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Composite numbers k with no single digit factors whose factors are all substrings of k (view source)

Revision as of 23:38, 23 February 2024

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Line 1:
{{draft task}}
 
Find the composite numbers '''k''' in base 10, that have no single digit prime factors and whose prime factors are all a substring of '''k'''.
Line 16:
 
 
 
=={{header|ALGOL 68}}==
<syntaxhighlight lang="algol68">BEGIN # find composite k with no single digit factors whose factors are all substrings of k #
# returns TRUE if the string representation of f is a substring of k str, FALSE otherwise #
PROC is substring = ( STRING k str, INT f )BOOL:
BEGIN
STRING f str = whole( f, 0 );
INT f len = ( UPB f str - LWB f str ) + 1;
BOOL result := FALSE;
INT f end := ( LWB k str + f len ) - 2;
FOR f pos FROM LWB k str TO ( UPB k str + 1 ) - f len WHILE NOT result DO
f end +:= 1;
result := k str[ f pos : f end ] = f str
OD;
result
END # is substring # ;
# task #
INT required numbers = 20;
INT k count := 0;
# k must be odd and > 9 #
FOR k FROM 11 BY 2 WHILE k count < required numbers DO
IF k MOD 3 /= 0 AND k MOD 5 /= 0 AND k MOD 7 /= 0 THEN
# no single digit odd prime factors #
BOOL is candidate := TRUE;
STRING k str = whole( k, 0 );
INT v := k;
INT f count := 0;
FOR f FROM 11 BY 2 TO ENTIER sqrt( k ) + 1 WHILE v > 1 AND is candidate DO
IF v MOD f = 0 THEN
# have a factor #
is candidate := is substring( k str, f );
IF is candidate THEN
# the digits of f ae a substring of v #
WHILE v OVERAB f;
f count +:= 1;
v MOD f = 0
DO SKIP OD
FI
FI
OD;
IF is candidate AND ( f count > 1 OR ( v /= k AND v > 1 ) ) THEN
# have a composite whose factors are up to the root are substrings #
IF v > 1 THEN
# there was a factor > the root #
is candidate := is substring( k str, v )
FI;
IF is candidate THEN
print( ( " ", whole( k, -8 ) ) );
k count +:= 1;
IF k count MOD 10 = 0 THEN print( ( newline ) ) FI
FI
FI
FI
OD
END</syntaxhighlight>
{{out}}
<pre>
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
</pre>
 
=={{header|Arturo}}==
 
<syntaxhighlight lang="rebol">valid?: function [n][
pf: factors.prime n
every? pf 'f ->
and? [contains? to :string n to :string f]
[1 <> size digits f]
]
 
cnt: 0
i: new 3
 
while [cnt < 10][
if and? [not? prime? i][valid? i][
print i
cnt: cnt + 1
]
'i + 2
]</syntaxhighlight>
 
{{out}}
 
<pre>15317
59177
83731
119911
183347
192413
1819231
2111317
2237411
3129361</pre>
 
=={{header|C}}==
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdbool.h>
 
bool is_substring(unsigned n, unsigned k) {
unsigned startMatch = 0;
 
for (unsigned pfx = k; n > 0; n /= 10) {
if (pfx % 10 == n % 10) {
pfx /= 10;
if (startMatch == 0) startMatch = n;
} else {
pfx = k;
if (startMatch != 0) n = startMatch;
startMatch = 0;
}
 
if (pfx == 0) return true;
}
return false;
}
 
bool factors_are_substrings(unsigned n) {
if (n%2==0 || n%3==0 || n%5==0 || n%7==0) return false;
 
unsigned factor_count = 0;
for (unsigned factor = 11, n_rest = n; factor <= n_rest; factor += 2) {
if (n_rest % factor != 0) continue;
while (n_rest % factor == 0) n_rest /= factor;
if (!is_substring(n, factor)) return false;
factor_count++;
}
return factor_count > 1;
}
 
int main(void) {
unsigned amount = 10;
for (unsigned n = 11; amount > 0; n += 2) {
if (factors_are_substrings(n)) {
printf("%u\n", n);
amount--;
}
}
return 0;
}</syntaxhighlight>
{{out}}
<pre>15317
59177
83731
119911
183347
192413
1819231
2111317
2237411
3129361</pre>
 
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <algorithm>
#include <cstdint>
#include <iostream>
#include <string>
#include <unordered_set>
#include <vector>
 
std::vector<uint32_t> primes;
 
void sieve_primes(const uint32_t& limit) {
std::vector<bool> marked_prime(limit + 1, true);
 
for ( uint32_t p = 2; p * p <= limit; ++p ) {
if ( marked_prime[p] ) {
for ( uint32_t i = p * p; i <= limit; i += p ) {
marked_prime[i] = false;
}
}
}
 
for ( uint32_t p = 2; p <= limit; ++p ) {
if ( marked_prime[p] ) {
primes.emplace_back(p);
}
}
}
 
bool is_substring(const uint32_t& k, const uint32_t& factor) {
const std::string string_k = std::to_string(k);
const std::string string_factor = std::to_string(factor);
return string_k.find(string_factor) != std::string::npos;
}
 
int main() {
sieve_primes(30'000'000);
 
std::unordered_set<uint32_t> distinct_factors;
std::vector<uint32_t> result;
uint32_t k = 11 * 11;
 
while ( result.size() < 10 ) {
while ( k % 3 == 0 || k % 5 == 0 || k % 7 == 0 ) {
k += 2;
}
 
distinct_factors.clear();
uint32_t copy_k = k;
uint32_t index = 4;
 
while ( copy_k > 1 ) {
while ( copy_k % primes[index] == 0 ) {
distinct_factors.insert(primes[index]);
copy_k /= primes[index];
}
index += 1;
}
 
if ( distinct_factors.size() > 1 ) {
if ( std::all_of(distinct_factors.begin(), distinct_factors.end(),
[&k](uint32_t factor) { return is_substring(k, factor); }) ) {
result.emplace_back(k);
}
}
 
k += 2;
}
 
for ( uint64_t i = 0; i < result.size(); ++i ) {
std::cout << result[i] << " ";
}
std::cout << std::endl;
}
</syntaxhighlight>
{{ out }}
<pre>
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
</pre>
 
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
Brute force method with a few obvious optimizations. Could be speeded up a lot, with some work.
 
