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Chernick's Carmichael numbers: Difference between revisions

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Chernick's Carmichael numbers (view source)

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{{draft task|Mathematics}}
[[category:Prime Numbers]]
In 1939, Jack Chernick proved that, for '''n ≥ 3''' and '''m ≥ 1''':
 
Line 52 ⟶ 53:
 
<br><br>
 
=={{header|C}}==
{{libheader|GMP}}
<langsyntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>
Line 105:
 
return 0;
}</langsyntaxhighlight>
{{out}}
<pre>
Line 117:
a(10) has m = 3208386195840
</pre>
 
 
=={{header|C++}}==
{{libheader|GMP}}
<langsyntaxhighlight lang="cpp">#include <gmp.h>
#include <iostream>
 
Line 206 ⟶ 204:
 
return 0;
}</langsyntaxhighlight>
{{out}}
<pre>
Line 219 ⟶ 217:
</pre>
(takes ~3.5 minutes)
 
=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_function Extensible Prime Generator (F#)]
<langsyntaxhighlight lang="fsharp">
// Generate Chernick's Carmichael numbers. Nigel Galloway: June 1st., 2019
let fMk m k=isPrime(6*m+1) && isPrime(12*m+1) && [1..k-2]|>List.forall(fun n->isPrime(9*(pown 2 n)*m+1))
Line 228 ⟶ 225:
let cherCar k=let m=Seq.head(fX k) in printfn "m=%d primes -> %A " m ([6*m+1;12*m+1]@List.init(k-2)(fun n->9*(pown 2 (n+1))*m+1))
[4..9] |> Seq.iter cherCar
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 238 ⟶ 235:
cherCar(9): m=950560 primes -> [5703361; 11406721; 17110081; 34220161; 68440321; 136880641; 273761281; 547522561; 1095045121]
</pre>
=={{header|FreeBASIC}}==
===Basic only===
<syntaxhighlight lang="freebasic">#include "isprime.bas"
 
Function PrimalityPretest(k As Integer) As Boolean
Dim As Integer ppp(1 To 8) = {3,5,7,11,13,17,19,23}
For i As Integer = 1 To Ubound(ppp)
If k Mod ppp(i) = 0 Then Return (k <= 23)
Next i
Return True
End Function
 
Function isChernick(n As Integer, m As Integer) As Boolean
Dim As Integer i, t = 9 * m
If Not PrimalityPretest(6 * m + 1) Then Return False
If Not PrimalityPretest(12 * m + 1) Then Return False
For i = 1 To n-1
If Not PrimalityPretest(t * (2 ^ i) + 1) Then Return False
Next i
If Not isPrime(6 * m + 1) Then Return False
If Not isPrime(12 * m + 1) Then Return False
For i = 1 To n - 2
If Not isPrime(t * (2 ^ i) + 1) Then Return False
Next i
Return True
End Function
 
Dim As Uinteger multiplier, k, m = 1
For n As Integer = 3 To 9
multiplier = Iif (n > 4, 2 ^ (n-4), 1)
If n > 5 Then multiplier *= 5
k = 1
Do
m = k * multiplier
If isChernick(n, m) Then
Print "a(" & n & ") has m = " & m
Exit Do
End If
k += 1
Loop
Next n
Sleep</syntaxhighlight>
=={{header|Go}}==
===Basic only===
<langsyntaxhighlight lang="go">package main
 
import (
Line 297 ⟶ 340:
func main() {
ccNumbers(3, 9)
}</langsyntaxhighlight>
 
{{out}}
Line 319 ⟶ 362:
 
The resulting executable is several hundred times faster than before and, even on my modest Celeron @1.6GHZ, reaches a(9) in under 10ms and a(10) in about 22 minutes.
<langsyntaxhighlight lang="go">package main
 
import (
Line 413 ⟶ 456:
func main() {
ccNumbers(min, max)
}</langsyntaxhighlight>
 
{{out}}
Line 449 ⟶ 492:
Factors: [19250317175041 38500634350081 57750951525121 115501903050241 231003806100481 462007612200961 924015224401921 1848030448803841 3696060897607681 7392121795215361]
</pre>
=={{header|J}}==
 
