<unsigned> suspected;
vector<unsigned> primes;
bool isPrime(unsigned n)
{
if (n == 0 || n == 1)
{
return false;
}
else if (n != 2)
{
if (n % 2 == 0)
{
return false;
}
else
{
unsigned root = sqrt(n);
for (unsigned k = 3; k <= root; k += 2)
{
if (n % k == 0)
{
return false;
}
}
}
}
return true;
}
int main(int argc, char argv[])
{
for (unsigned k = 1; k <= 9; k++)
{
suspected.push(k);
}
while (!suspected.empty())
{
int n = suspected.front();
suspected.pop();
if (isPrime(n))
{
primes.push_back(n);
}
// The value of n % 10 gives the least significient digit of n
//
for (unsigned k = n % 10 + 1; k <= 9; k++)
{
suspected.push(n * 10 + k);
}
}
copy(primes.begin(), primes.end(), ostream_iterator<unsigned>(cout, " "));
return EXIT_SUCCESS;
}</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
C#
<lang Csharp>using System; using System.Collections.Generic;
namespace ascendingprimes {
class Program
{
static bool isPrime(uint n)
{
if (n == 0 || n == 1)
return false;
if (n != 2)
{
if (n % 2 == 0)
return false;
uint root = (uint)Math.Sqrt(n);
for (uint k = 3; k <= root; k += 2)
if (n % k == 0)
return false;
}
return true;
}
static void Main(string[] args)
{
var queue = new Queue<uint>();
var primes = new List<uint>();
for (uint k = 1; k <= 9; k++)
queue.Enqueue(k);
while(queue.Count > 0)
{
uint n = queue.Dequeue();
if (isPrime(n))
primes.Add(n);
for (uint k = n % 10 + 1; k <= 9; k++)
queue.Enqueue(n * 10 + k);
}
foreach (uint p in primes)
{
Console.Write(p);
Console.Write(" ");
}
Console.WriteLine();
}
}
}</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // Ascending 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.. -1..1->(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>>(<)0),i*10)))([(2,3);(6,7);(8,9)],10)
|>List.concat|>List.sort|>List.iter(printf "%d "); printfn ""
</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Factor
The approach taken is to check the members of the powerset of [1..9] (of which there are only 512 if you include the empty set) for primality.
<lang factor>USING: grouping math math.combinatorics math.functions math.primes math.ranges prettyprint sequences sequences.extras ;
9 [1,b] all-subsets [ reverse 0 [ 10^ * + ] reduce-index ] [ prime? ] map-filter 10 group simple-table.</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Fortran
<lang Fortran>! Ascending primes ! ! Generate and show all primes with strictly ascending decimal digits. ! ! ! Solution ! ! We only consider positive numbers in the range 1 to 123456789. We would get ! 7027260 primes, because there are so many primes smaller than 123456789 (see ! also Wolfram Alpha). On the other hand, there are only 511 distinct positive ! integers having their digits arranged in ascending order. Therefore, it is ! better to start with numbers that have properly arranged digits and then check ! if they are prime numbers. The method of generating a sequence of such numbers ! is not indifferent. We want this sequence to be monotonically increasing, ! because then additional sorting of results will be unnecessary. It turns out ! that by using a queue we can easily get the desired effect. Additionally, the ! algorithm then does not use recursion (although the program probably does not ! have to comply with the MISRA standard). The problem to be solved is the queue ! size, the a priori assumption that 1000 is good enough, but a bit magical.