<syntaxhighlight lang="Delphi">
 
 
 
procedure MultidigitComposites(Memo: TMemo);
var I,Cnt: integer;
var IA: TIntegerDynArray;
var Sieve: TPrimeSieve;
 
 
function MatchCriteria(N: integer): boolean;
{Test N against Criteria}
var I,L: integer;
var SN,ST: string;
begin
Result:=False;
{No even numbers}
if (N and 1)=0 then exit;
{N can't be prime}
if Sieve[N] then exit;
I:=3;
SN:=IntToStr(N);
repeat
begin
{Is it a factor }
if (N mod I) = 0 then
begin
{No one-digit numbers}
if I<10 then exit;
{Factor string must be found in N's string}
ST:=IntToStr(I);
if Pos(ST,SN)<1 then exit;
N:=N div I;
end
else I:=I+2;
end
until N<=1;
Result:=True;
end;
 
 
begin
Sieve:=TPrimeSieve.Create;
try
{Create 30 million primes}
Sieve.Intialize(30000000);
Cnt:=0;
{Smallest prime factor}
I:=11*11;
while I<High(integer) do
begin
{Test if I matches criteria}
if MatchCriteria(I) then
begin
Inc(Cnt);
Memo.Lines.Add(IntToStr(Cnt)+' - '+FloatToStrF(I,ffNumber,18,0));
if Cnt>=20 then break;
end;
Inc(I,2);
end;
finally Sieve.Free; end;
end;
 
</syntaxhighlight>
{{out}}
<pre>
1 - 15,317
2 - 59,177
3 - 83,731
4 - 119,911
5 - 183,347
6 - 192,413
7 - 1,819,231
8 - 2,111,317
9 - 2,237,411
10 - 3,129,361
11 - 5,526,173
12 - 11,610,313
13 - 13,436,683
14 - 13,731,373
15 - 13,737,841
16 - 13,831,103
17 - 15,813,251
18 - 17,692,313
19 - 19,173,071
20 - 28,118,827
Elapsed Time: 02:39.291 min
</pre>
 
=={{header|EasyLang}}==
{{trans|C}} (optimized)
<syntaxhighlight>
fastfunc isin n k .
h = k
while n > 0
if h mod 10 = n mod 10
h = h div 10
if match = 0
match = n
.
else
h = k
if match <> 0
n = match
.
match = 0
.
if h = 0
return 1
.
n = n div 10
.
return 0
.
 
fastfunc test n .
if n mod 2 = 0 or n mod 3 = 0 or n mod 5 = 0 or n mod 7 = 0
return 0
.
rest = n
fact = 11
while fact <= rest
if rest mod fact = 0
while rest mod fact = 0
rest /= fact
.
if isin n fact = 0
return 0
.
nfacts += 1
.
fact += 2
if fact > sqrt n and nfacts = 0
return 0
.
.
if nfacts > 1
return 1
.
return 0
.
n = 11
while count < 10
if test n = 1
print n
count += 1
.
n += 2
.
</syntaxhighlight>
 
=={{header|F_Sharp|F#}}==
Can anything be described as a translation of J? I use a wheel as described in J's comments, but of course I use numerical methods not euyuk! strings.
<syntaxhighlight lang="fsharp">
// Composite numbers k with no single digit factors whose factors are all substrings of k. Nigel Galloway: January 28th., 2022
let fG n g=let rec fN i g e l=match i<g,g=0L,i%10L=g%10L with (true,_,_)->false |(_,true,_)->true |(_,_,true)->fN(i/10L)(g/10L) e l |_->fN l e e (l/10L) in fN n g g (n/10L)
let fN(g:int64)=Open.Numeric.Primes.Prime.Factors g|>Seq.skip 1|>Seq.distinct|>Seq.forall(fun n->fG g n)
Seq.unfold(fun n->Some(n|>List.filter(fun(n:int64)->not(Open.Numeric.Primes.Prime.Numbers.IsPrime &n) && fN n),n|>List.map((+)210L)))([1L..2L..209L]
|>List.filter(fun n->n%3L>0L && n%5L>0L && n%7L>0L))|>Seq.concat|>Seq.skip 1|>Seq.take 20|>Seq.iter(printfn "%d")
</syntaxhighlight>
{{out}}
<pre>
15317
59177
83731
119911
183347
192413
1819231
2111317
2237411
3129361
5526173
11610313
13436683
13731373
13737841
13831103
15813251
17692313
19173071
28118827
Real: 00:00:26.059
</pre>
 
=={{header|FreeBASIC}}==
{{trans|ALGOL 68}}
<syntaxhighlight lang="vbnet">Function isSubstring(kStr As String, f As Integer) As Integer
Dim As String fStr = Str(f)
Dim As Integer fLen = Len(fStr)
Dim As Integer result = 0
Dim As Integer fEnd = Len(kStr) - fLen + 1
For fPos As Integer = 1 To Len(kStr) - fLen + 1
If Mid(kStr, fPos, fLen) = fStr Then
result = -1
Exit For
End If
Next fPos
Return result
End Function
 
Dim As Integer requiredNumbers = 20
Dim As Integer kCount = 0
For k As Integer = 11 To 99999999 Step 2
If k Mod 3 <> 0 And k Mod 5 <> 0 And k Mod 7 <> 0 Then
Dim As Integer isCandidate = -1
Dim As String kStr = Str(k)
Dim As Integer v = k
Dim As Integer fCount = 0
For f As Integer = 11 To Sqr(k) + 1
If v Mod f = 0 Then
isCandidate = isSubstring(kStr, f)
If isCandidate Then
While v Mod f = 0
fCount += 1
v \= f
Wend
Else
Exit For
End If
End If
Next f
If isCandidate And (fCount > 1 Or (v <> k And v > 1)) Then
If v > 1 Then isCandidate = isSubstring(kStr, v)
If isCandidate Then
Print Using "#######,###"; k;
kCount += 1
If kCount Mod 10 = 0 Then Print
End If
End If
End If
If kCount >= requiredNumbers Then Exit For
Next k</syntaxhighlight>
{{out}}
<pre> 15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361
5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827</pre>
 
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
<syntaxhighlight lang="go">package main
 
import (
"fmt"
"rcu"
"strconv"
"strings"
)
 
func main() {
count := 0
k := 11 * 11
var res []int
for count < 20 {
if k%3 == 0 || k%5 == 0 || k%7 == 0 {
k += 2
continue
}
factors := rcu.PrimeFactors(k)
if len(factors) > 1 {
s := strconv.Itoa(k)
includesAll := true
prev := -1
for _, f := range factors {
if f == prev {
continue
}
fs := strconv.Itoa(f)
if strings.Index(s, fs) == -1 {
includesAll = false
break
}
}
if includesAll {
res = append(res, k)
count++
}
}
k += 2
}
for _, e := range res[0:10] {
fmt.Printf("%10s ", rcu.Commatize(e))
}
fmt.Println()
for _, e := range res[10:20] {
fmt.Printf("%10s ", rcu.Commatize(e))
}
fmt.Println()
}</syntaxhighlight>
 
{{out}}
<pre>
15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361
5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827
</pre>
 
=={{header|J}}==
<syntaxhighlight lang="j"> */2 3 5 7
210
#1+I.0=+/|:4 q:1+i.210
48</syntaxhighlight>
 
Or: 48 out of every 210 positive numbers have no single digit factors.
 