Brute force:
 
<syntaxhighlight lang="j">a=: {{)v
if.3=y do.1729 return.end.
m=. z=. 2^y-4
f=. 6 12,9*2^}.i.y-1
while.do.
uf=.1+f*m
if.*/1 p: uf do. */x:uf return.end.
m=.m+z
end.
}}</syntaxhighlight>
 
Task examples:
 
<syntaxhighlight lang="j"> a 3
1729
a 4
63973
a 5
26641259752490421121
a 6
1457836374916028334162241
a 7
24541683183872873851606952966798288052977151461406721
a 8
53487697914261966820654105730041031613370337776541835775672321
a 9
58571442634534443082821160508299574798027946748324125518533225605795841</syntaxhighlight>
=={{header|Java}}==
<langsyntaxhighlight lang="java">
import java.math.BigInteger;
import java.util.ArrayList;
Line 646 ⟶ 719:
 
}
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 657 ⟶ 730:
U(9, 950560) = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561 * 1095045121 = 58571442634534443082821160508299574798027946748324125518533225605795841
</pre>
 
=={{header|Julia}}==
<langsyntaxhighlight lang="julia">using Primes
 
function trial_pretest(k::UInt64)
Line 766 ⟶ 838:
end
 
cc_numbers(3, 10)</langsyntaxhighlight>
 
{{out}}
Line 781 ⟶ 853:
 
(takes ~6.5 minutes)
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[PrimeFactorCounts, U]
PrimeFactorCounts[n_Integer] := Total[FactorInteger[n][[All, 2]]]
U[n_, m_] := (6 m + 1) (12 m + 1) Product[2^i 9 m + 1, {i, 1, n - 2}]
FindFirstChernickCarmichaelNumber[n_Integer?Positive] :=
Module[{step, i, m, formula, value},
step = Ceiling[2^(n - 4)];
If[n > 5, step *= 5];
i = step;
formula = U[n, m];
PrintTemporary[Dynamic[i]];
While[True,
value = formula /. m -> i;
If[PrimeFactorCounts[value] == n,
Break[];
];
i += step
];
{i, value}
]
FindFirstChernickCarmichaelNumber[3]
FindFirstChernickCarmichaelNumber[4]
FindFirstChernickCarmichaelNumber[5]
FindFirstChernickCarmichaelNumber[6]
FindFirstChernickCarmichaelNumber[7]
FindFirstChernickCarmichaelNumber[8]
FindFirstChernickCarmichaelNumber[9]</syntaxhighlight>
{{out}}
<pre>{1,1729}
{1,63973}
{380,26641259752490421121}
{380,1457836374916028334162241}
{780320,24541683183872873851606952966798288052977151461406721}
{950560,53487697914261966820654105730041031613370337776541835775672321}
{950560,58571442634534443082821160508299574798027946748324125518533225605795841}</pre>
=={{header|Nim}}==
{{libheader|bignum}}
Until ''a(9)'' a simple primality test using divisions by odd numbers is sufficient. But for ''a(10)'', it is necessary to improve the test. We have used here some optimizations found in other solutions:
:– eliminating multiples of 3, 5, 7, 11, 13, 17, 19, 23;
:– using a probability test which implies to use big integers; so, we have to convert the tested number to a big integer;
:– for ''n'' >= 5, checking only values of ''m'' which are multiple of 5 (in fact, we check only the multiples of 5 × 2^(''n''-4).
 
With these optimizations, the program executes in 4-5 minutes.
 
<syntaxhighlight lang="nim">import strutils, sequtils
import bignum
 
const
Max = 10
Factors: array[3..Max, int] = [1, 1, 2, 4, 8, 16, 32, 64] # 1 for n=3 then 2^(n-4).
FirstPrimes = [3, 5, 7, 11, 13, 17, 19, 23]
 
#---------------------------------------------------------------------------------------------------
 
iterator factors(n, m: Natural): Natural =
## Yield the factors of U(n, m).
 
yield 6 * m + 1
yield 12 * m + 1
var k = 2
for _ in 1..(n - 2):
yield 9 * k * m + 1
inc k, k
 
#---------------------------------------------------------------------------------------------------
 
proc mayBePrime(n: int): bool =
## First primality test.
 
if n < 23: return true
 
for p in FirstPrimes:
if n mod p == 0:
return false
 
result = true
 
#---------------------------------------------------------------------------------------------------
 
proc isChernick(n, m: Natural): bool =
## Check if U(N, m) if a Chernick-Carmichael number.
 