program prog
parameter (MAXSIZE = 1000) logical isprime dimension iqueue(MAXSIZE) dimension iprimes(MAXSIZE) ibegin = 1 iend = 1 n = 0
do k = 1, 9
iqueue(iend) = k
iend = iend + 1
end do
do while (ibegin .lt. iend)
iv = iqueue(ibegin)
ibegin = ibegin + 1
if (isprime(iv)) then
n = n + 1
iprimes(n) = iv
end if
lsd1 = mod(iv, 10) + 1
if (lsd1 .le. 9) then
do k = lsd1, 9
iqueue(iend) = iv * 10 + k
iend = iend + 1
end do
end if
end do
print *, (iprimes(i), i = 1, n)
end program
logical function isprime(n)
! Slightly improved algorithm for checking if a number is prime. ! First, we check the special cases: 0, 1, 2. Then we check whether ! the number is divisible by 2. If it is not divisible by two, ! we check whether it is divisible by odd numbers not greater than ! the square root of that number. ! ! Positive numbers only. BTW, negative numbers are prime numbers ! if their absolute values are prime numbers.
isprime = .FALSE.
if (n .eq. 0 .or. n .eq. 1) then
return
end if
if (n .ne. 2) then
if (mod(n, 2) .eq. 0) then
return
end if
m = n**0.5
do k = 3, m, 2
if (mod(n, k) .eq. 0) then
return
end if
end do
end if
isprime = .TRUE.
end function</lang>
- Output:
The estimated execution time is 1.5 milliseconds on the same hardware on which the Java program was run. It should be remembered that modern CPUs do not have a constant clock speed and additionally the measured times depend on the system load with other tasks. Nevertheless, the Fortran program seems to be 4 times faster than the Java program.
2 3 5 7 13 17
19 23 29 37 47 59
67 79 89 127 137 139
149 157 167 179 239 257
269 347 349 359 367 379
389 457 467 479 569 1237
1249 1259 1279 1289 1367 1459
1489 1567 1579 1789 2347 2357
2389 2459 2467 2579 2689 2789
3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569
12589 12689 13457 13469 13567 13679
13789 15679 23459 23567 23689 23789
25679 34589 34679 123457 123479 124567
124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789
1245689 1456789 12356789 23456789
Go
Using a generator. <lang go>package main
import (
"fmt" "rcu" "sort"
)
var ascPrimesSet = make(map[int]bool) // avoids duplicates
func generate(first, cand, digits int) {
if digits == 0 {
if rcu.IsPrime(cand) {
ascPrimesSet[cand] = true
}
return
}
for i := first; i < 10; i++ {
next := cand*10 + i
generate(i+1, next, digits-1)
}
}
func main() {
for digits := 1; digits < 10; digits++ {
generate(1, 0, digits)
}
le := len(ascPrimesSet)
ascPrimes := make([]int, le)
i := 0
for k := range ascPrimesSet {
ascPrimes[i] = k
i++
}
sort.Ints(ascPrimes)
fmt.Println("There are", le, "ascending primes, namely:")
for i := 0; i < le; i++ {
fmt.Printf("%8d ", ascPrimes[i])
if (i+1)%10 == 0 {
fmt.Println()
}
}
}</lang>
- Output:
There are 100 ascending primes, namely:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
J
Compare with Descending primes.