So, we can generate a few hundred thousand lists of 48 numbers, discard the primes (and 1), then check what's left using substring matching on the factors. (We allow '0' as a 'factor' in our substring test so that we can work with a padded array of factors, avoiding variable length factor lists.)
 
<syntaxhighlight lang="j"> 2{._10 ]\(#~ */"1@((+./@(E. '0 ',])~&>)&:(":&.>)q:))(#~ 1-1&p:)}.,(1+I.0=+/|:4 q:1+i.210)+/~210*i.2e5
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827</syntaxhighlight>
 
Most of the time here is the substring testing, so this could be better optimized.
 
=={{header|Java}}==
<syntaxhighlight lang="java">
 
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.concurrent.ThreadLocalRandom;
 
public final class CompositeNumbersK {
 
public static void main(String[] aArgs) {
int k = 11 * 11;
List<Integer> result = new ArrayList<Integer>();
while ( result.size() < 20 ) {
while ( k % 3 == 0 || k % 5 == 0 || k % 7 == 0 ) {
k += 2;
}
List<Integer> factors = primeFactors(k);
if ( factors.size() > 1 ) {
String stringK = String.valueOf(k);
if ( factors.stream().allMatch( factor -> stringK.indexOf(String.valueOf(factor)) >= 0 ) ) {
result.add(k);
}
}
k += 2;
}
for ( int i = 0; i < result.size(); i++ ) {
System.out.print(String.format("%10d%s", result.get(i), ( i == 9 || i == 19 ? "\n" : "" )));
}
}
private static List<Integer> primeFactors(int aK) {
List<Integer> result = new ArrayList<Integer>();
if ( aK <= 1 ) {
return result;
}
BigInteger bigK = BigInteger.valueOf(aK);
if ( bigK.isProbablePrime(CERTAINTY_LEVEL) ) {
result.add(aK);
return result;
}
final int divisor = pollardsRho(bigK).intValueExact();
result.addAll(primeFactors(divisor));
result.addAll(primeFactors(aK / divisor));
Collections.sort(result);
return result;
}
private static BigInteger pollardsRho(BigInteger aN) {
final BigInteger constant = new BigInteger(aN.bitLength(), RANDOM);
BigInteger x = new BigInteger(aN.bitLength(), RANDOM);
BigInteger xx = x;
BigInteger divisor = null;
if ( aN.mod(BigInteger.TWO).signum() == 0 ) {
return BigInteger.TWO;
}
do {
x = x.multiply(x).mod(aN).add(constant).mod(aN);
xx = xx.multiply(xx).mod(aN).add(constant).mod(aN);
xx = xx.multiply(xx).mod(aN).add(constant).mod(aN);
divisor = x.subtract(xx).gcd(aN);
} while ( divisor.compareTo(BigInteger.ONE) == 0 );
return divisor;
}
private static final ThreadLocalRandom RANDOM = ThreadLocalRandom.current();
private static final int CERTAINTY_LEVEL = 10;
 
}
</syntaxhighlight>
{{ out }}
<pre>
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
</pre>
 
=={{header|Julia}}==
<langsyntaxhighlight lang="julia">using Lazy
using Primes
 
function containsitsonlytwodigfactors(n)
containsitsonlytwodigfactors(n) = (s = string(n); !isprime(n) && all(t -> length(t) > 1 && contains(s, t), map(x -> string(x), collect(keys(factor(n))))))
s = string(n)
return !isprime(n) && all(t -> length(t) > 1 && contains(s, t), map(string, collect(keys(factor(n)))))
end
 
seq = @>> Lazy.range(2) filter(containsitsonlytwodigfactors)
 
foreach(p -> print(lpad(last(p), 9), first(p) == 10 ? "\n" : ""), enumerate(take(20, seq)))
</langsyntaxhighlight>{{out}}
<pre>
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
Line 32 ⟶ 666:
</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[CompositeAndContainsPrimeFactor]
CompositeAndContainsPrimeFactor[k_Integer] := Module[{id, pf},
If[CompositeQ[k],
pf = FactorInteger[k][[All, 1]];
If[AllTrue[pf, GreaterThan[10]],
id = IntegerDigits[k];
AllTrue[pf, SequenceCount[id, IntegerDigits[#]] > 0 &]
,
False
]
,
False
]
]
out = Select[Range[30000000], CompositeAndContainsPrimeFactor]</syntaxhighlight>
{{out}}
<pre>{15317, 59177, 83731, 119911, 183347, 192413, 1819231, 2111317, 2237411, 3129361, 5526173, 11610313, 13436683, 13731373, 13737841, 13831103, 15813251, 17692313, 19173071, 28118827}</pre>
 
=={{header|Nim}}==
We use a sieve to build a list of prime factors. This is more efficient than computing the list of prime factors on the fly.
 
To find the 20 first elements of the sequence, the program takes less than 10 seconds on an Intel Core I5-8250U 4×1.6GHz.
<syntaxhighlight lang="Nim">import std/[strformat, strutils]
 
const Max = 80_000_000 # Maximal value for composite number.
 