# Use the first and quick test.
for factor in factors(n, m):
if not factor.mayBePrime():
return false
 
# Use the slow probability test (need to use a big int).
for factor in factors(n, m):
if probablyPrime(newInt(factor), 25) == 0:
return false
 
result = true
 
#---------------------------------------------------------------------------------------------------
 
proc a(n: Natural): tuple[m: Natural, factors: seq[Natural]] =
## For a given "n", find the smallest Charnick-Carmichael number.
 
var m: Natural = 0
var incr = (if n >= 5: 5 else: 1) * Factors[n] # For n >= 5, a(n) is a multiple of 5.
 
while true:
inc m, incr
if isChernick(n, m):
return (m, toSeq(factors(n, m)))
 
#———————————————————————————————————————————————————————————————————————————————————————————————————
 
import strformat
 
for n in 3..Max:
let (m, factors) = a(n)
 
stdout.write fmt"a({n}) = U({n}, {m}) = "
var s = ""
for factor in factors:
s.addSep(" × ")
s.add($factor)
stdout.write s, '\n'</syntaxhighlight>
 
{{out}}
<pre>a(3) = U(3, 1) = 7 × 13 × 19
a(4) = U(4, 1) = 7 × 13 × 19 × 37
a(5) = U(5, 380) = 2281 × 4561 × 6841 × 13681 × 27361
a(6) = U(6, 380) = 2281 × 4561 × 6841 × 13681 × 27361 × 54721
a(7) = U(7, 780320) = 4681921 × 9363841 × 14045761 × 28091521 × 56183041 × 112366081 × 224732161
a(8) = U(8, 950560) = 5703361 × 11406721 × 17110081 × 34220161 × 68440321 × 136880641 × 273761281 × 547522561
a(9) = U(9, 950560) = 5703361 × 11406721 × 17110081 × 34220161 × 68440321 × 136880641 × 273761281 × 547522561 × 1095045121
a(10) = U(10, 3208386195840) = 19250317175041 × 38500634350081 × 57750951525121 × 115501903050241 × 231003806100481 × 462007612200961 × 924015224401921 × 1848030448803841 × 3696060897607681 × 7392121795215361</pre>
=={{header|PARI/GP}}==
<langsyntaxhighlight lang="parigp">
cherCar(n)={
my(C=vector(n));C[1]=6; C[2]=12; for(g=3,n,C[g]=2^(g-2)*9);
Line 791 ⟶ 992:
printf("cherCar(%d): m = %d\n",n,m)}
for(x=3,9,cherCar(x))
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 803 ⟶ 1,004:
cherCar(10): m = 3208386195840
</pre>
 
=={{header|Perl}}==
{{libheader|ntheory}}
<langsyntaxhighlight lang="perl">use 5.020;
use warnings;
use ntheory qw/:all/;
Line 829 ⟶ 1,029:
foreach my $n (3..9) {
chernick_carmichael_number($n, sub (@f) { say "a($n) = ", vecprod(@f) });
}</langsyntaxhighlight>
 