<lang J> extend=: {{ y;(1+each i._1+{.y),L:0 y }}
$(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9
100
10 10$(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9
2 3 13 23 5 7 17 37 47 67
127 137 347 157 257 457 167 367 467 1237
2347 2357 3457 1367 2467 3467 1567 4567 12347 12457
13457 13567 23567 123457 124567 19 29 59 79 89
139 239 149 349 359 269 569 179 379 479
389 1249 1259 1459 2459 3469 1279 1579 2579 4679
1289 2389 1489 2689 5689 1789 2789 4789 23459 13469
12569 12379 12479 13679 34679 15679 25679 12589 34589 12689
23689 13789 23789 123479 124679 235679 145679 345679 234589 345689
134789 125789 235789 245789 1245689 1234789 1235789 1456789 12356789 23456789
timex'(#~ 1 p: ])10#.&>([:~.@;extend each)^:# >:i.9' NB. seconds (take with grain of salt)
0.003818 </lang>
cpu here was a 1.2ghz i3-1005g1
Java
<lang Java>/*
* Ascending primes * * Generate and show all primes with strictly ascending decimal digits. * * * Solution * * We only consider positive numbers in the range 1 to 123456789. We would * get 7027260 primes, because there are so many primes smaller than 123456789 * (see also Wolfram Alpha).On the other hand, there are only 511 distinct * positive integers having their digits arranged in ascending order. * Therefore, it is better to start with numbers that have properly arranged * digits and then check if they are prime numbers.The method of generating * a sequence of such numbers is not indifferent.We want this sequence to be * monotonically increasing, because then additional sorting of results will * be unnecessary. It turns out that by using a queue we can easily get the * desired effect. Additionally, the algorithm then does not use recursion * (although the program probably does not have to comply with the MISRA * standard). The problem to be solved is the queue size, the a priori * assumption that 1000 is good enough, but a bit magical. */
package example.rossetacode.ascendingprimes;
import java.util.Arrays;
public class Program implements Runnable {
public static void main(String[] args) {
long t1 = System.nanoTime();
new Program().run();
long t2 = System.nanoTime();
System.out.println(
"total time consumed = " + (t2 - t1) * 1E-6 + " milliseconds");
}
public void run() {
final int MAX_SIZE = 1000;
final int[] queue = new int[MAX_SIZE];
int begin = 0;
int end = 0;
for (int k = 1; k <= 9; k++) {
queue[end++] = k;
}
while (begin < end) {
int n = queue[begin++];
for (int k = n % 10 + 1; k <= 9; k++) {
queue[end++] = n * 10 + k;
}
}
// We can use a parallel stream (and then sort the results)
// to use multiple cores.
//
System.out.println(Arrays.stream(queue).filter(this::isPrime).boxed().toList());
}
private boolean isPrime(int value) {
if (value == 2) {
return true;
}
if (value == 0 || value == 1 || value % 2 == 0) {
return false;
}
int root = (int) Math.sqrt(value);
for (int k = 3; k <= root; k += 2) {
if (value % k == 0) {
return false;
}
}
return true;
}
}</lang>
- Output:
[2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789] total time consumed = 4.964799999999999 milliseconds
JavaScript
<lang javascript><!DOCTYPE html> <html> <body>
<noscript> No script, no fun. Turn on Javascript on. </noscript>
<script>
(()=>{
function isPrime(n) {
if (n == 2)
return true;
if (n == 0 || n == 1 || n % 2 == 0)
return false;
root = Math.sqrt(n)
for (let k = 3; k <= root; k += 2)
if (n % k == 0)
return false;
return true;
}
let queue = []; let primes = [];
for (let k = 1; k <= 9; k++)
queue.push(k);
while (queue.length != 0)
{
let n = queue.shift();
if (isPrime(n))
primes.push(n);
for (let k = n % 10 + 1; k <= 9; k++)
queue.push(n * 10 + k);
}
document.writeln(primes);
})(); </script>
</body> </html></lang>
- Output:
2,3,5,7,13,17,19,23,29,37,47,59,67,79,89,127,137,139,149,157,167,179,239,257,269,347,349,359,367,379,389,457,467,479,569,1237,1249,1259,1279,1289,1367,1459,1489,1567,1579,1789,2347,2357,2389,2459,2467,2579,2689,2789,3457,3467,3469,4567,4679,4789,5689,12347,12379,12457,12479,12569,12589,12689,13457,13469,13567,13679,13789,15679,23459,23567,23689,23789,25679,34589,34679,123457,123479,124567,124679,125789,134789,145679,234589,235679,235789,245789,345679,345689,1234789,1235789,1245689,1456789,12356789,23456789
jq
Works with gojq, the Go implementation of jq
See Erdős-primes#jq for a suitable definition of `is_prime` as used here.