# Prime factors of odd numbers.
# If a number is prime, its factor list is empty.
var factors: array[0..(Max - 3) div 2, seq[uint32]]
 
template primeFactors(n: Natural): seq[uint32] =
factors[(n - 3) shr 1]
 
# Build the list of factors.
for n in countup(3u32, Max div 11, 2):
if primeFactors(n).len == 0:
# "n" is prime.
for k in countup(n + n + n, Max, 2 * n):
primeFactors(k).add n
 
const N = 20 # Number of results.
var n = 11 * 11
var count = 0
while count < N:
if primeFactors(n).len > 0:
let nStr = $n
block Check:
for f in primeFactors(n):
if f < 11 or $f notin nStr: break Check
inc count
echo &"{count:2}: {insertSep($n)}"
inc n, 2
</syntaxhighlight>
 
{{out}}
<pre> 1: 15_317
2: 59_177
3: 83_731
4: 119_911
5: 183_347
6: 192_413
7: 1_819_231
8: 2_111_317
9: 2_237_411
10: 3_129_361
11: 5_526_173
12: 11_610_313
13: 13_436_683
14: 13_731_373
15: 13_737_841
16: 13_831_103
17: 15_813_251
18: 17_692_313
19: 19_173_071
20: 28_118_827
</pre>
 
=={{header|PARI/GP}}==
<syntaxhighlight lang="PARI/GP">
/* Returns a substring of str starting at s with length n */
ssubstr(str, s = 1, n = 0) = {
my(vt = Vecsmall(str), ve, vr, vtn = #str, n1);
if (vtn == 0, return(""));
if (s < 1 || s > vtn, return(str));
n1 = vtn - s + 1; if (n == 0, n = n1); if (n > n1, n = n1);
ve = vector(n, z, z - 1 + s); vr = vecextract(vt, ve); return(Strchr(vr));
}
 
/* Checks if subStr is a substring of mainStr */
isSubstring(mainStr, subStr) = {
mainLen = #Vecsmall(mainStr);
subLen = #Vecsmall(subStr);
for (startPos = 1, mainLen - subLen + 1,
if (ssubstr(mainStr, startPos, subLen) == subStr,
return(1); /* True: subStr found in mainStr */
)
);
return(0); /* False: subStr not found */
}
 
/* Determines if a number's factors, all > 9, are substrings of its decimal representation */
contains_its_prime_factors_all_over_9(n) = {
if (n < 10 || isprime(n), return(0)); /* Skip if n < 10 or n is prime */
strn = Str(n); /* Convert n to string */
pfacs = factor(n)[, 1]; /* Get unique prime factors of n */
for (i = 1, #pfacs,
if (pfacs[i] <= 9, return(0)); /* Skip factors ≤ 9 */
if (!isSubstring(strn, Str(pfacs[i])), return(0)); /* Check if factor is a substring */
);
return(1); /* All checks passed */
}
 
/* Main loop to find and print numbers meeting the criteria */
{
found = 0; /* Counter for numbers found */
for (n = 0, 30 * 10^6, /* Iterate from 0 to 30 million */
if (contains_its_prime_factors_all_over_9(n),
found += 1; /* Increment counter if n meets criteria */
print1(n, " "); /* Print n followed by a space */
if (found % 10 == 0, print("")); /* Newline every 10 numbers */
if (found == 20, break); /* Stop after finding 20 numbers */
);
);
}
</syntaxhighlight>
{{out}}
<pre>
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
</pre>
 
=={{header|Pascal}}==
==={{header|Free Pascal}}===
modified [[Factors_of_an_integer#using_Prime_decomposition]]
<syntaxhighlight lang="pascal">program FacOfInt;
// gets factors of consecutive integers fast
// limited to 1.2e11
{$IFDEF FPC}
{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
sysutils,
strutils //Numb2USA
{$IFDEF WINDOWS},Windows{$ENDIF}
;
//######################################################################
//prime decomposition
const
//HCN(86) > 1.2E11 = 128,501,493,120 count of divs = 4096 7 3 1 1 1 1 1 1 1
HCN_DivCnt = 4096;
type
tItem = Uint64;
tDivisors = array [0..HCN_DivCnt] of tItem;
tpDivisor = pUint64;
const
//used odd size for test only
SizePrDeFe = 32768;//*72 <= 64kb level I or 2 Mb ~ level 2 cache
type
tdigits = array [0..31] of Uint32;
//the first number with 11 different prime factors =
//2*3*5*7*11*13*17*19*23*29*31 = 2E11
//56 byte
tprimeFac = packed record
pfSumOfDivs,
pfRemain : Uint64;
pfDivCnt : Uint32;
pfMaxIdx : Uint32;
pfpotPrimIdx : array[0..9] of word;
pfpotMax : array[0..11] of byte;
end;
tpPrimeFac = ^tprimeFac;
tPrimeDecompField = array[0..SizePrDeFe-1] of tprimeFac;
tPrimes = array[0..65535] of Uint32;
var
{$ALIGN 8}
SmallPrimes: tPrimes;
{$ALIGN 32}
PrimeDecompField :tPrimeDecompField;
pdfIDX,pdfOfs: NativeInt;
procedure InitSmallPrimes;
//get primes. #0..65535.Sieving only odd numbers
const
MAXLIMIT = (821641-1) shr 1;
var
pr : array[0..MAXLIMIT] of byte;
p,j,d,flipflop :NativeUInt;
Begin
SmallPrimes[0] := 2;
fillchar(pr[0],SizeOf(pr),#0);
p := 0;
repeat
repeat
p +=1
until pr[p]= 0;
j := (p+1)*p*2;
if j>MAXLIMIT then
BREAK;
d := 2*p+1;
repeat
pr[j] := 1;
j += d;
until j>MAXLIMIT;
until false;
SmallPrimes[1] := 3;
SmallPrimes[2] := 5;
j := 3;
d := 7;
flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23
p := 3;
repeat
if pr[p] = 0 then
begin
SmallPrimes[j] := d;
inc(j);
end;
d += 2*flipflop;
p+=flipflop;
flipflop := 3-flipflop;
until (p > MAXLIMIT) OR (j>High(SmallPrimes));
end;
function OutPots(pD:tpPrimeFac;n:NativeInt):Ansistring;
var
s: String[31];
chk,p,i: NativeInt;
Begin
str(n,s);
result := Format('%15s : ',[Numb2USA(s)]);
 
with pd^ do
begin
chk := 1;
For n := 0 to pfMaxIdx-1 do
Begin
if n>0 then
result += '*';
p := SmallPrimes[pfpotPrimIdx[n]];
chk *= p;
str(p,s);
result += s;
i := pfpotMax[n];
if i >1 then
Begin
str(pfpotMax[n],s);
result += '^'+s;
repeat
chk *= p;
dec(i);
until i <= 1;
end;
end;
p := pfRemain;
If p >1 then
Begin
str(p,s);
chk *= p;
result += '*'+s;
end;
end;
end;
 