{{out}}
Line 841 ⟶ 1,041:
a(9) = 58571442634534443082821160508299574798027946748324125518533225605795841
</pre>
=={{header|Phix}}==
{{libheader|Phix/mpfr}}
{{trans|Sidef}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">chernick_carmichael_factors</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">*</span><span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">12</span><span style="color: #0000FF;">*</span><span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}</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: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">m_prime</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">mpz_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">is_chernick_carmichael</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">==</span><span style="color: #000000;">2</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">m_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">*</span><span style="color: #000000;">m</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: #000000;">m_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">12</span><span style="color: #0000FF;">*</span><span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">:</span> <span style="color: #000000;">m_prime</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">m</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: #000000;">is_chernick_carmichael</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">chernick_carmichael_number</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">4</span> <span style="color: #0000FF;">?</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">mm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m</span>
<span style="color: #008080;">while</span> <span style="color: #008080;">not</span> <span style="color: #000000;">is_chernick_carmichael</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mm</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">mm</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">m</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">chernick_carmichael_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mm</span><span style="color: #0000FF;">),</span><span style="color: #000000;">mm</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">chernick_carmichael_number</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</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: #7060A8;">mpz_mul_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</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;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</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: #008080;">end</span> <span style="color: #008080;">for</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;">"U(%d,%d): %s = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" * "</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre style="font-size: 10px">
U(3,1): 1729 = 7 * 13 * 19
U(4,1): 63973 = 7 * 13 * 19 * 37
U(5,380): 26641259752490421121 = 2281 * 4561 * 6841 * 13681 * 27361
U(6,380): 1457836374916028334162241 = 2281 * 4561 * 6841 * 13681 * 27361 * 54721
U(7,780320): 24541683183872873851606952966798288052977151461406721 = 4681921 * 9363841 * 14045761 * 28091521 * 56183041 * 112366081 * 224732161
U(8,950560): 53487697914261966820654105730041031613370337776541835775672321 = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561
U(9,950560): 58571442634534443082821160508299574798027946748324125518533225605795841 = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561 * 1095045121
</pre>
Pleasingly fast, note however that a(10) remains well out of reach / would probably need a complete rewrite.
 
=== with cheat ===
=={{header|Perl 6}}==
{{trans|C}} with added cheat for the a(10) case - I found a nice big prime factor of k and added that on each iteration instead of 1.<br>
{{works with|Rakudo|2019.03}}
You could also use the sequence {1,1,1,1,19,19,4877,457,457,12564169}, if you know a way to build that, and then it wouldn't be cheating anymore...
{{trans|Perl}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
Use the ntheory library from Perl 5 for primality testing since it is much, ''much'' faster than Perl 6s built-in .is-prime method.
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ppp</span> <span style="color: #0000FF;">=</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;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">23</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">primality_pretest</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">)</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;">ppp</span><span style="color: #0000FF;">)</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;">ppp</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">23</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;">for</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">probprime</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_set_d</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: #008080;">return</span> <span style="color: #7060A8;">mpz_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">is_chernick</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">mpz</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">9</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">primality_pretest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">primality_pretest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">12</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</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: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">primality_pretest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</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;">probprime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">probprime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">12</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</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: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">probprime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</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;">return</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</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: #004080;">mpz</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">multiplier</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">4</span> <span style="color: #0000FF;">?</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">5</span> <span style="color: #008080;">then</span> <span style="color: #000000;">multiplier</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">5</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</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: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">10</span> <span style="color: #008080;">then</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">12564168</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- cheat!</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">multiplier</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">is_chernick</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</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;">"a(%d) has m = %d\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">})</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;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
a(3) has m = 1
a(4) has m = 1
a(5) has m = 380
a(6) has m = 380
a(7) has m = 780320
a(8) has m = 950560
a(9) has m = 950560
a(10) has m = 3208386195840
"0.1s"
</pre>
=={{header|Prolog}}==
SWI Prolog is too slow to solve for a(10), even with optimizing by increasing the multiplier and implementing a trial division check. (actually, my implementation of Miller-Rabin in Prolog already starts with a trial division by small primes.)
<syntaxhighlight lang="prolog">
?- use_module(library(primality)).
 
u(3, M, A * B * C) :-
<lang perl6>use Inline::Perl5;
A is 6*M + 1, B is 12*M + 1, C is 18*M + 1, !.
u(N, M, U0 * D) :-
succ(Pn, N), u(Pn, M, U0),
D is 9*(1 << (N - 2))*M + 1.
 
prime_factorization(A*B) :- prime(B), prime_factorization(A), !.
prime_factorization(A) :- prime(A).
 
step(N, 1) :- N < 5, !.
step(5, 2) :- !.
step(N, K) :- K is 5*(1 << (N - 4)).
 
a(N, Factors) :- % due to backtracking nature of Prolog, a(n) will return all chernick-carmichael numbers.
N > 2, !,
step(N, I),
between(1, infinite, J), M is I * J,
u(N, M, Factors),
prime_factorization(Factors).
 
main :-
forall(
(between(3, 9, K), once(a(K, Factorization)), N is Factorization),
format("~w: ~w = ~w~n", [K, Factorization, N])),
halt.
 