<lang jq>
- Output: the stream of ascending primes, in order
def ascendingPrimes:
# Generate the stream of primes beginning with the digit .
# and with strictly ascending digits, without regard to order
def generate:
# strings
def g:
. as $first
| tonumber as $n
| select($n <= 9)
| $first,
((range($n + 1;10) | tostring | g) as $x
| $first + $x );
tostring | g | tonumber | select(is_prime);
[range(1;10) | generate] | sort[];
def task:
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
[ascendingPrimes]
| "There are \(length) ascending primes, namely:",
( _nwise(10) | map(lpad(10)) | join(" ") );
task</lang>
- Output:
There are 100 ascending primes, namely:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Julia
<lang julia>using Combinatorics using Primes
function ascendingprimes()
return filter(isprime, [evalpoly(10, reverse(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(ascendingprimes()))
@time ascendingprimes()
</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 0.000150 seconds (2.19 k allocations: 159.078 KiB
Lua
Exactly 511 calls to is_prime required.
<lang Lua>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 ascending_primes()
local digits, candidates, primes = {1,2,3,4,5,6,7,8,9}, {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(ascending_primes(), ", "))</lang>
- Output:
2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789
Matlab
<lang matlab>queue = 1:9;
j = 1; while j < length(queue)
n = queue(j);
j = j + 1;
a = n * 10 + mod(n, 10) + 1;
b = n * 10 + 9;
if a <= b
queue = [queue, a:b];
end
end
queue(isprime(queue))</lang>
- Output:
ans =
Columns 1 through 8
2 3 5 7 13 17 19 23
Columns 9 through 16
29 37 47 59 67 79 89 127
Columns 17 through 24
137 139 149 157 167 179 239 257
Columns 25 through 32
269 347 349 359 367 379 389 457
Columns 33 through 40
467 479 569 1237 1249 1259 1279 1289
Columns 41 through 48
1367 1459 1489 1567 1579 1789 2347 2357
Columns 49 through 56
2389 2459 2467 2579 2689 2789 3457 3467
Columns 57 through 64
3469 4567 4679 4789 5689 12347 12379 12457
Columns 65 through 72
12479 12569 12589 12689 13457 13469 13567 13679
Columns 73 through 80
13789 15679 23459 23567 23689 23789 25679 34589
Columns 81 through 88
34679 123457 123479 124567 124679 125789 134789 145679
Columns 89 through 96
234589 235679 235789 245789 345679 345689 1234789 1235789
Columns 97 through 100
1245689 1456789 12356789 23456789
Mathematica/Wolfram Language
<lang Mathematica>ps=Sort@Select[FromDigits /@ Subsets[Range@9, {1, \[Infinity]}], PrimeQ]; Multicolumn[ps, {Automatic, 6}, Appearance -> "Horizontal"]</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Pascal
<lang pascal>{$mode Delphi}
{ Note that for the program to work properly,
integer variables must be at least 28-bit. Free Pascal Compiler uses 16-bit integers by default, so a directive like above is needed. }
program ascendingprimes(output);
const maxsize = 1000;
var
queue, primes : array[1..maxsize] of integer; b, e, n, k, v : integer;
function isprime(n: integer): boolean;
var
ans : boolean;
root, k : integer;
begin
ans := false;
if (n <> 0) and (n <> 1) then
begin
if n = 2 then
ans := true
else if (n mod 2) <> 0 then
begin
ans := true;
root := trunc(sqrt(n));
k := 3;
while (k <= root) and ans do
if n mod k = 0 then
ans := false
else
k := k + 2;
end
end;
isprime := ans
end;
begin
b := 1; e := 1; n := 0;
for k := 1 to 9 do begin queue[e] := k; e := e + 1 end;
while b < e do
begin
v := queue[b];
b := b + 1;
if isprime(v) then
begin
n := n + 1;
primes[n] := v
end;
for k := v mod 10 + 1 to 9 do
begin
queue[e] := v * 10 + k;
e := e + 1
end
end;