function CnvtoBASE(var dgt:tDigits;n:Uint64;base:NativeUint):NativeInt;
//n must be multiple of base aka n mod base must be 0
var
q,r: Uint64;
i : NativeInt;
Begin
fillchar(dgt,SizeOf(dgt),#0);
i := 0;
n := n div base;
result := 0;
repeat
r := n;
q := n div base;
r -= q*base;
n := q;
dgt[i] := r;
inc(i);
until (q = 0);
//searching lowest pot in base
result := 0;
while (result<i) AND (dgt[result] = 0) do
inc(result);
inc(result);
end;
function IncByBaseInBase(var dgt:tDigits;base:NativeInt):NativeInt;
var
q :NativeInt;
Begin
result := 0;
q := dgt[result]+1;
if q = base then
repeat
dgt[result] := 0;
inc(result);
q := dgt[result]+1;
until q <> base;
dgt[result] := q;
result +=1;
end;
function SieveOneSieve(var pdf:tPrimeDecompField):boolean;
var
dgt:tDigits;
i,j,k,pr,fac,n,MaxP : Uint64;
begin
n := pdfOfs;
if n+SizePrDeFe >= sqr(SmallPrimes[High(SmallPrimes)]) then
EXIT(FALSE);
//init
for i := 0 to SizePrDeFe-1 do
begin
with pdf[i] do
Begin
pfDivCnt := 1;
pfSumOfDivs := 1;
pfRemain := n+i;
pfMaxIdx := 0;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := 0;
end;
end;
//first factor 2. Make n+i even
i := (pdfIdx+n) AND 1;
IF (n = 0) AND (pdfIdx<2) then
i := 2;
repeat
with pdf[i] do
begin
j := BsfQWord(n+i);
pfMaxIdx := 1;
pfpotPrimIdx[0] := 0;
pfpotMax[0] := j;
pfRemain := (n+i) shr j;
pfSumOfDivs := (Uint64(1) shl (j+1))-1;
pfDivCnt := j+1;
end;
i += 2;
until i >=SizePrDeFe;
//i now index in SmallPrimes
i := 0;
maxP := trunc(sqrt(n+SizePrDeFe))+1;
repeat
//search next prime that is in bounds of sieve
if n = 0 then
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if k < SizePrDeFe then
break;
until pr > MaxP;
end
else
begin
repeat
inc(i);
pr := SmallPrimes[i];
k := pr-n MOD pr;
if (k = pr) AND (n>0) then
k:= 0;
if k < SizePrDeFe then
break;
until pr > MaxP;
end;
//no need to use higher primes
if pr*pr > n+SizePrDeFe then
BREAK;
//j is power of prime
j := CnvtoBASE(dgt,n+k,pr);
repeat
with pdf[k] do
Begin
pfpotPrimIdx[pfMaxIdx] := i;
pfpotMax[pfMaxIdx] := j;
pfDivCnt *= j+1;
fac := pr;
repeat
pfRemain := pfRemain DIV pr;
dec(j);
fac *= pr;
until j<= 0;
pfSumOfDivs *= (fac-1)DIV(pr-1);
inc(pfMaxIdx);
k += pr;
j := IncByBaseInBase(dgt,pr);
end;
until k >= SizePrDeFe;
until false;
//correct sum of & count of divisors
for i := 0 to High(pdf) do
Begin
with pdf[i] do
begin
j := pfRemain;
if j <> 1 then
begin
pfSumOFDivs *= (j+1);
pfDivCnt *=2;
end;
end;
end;
result := true;
end;
function NextSieve:boolean;
begin
dec(pdfIDX,SizePrDeFe);
inc(pdfOfs,SizePrDeFe);
result := SieveOneSieve(PrimeDecompField);
end;
function GetNextPrimeDecomp:tpPrimeFac;
begin
if pdfIDX >= SizePrDeFe then
if Not(NextSieve) then
EXIT(NIL);
result := @PrimeDecompField[pdfIDX];
inc(pdfIDX);
end;
function Init_Sieve(n:NativeUint):boolean;
//Init Sieve pdfIdx,pdfOfs are Global
begin
pdfIdx := n MOD SizePrDeFe;
pdfOfs := n-pdfIdx;
result := SieveOneSieve(PrimeDecompField);
end;
var
s,pr : string[31];
pPrimeDecomp :tpPrimeFac;
T0:Int64;
n,i,cnt : NativeUInt;
checked : boolean;
Begin
InitSmallPrimes;
T0 := GetTickCount64;
cnt := 0;
n := 0;
Init_Sieve(n);
repeat
pPrimeDecomp:= GetNextPrimeDecomp;
with pPrimeDecomp^ do
begin
//composite with smallest factor 11
if (pfDivCnt>=4) AND (pfpotPrimIdx[0]>3) then
begin
str(n,s);
for i := 0 to pfMaxIdx-1 do
begin
str(smallprimes[pfpotPrimIdx[i]],pr);
checked := (pos(pr,s)>0);
if Not(checked) then
Break;
end;
if checked then
begin
//writeln(cnt:4,OutPots(pPrimeDecomp,n));
if pfRemain >1 then
begin
str(pfRemain,pr);
checked := (pos(pr,s)>0);
end;
if checked then
begin
inc(cnt);
writeln(cnt:4,OutPots(pPrimeDecomp,n));
end;
end;
end;
end;
inc(n);
until n > 28118827;//10*1000*1000*1000+1;//
T0 := GetTickCount64-T0;
writeln('runtime ',T0/1000:0:3,' s');
end.
</syntaxhighlight>
{{out|@TIO.RUN}}
<pre style="height:480px">
Real time: 2.166 s CPU share: 99.20 %//500*1000*1000 Real time: 38.895 s CPU share: 99.28 %
1 15,317 : 17^2*53
2 59,177 : 17*59^2
3 83,731 : 31*37*73
4 119,911 : 11^2*991
5 183,347 : 47^2*83
6 192,413 : 13*19^2*41
7 1,819,231 : 19*23^2*181
8 2,111,317 : 13^3*31^2
9 2,237,411 : 11^3*41^2
10 3,129,361 : 29^2*61^2
11 5,526,173 : 17*61*73^2
12 11,610,313 : 11^4*13*61
13 13,436,683 : 13^2*43^3
14 13,731,373 : 73*137*1373
15 13,737,841 : 13^5*37
16 13,831,103 : 11*13*311^2
17 15,813,251 : 251^3
18 17,692,313 : 23*769231
19 19,173,071 : 19^2*173*307
20 28,118,827 : 11^2*281*827
runtime 2.011 s
 