?- main.
</syntaxhighlight>
isprime predicate:
<syntaxhighlight lang="prolog">
prime(N) :-
integer(N),
N > 1,
divcheck(
N,
[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79,
83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137,
139, 149],
Result),
((Result = prime, !); miller_rabin_primality_test(N)).
 
divcheck(_, [], unknown) :- !.
divcheck(N, [P|_], prime) :- P*P > N, !.
divcheck(N, [P|Ps], State) :- N mod P =\= 0, divcheck(N, Ps, State).
 
miller_rabin_primality_test(N) :-
bases(Bases, N),
forall(member(A, Bases), strong_fermat_pseudoprime(N, A)).
 
miller_rabin_precision(16).
 
bases([31, 73], N) :- N < 9_080_191, !.
bases([2, 7, 61], N) :- N < 4_759_123_141, !.
bases([2, 325, 9_375, 28_178, 450_775, 9_780_504, 1_795_265_022], N) :-
N < 18_446_744_073_709_551_616, !. % 2^64
bases(Bases, N) :-
miller_rabin_precision(T), RndLimit is N - 2,
length(Bases, T), maplist(random_between(2, RndLimit), Bases).
 
strong_fermat_pseudoprime(N, A) :- % miller-rabin strong pseudoprime test with base A.
succ(Pn, N), factor_2s(Pn, S, D),
X is powm(A, D, N),
((X =:= 1, !); \+ composite_witness(N, S, X)).
 
composite_witness(_, 0, _) :- !.
composite_witness(N, K, X) :-
X =\= N-1,
succ(Pk, K), X2 is (X*X) mod N, composite_witness(N, Pk, X2).
 
factor_2s(N, S, D) :- factor_2s(0, N, S, D).
factor_2s(S, D, S, D) :- D /\ 1 =\= 0, !.
factor_2s(S0, D0, S, D) :-
succ(S0, S1), D1 is D0 >> 1,
factor_2s(S1, D1, S, D).
</syntaxhighlight>
{{Out}}
<pre>
3: 7*13*19 = 1729
4: 7*13*19*37 = 63973
5: 2281*4561*6841*13681*27361 = 26641259752490421121
6: 2281*4561*6841*13681*27361*54721 = 1457836374916028334162241
7: 4681921*9363841*14045761*28091521*56183041*112366081*224732161 = 24541683183872873851606952966798288052977151461406721
8: 5703361*11406721*17110081*34220161*68440321*136880641*273761281*547522561 = 53487697914261966820654105730041031613370337776541835775672321
9: 5703361*11406721*17110081*34220161*68440321*136880641*273761281*547522561*1095045121 = 58571442634534443082821160508299574798027946748324125518533225605795841
</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">
"""
 
Python implementation of
http://rosettacode.org/wiki/Chernick%27s_Carmichael_numbers
 
"""
 
# use sympy for prime test
 
from sympy import isprime
 
# based on C version
 
def primality_pretest(k):
if not (k % 3) or not (k % 5) or not (k % 7) or not (k % 11) or not(k % 13) or not (k % 17) or not (k % 19) or not (k % 23):
return (k <= 23)
return True
 
def is_chernick(n, m):
 
t = 9 * m
if not primality_pretest(6 * m + 1):
return False
if not primality_pretest(12 * m + 1):
return False
for i in range(1,n-1):
if not primality_pretest((t << i) + 1):
return False
if not isprime(6 * m + 1):
return False
if not isprime(12 * m + 1):
return False
for i in range(1,n - 1):
if not isprime((t << i) + 1):
return False
return True
for n in range(3,10):
 
if n > 4:
multiplier = 1 << (n - 4)
else:
multiplier = 1
if n > 5:
multiplier *= 5
k = 1
while True:
m = k * multiplier
if is_chernick(n, m):
print("a("+str(n)+") has m = "+str(m))
break
k += 1
</syntaxhighlight>
 