for k := 1 to n do write(primes[k], ' '); writeln()
end.</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Perl
<lang perl>#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Ascending_primes use warnings; use ntheory qw( is_prime );
print join(, map { sprintf "%10d", $_ } sort { $a <=> $b }
grep /./ && is_prime($_),
glob join , map "{$_,}", 1 .. 9) =~ s/.{50}\K/\n/gr;</lang>
- Output:
2 3 5 7 13
17 19 23 29 37
47 59 67 79 89
127 137 139 149 157
167 179 239 257 269
347 349 359 367 379
389 457 467 479 569
1237 1249 1259 1279 1289
1367 1459 1489 1567 1579
1789 2347 2357 2389 2459
2467 2579 2689 2789 3457
3467 3469 4567 4679 4789
5689 12347 12379 12457 12479
12569 12589 12689 13457 13469
13567 13679 13789 15679 23459
23567 23689 23789 25679 34589
34679 123457 123479 124567 124679
125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789
1235789 1245689 1456789 12356789 23456789
Phix
with javascript_semantics function ascending_primes(sequence res, atom p=0) for d=remainder(p,10)+1 to 9 do integer np = p*10+d if odd(d) and is_prime(np) then res &= np end if res = ascending_primes(res,np) end for return res end function sequence r = apply(true,sprintf,{{"%8d"},sort(ascending_primes({2}))}) printf(1,"There are %,d ascending primes:\n%s\n",{length(r),join_by(r,1,10," ")})
- Output:
There are 100 ascending primes:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
powerset
Using a powerset, the basic idea of which was taken from the Factor entry above, here incrementally built, does not need either recursion or a sort, same output
with javascript_semantics function ascending_primes() sequence res = {}, powerset = {0} while length(powerset) do sequence next = {} for i=1 to length(powerset) do for d=remainder(powerset[i],10)+1 to 9 do next &= powerset[i]*10+d end for end for powerset = next res &= filter(powerset,is_prime) end while return res end function sequence r = apply(true,sprintf,{{"%8d"},ascending_primes()}) printf(1,"There are %,d ascending primes:\n%s\n",{length(r),join_by(r,1,10," ")})
By way of explanation, specifically "no sort rqd", if you pp(shorten(powerset,"entries",3)) at the end of each iteration then you get:
{1,2,3, `...`, 7,8,9, ` (9 entries)`}
{12,13,14, `...`, 78,79,89, ` (36 entries)`}
{123,124,125, `...`, 679,689,789, ` (84 entries)`}
{1234,1235,1236, `...`, 5689,5789,6789, ` (126 entries)`}
{12345,12346,12347, `...`, 45789,46789,56789, ` (126 entries)`}
{123456,123457,123458, `...`, 346789,356789,456789, ` (84 entries)`}
{1234567,1234568,1234569, `...`, 2356789,2456789,3456789, ` (36 entries)`}
{12345678,12345679,12345689, `...`, 12456789,13456789,23456789, ` (9 entries)`}
{123456789}
{}
PHP
<lang php><?php
function isPrime($n) {
if ($n == 0 || $n == 1)
return false;
if ($n == 2)
return true;
if ($n % 2 == 0)
return false;
$root = intval(sqrt($n));
for ($k = 3; $k <= $root; $k += 2)
if ($n % $k == 0)
return false;
return true;
}
$queue = []; $primes = [];
$begin = 0; $end = 0;
for ($k = 1; $k <= 9; $k++)
$queue[$end++] = $k;
while ($begin < $end) {
$n = $queue[$begin++];
if (isPrime($n))
$primes[] = $n;
for ($k = $n % 10 + 1; $k <= 9; $k++)
$queue[$end++] = $n * 10 + $k;
}
foreach($primes as $p)
echo "$p ";</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Picat
<lang Picat>import util.
main =>
DP = [N : S in power_set("123456789"), 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)</lang>
- Output:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
len = 100
PicoLisp
<lang PicoLisp>(de prime? (N)
(or
(= N 2)
(and
(> N 1)
(bit? 1 N)
(for (D 3 T (+ D 2))
(T (> D (sqrt N)) T)
(T (=0 (% N D)) NIL) ) ) ) )
(let
(D 2
L (1 2 2 . (4 2 4 2 4 6 2 6 .))