//@home til 1E10 .. 188 9,898,707,359 : 59^2*89^2*359
21 31,373,137 : 73*137*3137
22 47,458,321 : 83^4
23 55,251,877 : 251^2*877
24 62,499,251 : 251*499^2
25 79,710,361 : 103*797*971
26 81,227,897 : 89*97^3
27 97,337,269 : 37^2*97*733
28 103,192,211 : 19^2*31*9221
29 107,132,311 : 11^2*13^4*31
30 119,503,483 : 11*19*83^3
31 119,759,299 : 11*19*29*19759
32 124,251,499 : 499^3
33 131,079,601 : 107^4
34 142,153,597 : 59^2*97*421
35 147,008,443 : 43^5
36 171,197,531 : 17^2*31*97*197
37 179,717,969 : 71*79*179^2
38 183,171,409 : 71*1409*1831
39 215,797,193 : 19*1579*7193
40 241,153,517 : 11*17*241*5351
41 248,791,373 : 73*373*9137
42 261,113,281 : 11^2*13^2*113^2
43 272,433,191 : 19*331*43319
44 277,337,147 : 71*73^2*733
45 291,579,719 : 19*1579*9719
46 312,239,471 : 31^3*47*223
47 344,972,429 : 29*3449^2
48 364,181,311 : 13^4*41*311
49 381,317,911 : 13^6*79
50 385,494,799 : 47^4*79
51 392,616,923 : 23^5*61
52 399,311,341 : 11*13^4*31*41
53 410,963,311 : 11^2*31*331^2
54 413,363,353 : 13^4*41*353
55 423,564,751 : 751^3
56 471,751,831 : 31*47^2*83^2
57 492,913,739 : 73*739*9137
58 501,225,163 : 163*251*12251
59 591,331,169 : 11*13^2*31^2*331
60 592,878,929 : 29^2*89^3
61 594,391,193 : 11*19^2*43*59^2
62 647,959,343 : 47^3*79^2
63 717,528,911 : 11^2*17^4*71
64 723,104,383 : 23^2*43*83*383
65 772,253,089 : 53^2*89*3089
66 799,216,219 : 79^3*1621
67 847,253,389 : 53^2*89*3389
68 889,253,557 : 53^2*89*3557
69 889,753,559 : 53^2*89*3559
70 892,753,571 : 53^2*89*3571
71 892,961,737 : 17^2*37^3*61
72 895,253,581 : 53^2*89*3581
73 895,753,583 : 53^2*89*3583
74 898,253,593 : 53^2*89*3593
75 972,253,889 : 53^2*89*3889
76 997,253,989 : 53^2*89*3989
77 1,005,371,999 : 53^2*71^3
78 1,011,819,919 : 11*101*919*991
79 1,019,457,337 : 37^2*73*101^2
80 1,029,761,609 : 29^2*761*1609
81 1,031,176,157 : 11^2*17*31*103*157
82 1,109,183,317 : 11*31^2*317*331
83 1,119,587,711 : 11^2*19^4*71
84 1,137,041,971 : 13^4*41*971
85 1,158,169,331 : 11*31^2*331^2
86 1,161,675,547 : 47^3*67*167
87 1,189,683,737 : 11^5*83*89
88 1,190,911,909 : 11*9091*11909
89 1,193,961,571 : 11^3*571*1571
90 1,274,418,211 : 11*41^5
91 1,311,979,279 : 13^2*19*131*3119
92 1,316,779,217 : 13^2*17*677^2
93 1,334,717,327 : 47*73^4
94 1,356,431,947 : 13*43^2*56431
95 1,363,214,333 : 13^3*433*1433
96 1,371,981,127 : 11^2*19*37*127^2
97 1,379,703,847 : 47^3*97*137
98 1,382,331,137 : 11*31*37*331^2
99 1,389,214,193 : 41*193*419^2
100 1,497,392,977 : 97*3929^2
101 1,502,797,333 : 733^2*2797
102 1,583,717,977 : 17^2*71*79*977
103 1,593,519,731 : 59*5197^2
104 1,713,767,399 : 17^6*71
105 1,729,719,587 : 17*19^2*29*9719
106 1,733,793,487 : 79^2*379*733
107 1,761,789,373 : 17^2*37^2*61*73
108 1,871,688,013 : 13^5*71^2
109 1,907,307,719 : 71^3*73^2
110 1,948,441,249 : 1249^3
111 1,963,137,527 : 13*31^3*37*137
112 1,969,555,417 : 17*41^5
113 1,982,119,441 : 211^4
114 1,997,841,197 : 11*97^3*199
115 2,043,853,681 : 53^2*853^2
116 2,070,507,919 : 19^2*79^2*919
117 2,073,071,593 : 73^5
118 2,278,326,179 : 17*83*617*2617
119 2,297,126,743 : 29^3*97*971
120 2,301,131,209 : 13^4*23*31*113
121 2,323,519,823 : 19^2*23^5
122 2,371,392,959 : 13^2*29*59^2*139
123 2,647,985,311 : 31*47*53^2*647
124 2,667,165,611 : 11^5*16561
125 2,722,413,361 : 241*3361^2
126 2,736,047,519 : 19^2*47^3*73
127 2,881,415,311 : 31^3*311^2
128 2,911,317,539 : 13^2*31*317*1753
129 2,924,190,611 : 19^3*29*61*241
130 3,015,962,419 : 41*419^3
131 3,112,317,013 : 13^2*23^2*31*1123
132 3,131,733,761 : 13^2*17^2*37*1733
133 3,150,989,441 : 41*509*150989
134 3,151,811,881 : 31^2*1811^2
135 3,423,536,177 : 17*23^2*617^2
136 3,461,792,569 : 17^2*3461^2
137 3,559,281,161 : 281*3559^2
138 3,730,774,997 : 499*997*7499
139 3,795,321,361 : 13*37*53^4
140 3,877,179,289 : 71^2*877^2
141 4,070,131,949 : 13^2*19*31^2*1319
142 4,134,555,661 : 41^2*61^2*661
143 4,143,189,277 : 31*41^2*43^3
144 4,162,322,419 : 19^5*41^2
145 4,311,603,593 : 11*43^2*59*3593
146 4,339,091,119 : 11*4339*90911
147 4,340,365,711 : 11^3*571*5711
148 4,375,770,311 : 11^4*31^2*311
149 4,427,192,717 : 17*19*71^2*2719
150 4,530,018,503 : 503*3001^2
151 4,541,687,137 : 13*37*41^3*137
152 4,541,938,631 : 41*419^2*631
153 4,590,757,613 : 13*613*757*761
154 4,750,104,241 : 41^6
155 4,796,438,239 : 23^3*479*823
156 4,985,739,599 : 59*8573*9857
157 5,036,760,823 : 23^3*503*823
158 5,094,014,879 : 79*401^3
159 5,107,117,543 : 11^4*17^3*71
160 5,137,905,383 : 13^2*53^2*79*137
161 5,181,876,331 : 31^5*181
162 5,276,191,811 : 11^5*181^2
163 5,319,967,909 : 19*53^2*99679
164 5,411,964,371 : 11*41^2*541^2
165 5,445,241,447 : 41^5*47
166 5,892,813,173 : 13^3*17^2*9281
167 6,021,989,371 : 19^3*937^2
168 6,122,529,619 : 19*29^2*619^2
169 6,138,239,333 : 23^3*613*823
170 6,230,438,329 : 23*29^4*383
171 6,612,362,989 : 23^4*23629
172 6,645,125,311 : 11^8*31
173 7,155,432,157 : 43^2*157^3
174 7,232,294,717 : 17*29^2*47^2*229
175 7,293,289,141 : 29*41^4*89
176 7,491,092,411 : 11*41^4*241
177 8,144,543,377 : 433*4337^2
178 8,194,561,699 : 19*4561*94561
179 8,336,743,231 : 23^4*31^3
180 8,413,553,317 : 13*17*53^2*13553
181 8,435,454,179 : 17*43^3*79^2
182 8,966,127,229 : 29^2*127^2*661
183 9,091,190,911 : 11*9091*90911
184 9,373,076,171 : 37^2*937*7307
185 9,418,073,141 : 31*41^2*180731
186 9,419,992,843 : 19^4*41^2*43
187 9,523,894,717 : 17^3*23*89*947
188 9,898,707,359 : 59^2*89^2*359
runtime 539.800 s
</pre>
 
=={{header|Perl}}==
{{trans|Raku}}
{{libheader|ntheory}}
<syntaxhighlight lang="perl"> use strict;
use warnings;
use ntheory qw<is_prime factor gcd>;
 
my($values,$cnt);
LOOP: for (my $k = 11; $k < 1E10; $k += 2) {
next if 1 < gcd($k,2*3*5*7) or is_prime $k;
map { next if index($k, $_) < 0 } factor $k;
$values .= sprintf "%10d", $k;
last LOOP if ++$cnt == 20;
}
print $values =~ s/.{1,100}\K/\n/gr;</syntaxhighlight>
{{out}}
<pre> 15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827</pre>
 
=={{header|Phix}}==
{{trans|Wren}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">*</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10</span><span style="color: #0000FF;">:</span><span style="color: #000000;">20</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">(),</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><</span><span style="color: #000000;">limit</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">gcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">5</span><span style="color: #0000FF;">*</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">or</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">and</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">valid</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"x"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %,10d = %-17s (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Total time:%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
<!--</syntaxhighlight>-->
{{out}}
<small>(As usual, limiting to the first 10 under pwa/p2js keeps the time staring at a blank screen under 10s)</small>
<pre>
1: 15,317 = 17x17x53 (0s)
2: 59,177 = 17x59x59 (0.1s)
3: 83,731 = 31x37x73 (0.0s)
4: 119,911 = 11x11x991 (0.0s)
5: 183,347 = 47x47x83 (0.1s)
6: 192,413 = 13x19x19x41 (0.0s)
7: 1,819,231 = 19x23x23x181 (3.5s)
8: 2,111,317 = 13x13x13x31x31 (0.7s)
9: 2,237,411 = 11x11x11x41x41 (0.4s)
10: 3,129,361 = 29x29x61x61 (2.6s)
11: 5,526,173 = 17x61x73x73 (7.5s)
12: 11,610,313 = 11x11x11x11x13x61 (23.2s)
13: 13,436,683 = 13x13x43x43x43 (7.9s)
14: 13,731,373 = 73x137x1373 (1.3s)
15: 13,737,841 = 13x13x13x13x13x37 (0.0s)
16: 13,831,103 = 11x13x311x311 (0.4s)
17: 15,813,251 = 251x251x251 (8.9s)
18: 17,692,313 = 23x769231 (9.0s)
19: 19,173,071 = 19x19x173x307 (7.1s)
20: 28,118,827 = 11x11x281x827 (46.2s)
Total time:1 minute and 59s
</pre>
===slightly faster===
{{trans|XPL0}}
The obvious problem with the above is that prime_factors() quite literally does not know when to quit.
Output as above, except Total time is reduced to 47s.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">*</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">10</span><span style="color: #0000FF;">:</span><span style="color: #000000;">20</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">(),</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><</span><span style="color: #000000;">limit</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)),</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;"><</span><span style="color: #000000;">10</span> <span style="color: #008080;">or</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">f</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">f</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">></span><span style="color: #000000;">l</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span> <span style="color: #008080;">or</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">),</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">valid</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">;</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"x"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %,10d = %-17s (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Total time:%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
<!--</syntaxhighlight>-->
 
=={{header|Python}}==
<syntaxhighlight lang="python">from sympy import isprime, factorint
 
def contains_its_prime_factors_all_over_7(n):
if n < 10 or isprime(n):
return False
strn = str(n)
pfacs = factorint(n).keys()
return all(f > 9 and str(f) in strn for f in pfacs)
 
found = 0
for n in range(1_000_000_000):
if contains_its_prime_factors_all_over_7(n):
found += 1
print(f'{n: 12,}', end = '\n' if found % 10 == 0 else '')
if found == 20:
break
</syntaxhighlight>{{out}}
<pre>
15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361
5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827
</pre>
 
=={{header|Raku}}==
 
<syntaxhighlight lang="raku" perl6line>use Prime::Factor;
use Lingua::EN::Numbers;
 
Line 41 ⟶ 1,508:
next if (1 < $_ gcd 210) || .is-prime || any .&prime-factors.map: -> $n { !.contains: $n };
$_
} )[^20].batch(10)».&comma».fmt("%10s").join: "\n";</langsyntaxhighlight>
 
{{out}}
<pre> 15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361
5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827</pre>
 