Lst
(make
(while (>= 23456789 D)
(and
(prime? D)
(apply < (chop D))
(link D) )
(inc 'D (++ L)) ) ) )
(let Fmt (need 10 10)
(while (cut 10 'Lst)
(apply tab @ Fmt) ) ) )</lang>
- Output:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Python
Recursive solution, with a number generator and sorting of results.
<lang Python>from sympy import isprime
def ascending(x=0):
for y in range(x*10 + (x%10) + 1, x*10 + 10):
yield from ascending(y)
yield(y)
print(sorted(x for x in ascending() if isprime(x)))</lang>
- Output:
[2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789]
Queue-based solution that does not need sorting.
<lang python>def isprime(n):
if n == 2: return True
if n == 0 or n == 1 or n % 2 == 0: return False
root1 = int(n**0.5) + 1;
for k in range(3, root1, 2):
if n % k == 0: return False
return True
queue = [k for k in range(1, 10)] primes = []
while queue:
n = queue.pop(0)
if isprime(n):
primes.append(n)
queue.extend(n * 10 + k for k in range(n % 10 + 1, 10))
print(primes)</lang>
- Output:
[2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 127, 137, 139, 149, 157, 167, 179, 239, 257, 269, 347, 349, 359, 367, 379, 389, 457, 467, 479, 569, 1237, 1249, 1259, 1279, 1289, 1367, 1459, 1489, 1567, 1579, 1789, 2347, 2357, 2389, 2459, 2467, 2579, 2689, 2789, 3457, 3467, 3469, 4567, 4679, 4789, 5689, 12347, 12379, 12457, 12479, 12569, 12589, 12689, 13457, 13469, 13567, 13679, 13789, 15679, 23459, 23567, 23689, 23789, 25679, 34589, 34679, 123457, 123479, 124567, 124679, 125789, 134789, 145679, 234589, 235679, 235789, 245789, 345679, 345689, 1234789, 1235789, 1245689, 1456789, 12356789, 23456789]
Quackery
powerset is defined at Power set#Quackery, and isprime is defined at Primality by trial division#Quackery.
<lang Quackery> [ 0 swap witheach
[ swap 10 * + ] ] is digits->n ( [ --> n )
[]
' [ 1 2 3 4 5 6 7 8 9 ] powerset
witheach
[ digits->n dup isprime
iff join else drop ]
sort echo</lang>
- Output:
[ 2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789 ]
Raku
<lang perl6>put (flat 2, 3, 5, 7, sort +*, gather (1..8).map: &recurse ).batch(10)».fmt("%8d").join: "\n";
sub recurse ($str) {
.take for ($str X~ (3, 7, 9)).grep: { .is-prime && [<] .comb };
recurse $str × 10 + $_ for $str % 10 ^.. 9;
}
printf "%.3f seconds", now - INIT now;</lang>
- Output:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
0.075 seconds
Ring
<lang ring>show("ascending primes", sort(cending_primes(seq(1, 9))))
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)</lang>
- Output:
100 ascending primes:
2 3 5 7 13
17 19 23 29 37
47 59 67 79 89
127 137 139 149 157
167 179 239 257 269
347 349 359 367 379
389 457 467 479 569
1237 1249 1259 1279 1289
1367 1459 1489 1567 1579
1789 2347 2357 2389 2459
2467 2579 2689 2789 3457
3467 3469 4567 4679 4789
5689 12347 12379 12457 12479
12569 12589 12689 13457 13469
13567 13679 13789 15679 23459
23567 23689 23789 25679 34589
34679 123457 123479 124567 124679
125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789
1235789 1245689 1456789 12356789 23456789
Ruby
<lang ruby>require 'prime'
digits = [9,8,7,6,5,4,3,2,1] 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(",")</lang>
- Output:
2,3,5,7,13,17,19,23,29,37,47,59,67,79,89,127,137,139,149,157,167,179,239,257,269,347,349,359,367,379,389,457,467,479,569,1237,1249,1259,1279,1289,1367,1459,1489,1567,1579,1789,2347,2357,2389,2459,2467,2579,2689,2789,3457,3467,3469,4567,4679,4789,5689,12347,12379,12457,12479,12569,12589,12689,13457,13469,13567,13679,13789,15679,23459,23567,23689,23789,25679,34589,34679,123457,123479,124567,124679,125789,134789,145679,234589,235679,235789,245789,345679,345689,1234789,1235789,1245689,1456789,12356789,23456789
Sidef
<lang ruby>func primes_with_ascending_digits(base = 10) {
var list = [] var digits = @(1..^base -> flip)
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 arr = primes_with_ascending_digits()
say "There are #{arr.len} ascending primes.\n"
arr.each_slice(10, {|*a|
say a.map { '%8s' % _ }.join(' ')
})</lang>
- Output:
There are 100 ascending primes.