=={{header|RPL}}==
{{works with|HP|49}}
≪ '''IF''' DUP ISPRIME? '''THEN''' DROP <span style="color:red">0</span> '''ELSE'''
DUP FACTORS DUP SIZE
ROT →STR → n
≪ { }
<span style="color:red">1</span> ROT '''FOR''' j
OVER j GET →STR + <span style="color:grey">@ extract prime factors and convert into strings</span>
<span style="color:red">2</span> '''STEP''' NIP
≪ n SWAP POS ≫ MAP <span style="color:red">1</span> + ΠLIST <span style="color:grey">@ + 1 to avoid arror with singletons</span>
≫
'''END'''
≫ '<span style="color:blue">MATRIOSHKA?</span>' STO
≪ 999999999 → max
≪ { }
<span style="color:red">11 </span>max '''FOR''' j
'''IF''' j <span style="color:red">105</span> GCD 1 == '''THEN''' <span style="color:grey">@ if no single digit factor</span>
'''IF''' j <span style="color:blue">MATRIOSHKA?</span> '''THEN'''
j +
'''IF''' DUP SIZE <span style="color:red">6</span> == '''THEN''' max 'j' STO '''END'''
'''END'''
'''END'''
<span style="color:red">2</span> '''STEP'''
≫ '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: {15317 59177 83731 119911 183347 192413}
</pre>
Finding the first six numbers takes 4 minutes 20 seconds with an iOS HP-49 emulator, meaning that about two hours would be required to get ten. We're gonna need a bigger boat.
 
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
 
generator2357 = Enumerator.new do |y|
gen23 = Prime::Generator23.new
gen23.each {|n| y << n unless (n%5 == 0 || n%7 == 0) }
end
 
res = generator2357.lazy.select do |n|
primes, exp = n.prime_division.transpose
next if exp.sum < 2 #exclude primes
s = n.to_s
primes.all?{|pr| s.match?(-pr.to_s) }
end
 
res.take(10).each{|n| puts n}</syntaxhighlight>
{{out}}
<pre>15317
59177
83731
119911
183347
192413
1819231
2111317
2237411
3129361
</pre>
 
=={{header|Rust}}==
<syntaxhighlight lang="rust">use primes::{is_prime,factors_uniq};
 
/// True if non-prime n's factors, all > 9, are all substrings of its representation in base 10
fn contains_its_prime_factors_all_over_7(n: u64) -> bool {
if n < 10 || is_prime(n) {
return false;
}
let strn = &n.to_string();
let pfacs = factors_uniq(n);
return pfacs.iter().all(|f| f > &9 && strn.contains(&f.to_string()));
}
 
fn main() {
let mut found = 0;
// 20 of these < 30 million
for n in 0..30_000_000 {
if contains_its_prime_factors_all_over_7(n) {
found += 1;
print!("{:12}{}", n, {if found % 10 == 0 {"\n"} else {""}});
if found == 20 {
break;
}
}
}
}
</syntaxhighlight>{{out}}
<pre>
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
</pre>
=={{header|Scala}}==
for Scala3
<syntaxhighlight lang="scala">
def isComposite(num: Int): Boolean = {
val numStr = num.toString
def iter(n: Int, start: Int): Boolean = {
val limit = math.sqrt(n).floor.toInt
(start to limit by 2).dropWhile(n % _ > 0).headOption match {
case Some(v) if v < 10 => false
case Some(v) =>
if (v == start || numStr.contains(v.toString)) iter(n / v, v)
else false
case None => n < num && numStr.contains(n.toString)
}
}
iter(num, 3)
}
 
def composites = Iterator.from(121, 2).filter(isComposite(_))
 
@main def main = {
val start = System.currentTimeMillis
composites.take(20)
.grouped(10)
.foreach(grp => println(grp.map("%8d".format(_)).mkString(" ")))
val time = System.currentTimeMillis - start
println(s"time elapsed: $time ms")
}
</syntaxhighlight>
{{out}}
<pre>
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361
5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
time elapsed: 59821 ms
</pre>
 
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">var e = Enumerator({|f|
 
var c = (9.primorial)
var a = (1..c -> grep { .is_coprime(c) })
 
loop {
var n = a.shift
 
a.push(n + c)
n.is_composite || next
 
f(n) if n.factor.all {|p| Str(n).contains(p) }
}
})
 
var count = 10
 
e.each {|n|
say n
break if (--count <= 0)
}</syntaxhighlight>
{{out}}
<pre>
15317
59177
83731
119911
183347
192413
1819231
2111317
2237411
3129361
</pre>
 
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-seq}}
<lang ecmascript>import "/math" for Int
{{libheader|Wren-fmt}}
import "/fmt" for Fmt
<syntaxhighlight lang="wren">import "./math" for Int
import "./seq" for Lst
import "./fmt" for Fmt
 
var count = 0
var k = 11 * 11
var res = []
while (count < 20) {
Line 62 ⟶ 1,695:
var factors = Int.primeFactors(k)
if (factors.count > 1) {
Lst.prune(factors)
var s = k.toString
var includesAll = true
Line 78 ⟶ 1,712:
}
Fmt.print("$,10d", res[0..9])
Fmt.print("$,10d", res[10..19])</langsyntaxhighlight>
 
{{out}}
Line 84 ⟶ 1,718:
15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361
5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827
</pre>
 
=={{header|XPL0}}==
Runs in 33.6 seconds on Raspberry Pi 4.
<syntaxhighlight lang="xpl0">include xpllib; \for ItoA, StrFind and RlOutC
int K, C;
 
proc Factor; \Show certain K factors
int L, N, F, Q;
char SA(10), SB(10);
[ItoA(K, SB);
L:= sqrt(K); \limit for speed
N:= K; F:= 3;
if (N&1) = 0 then return; \reject if 2 is a factor
loop [Q:= N/F;
if rem(0) = 0 then \found a factor, F
[if F < 10 then return; \reject if too small (3, 5, 7)
ItoA(F, SA); \reject if not a sub-string
if StrFind(SB, SA) = 0 then return;
N:= Q;
if F>N then quit; \all factors found
]
else [F:= F+2; \try next prime factor
if F>L then
[if N=K then return; \reject prime K
ItoA(N, SA); \ (it's not composite)
if StrFind(SB, SA) = 0 then return;
quit; \passed all restrictions
];
];
];
Format(9, 0);
RlOutC(0, float(K));
C:= C+1;
if rem(C/10) = 0 then CrLf(0);
];
 
[C:= 0; \initialize element counter
K:= 11*11; \must have at least two 2-digit composites
repeat Factor;
K:= K+2; \must be odd because all factors > 2 are odd primes
until C >= 20;
]</syntaxhighlight>
 
{{out}}
<pre>
15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361
5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827
</pre>
Jjuanhdez
2,122

edits

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