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Visual Basic .NET
<lang vbnet>Module AscendingPrimes
Function isPrime(n As Integer)
n = Math.Abs(n)
If n = 2 Then
Return True
End If
If n = 0 Or n = 1 Or n Mod 2 = 0 Then
Return False
End If
Dim root As Integer = Math.Sqrt(n)
For k = 3 To root Step 2
If n Mod k = 0 Then
Return False
End If
Next
Return True
End Function
Sub Main()
Dim queue As Queue(Of Integer) = New Queue(Of Integer)
Dim primes As List(Of Integer) = New List(Of Integer)
For k = 1 To 9
queue.Enqueue(k)
Next
While queue.Count > 0
Dim n As Integer = queue.Dequeue()
If (isPrime(n)) Then
primes.Add(n)
End If
For k = n Mod 10 + 1 To 9
queue.Enqueue(n * 10 + k)
Next
End While
For Each p As Integer In primes
Console.Write(p)
Console.Write(" ")
Next
Console.WriteLine()
End Sub
End Module</lang>
- Output:
2 3 5 7 13 17 19 23 29 37 47 59 67 79 89 127 137 139 149 157 167 179 239 257 269 347 349 359 367 379 389 457 467 479 569 1237 1249 1259 1279 1289 1367 1459 1489 1567 1579 1789 2347 2357 2389 2459 2467 2579 2689 2789 3457 3467 3469 4567 4679 4789 5689 12347 12379 12457 12479 12569 12589 12689 13457 13469 13567 13679 13789 15679 23459 23567 23689 23789 25679 34589 34679 123457 123479 124567 124679 125789 134789 145679 234589 235679 235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Vlang
<lang vlang>fn is_prime(n int) bool {
if n < 2 {
return false
} else if n%2 == 0 {
return n == 2
} else if n%3 == 0 {
return n == 3
} else {
mut d := 5
for d*d <= n {
if n%d == 0 {
return false
}
d += 2
if n%d == 0 {
return false
}
d += 4
}
return true
}
} fn generate(first int, cand int, digits int, mut asc map[int]bool) {
if digits == 0 {
if is_prime(cand) {
asc[cand] = true
}
return
}
for i in first..10 {
next := cand*10 + i
generate(i+1, next, digits-1, mut asc)
}
}
fn main() {
mut asc_primes_set := map[int]bool{} // avoids duplicates
for digits in 1..10 {
generate(1, 0, digits, mut asc_primes_set)
}
le := asc_primes_set.keys().len
mut asc_primes := []int{len: le}
mut i := 0
for k,_ in asc_primes_set {
asc_primes[i] = k
i++
}
asc_primes.sort()
println("There are $le ascending primes, namely:")
for q in 0..le {
print("${asc_primes[q]:8} ")
if (q+1)%10 == 0 {
println()
}
}
}</lang>
- Output:
There are 100 ascending primes, namely:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Wren
Version 1 (Sieve)
Although they use a lot of memory, sieves usually produce good results in Wren and here we only need to sieve for primes up to 3456789 as there are just 9 possible candidates with 8 digits and 1 possible candidate with 9 digits which we can test for primality individually. The following runs in around 0.43 seconds. <lang ecmascript>import "./math" for Int import "./seq" for Lst import "./fmt" for Fmt
var isAscending = Fn.new { |n|
if (n < 10) return true
var digits = Int.digits(n)
for (i in 1...digits.count) {
if (digits[i] <= digits[i-1]) return false
}
return true
}
var higherPrimes = [] var candidates = [
12345678, 12345679, 12345689, 12345789, 12346789, 12356789, 12456789, 13456789, 23456789, 123456789
] for (cand in candidates) if (Int.isPrime(cand)) higherPrimes.add(cand)
var primes = Int.primeSieve(3456789) var ascPrimes = [] for (p in primes) if (isAscending.call(p)) ascPrimes.add(p) ascPrimes.addAll(higherPrimes) System.print("There are %(ascPrimes.count) ascending primes, namely:") for (chunk in Lst.chunks(ascPrimes, 10)) Fmt.print("$8d", chunk)</lang>
- Output:
There are 100 ascending primes, namely:
2 3 5 7 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
Version 2 (Generator)
Here we generate all possible positive integers with ascending non-zero digits and filter out those that are prime.
Much quicker than the 'sieve' approach at 0.013 seconds. I also tried using a powerset but that was slightly slower at 0.015 seconds. <lang ecmascript>import "./set" for Set import "./math" for Int import "./seq" for Lst import "./fmt" for Fmt
var ascPrimes = Set.new() // avoids duplicates
var generate // recursive function generate = Fn.new { |first, cand, digits|
if (digits == 0) {
if (Int.isPrime(cand)) ascPrimes.add(cand)
return
}
var i = first
while (i <= 9) {
var next = cand * 10 + i
generate.call(i + 1, next, digits - 1)
i = i + 1
}
}
for (digits in 1..9) generate.call(1, 0, digits) ascPrimes = ascPrimes.toList ascPrimes.sort() System.print("There are %(ascPrimes.count) ascending primes, namely:") for (chunk in Lst.chunks(ascPrimes, 10)) Fmt.print("$8s", chunk)</lang>
- Output:
Same as before.
XPL0
Brute force solution: 4.3 seconds on Pi4. <lang XPL0>func IsPrime(N); \Return 'true' if N is prime int N, I; [if N <= 2 then return N = 2; if (N&1) = 0 then \even >2\ return false; for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false; I:= I+1; ];
return true; ];
func Ascending(N); \Return 'true' if digits are ascending int N, D; [N:= N/10; D:= rem(0); while N do
[N:= N/10; if rem(0) >= D then return false; D:= rem(0); ];
return true; ];
int Cnt, N; [Cnt:= 0; Format(9, 0); for N:= 2 to 123_456_789 do
if Ascending(N) then
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 13 17 19 23 29 37
47 59 67 79 89 127 137 139 149 157
167 179 239 257 269 347 349 359 367 379
389 457 467 479 569 1237 1249 1259 1279 1289
1367 1459 1489 1567 1579 1789 2347 2357 2389 2459
2467 2579 2689 2789 3457 3467 3469 4567 4679 4789
5689 12347 12379 12457 12479 12569 12589 12689 13457 13469
13567 13679 13789 15679 23459 23567 23689 23789 25679 34589
34679 123457 123479 124567 124679 125789 134789 145679 234589 235679
235789 245789 345679 345689 1234789 1235789 1245689 1456789 12356789 23456789
powerset
Aaah! Power set, from Factor. Runs in less than 1 millisecond. A better way of measuring duration than using Linux's time utility gave a more credible 35 milliseconds. <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:= 1;
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:
Same as before.
- Programming Tasks
- Solutions by Programming Task
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