{{out}}
<pre>
a(3) has m = 1
a(4) has m = 1
a(5) has m = 380
a(6) has m = 380
a(7) has m = 780320
a(8) has m = 950560
a(9) has m = 950560
</pre>
=={{header|Raku}}==
(formerly Perl 6)
 
Use the ntheory library from Perl for primality testing since it is much, ''much'' faster than Raku's built-in .is-prime method.
{{trans|Perl}}
{{libheader|ntheory}}
<syntaxhighlight lang="raku" line>use Inline::Perl5;
use ntheory:from<Perl5> <:all>;
 
sub chernick-factors ($n, $m) {
6*6×$m + 1, 12*12×$m + 1, |((1 .. $n-2).map: { (1 +< $_) *× 9*9×$m + 1 } )
}
 
Line 857 ⟶ 1,351:
 
my $multiplier = 1 +< (($n-4) max 0);
my $iterator = $n < 5 ?? (1 .. *) !! (1 .. *).map: * *× 5;
 
$multiplier *× $iterator.first: -> $m {
[&&] chernick-factors($n, $m *× $multiplier).map: { is_prime($_) }
}
 
Line 868 ⟶ 1,362:
my $m = chernick-carmichael-number($n);
my @f = chernick-factors($n, $m);
say "U($n, $m): {[*×] @f} = {@f.join(' ⨉ ')}";
}</langsyntaxhighlight>
{{out}}
<pre>U(3, 1): 1729 = 7 ⨉ 13 ⨉ 19
Line 878 ⟶ 1,372:
U(8, 950560): 53487697914261966820654105730041031613370337776541835775672321 = 5703361 ⨉ 11406721 ⨉ 17110081 ⨉ 34220161 ⨉ 68440321 ⨉ 136880641 ⨉ 273761281 ⨉ 547522561
U(9, 950560): 58571442634534443082821160508299574798027946748324125518533225605795841 = 5703361 ⨉ 11406721 ⨉ 17110081 ⨉ 34220161 ⨉ 68440321 ⨉ 136880641 ⨉ 273761281 ⨉ 547522561 ⨉ 1095045121</pre>
 
=={{header|Phix}}==
{{libheader|mpfr}}
{{trans|Sidef}}
<lang Phix>function chernick_carmichael_factors(integer n, m)
sequence res = {6*m + 1, 12*m + 1}
for i=1 to n-2 do
res &= power(2,i) * 9*m + 1
end for
return res
end function
 
include mpfr.e
mpz p = mpz_init()
randstate state = gmp_randinit_mt()
 
function m_prime(atom a)
mpz_set_d(p,a)
return mpz_probable_prime_p(p, state)
end function
 
function is_chernick_carmichael(integer n, m)
return iff(n==2 ? m_prime(6*m + 1) and m_prime(12*m + 1)
: m_prime(power(2,n-2) * 9*m + 1) and
is_chernick_carmichael(n-1, m))
end function
function chernick_carmichael_number(integer n)
integer multiplier = iff(n>4 ? power(2,n-4) : 1), m = 1
while not is_chernick_carmichael(n, m * multiplier) do m += 1 end while
return chernick_carmichael_factors(n, m * multiplier)
end function
for n=3 to 9 do
sequence f = chernick_carmichael_number(n)
for i=1 to length(f) do f[i] = sprintf("%d",f[i]) end for
printf(1,"a(%d) = %s\n",{n,join(f," * ")})
end for</lang>
{{out}}
<pre>
a(3) = 7 * 13 * 19
a(4) = 7 * 13 * 19 * 37
a(5) = 2281 * 4561 * 6841 * 13681 * 27361
a(6) = 2281 * 4561 * 6841 * 13681 * 27361 * 54721
a(7) = 4681921 * 9363841 * 14045761 * 28091521 * 56183041 * 112366081 * 224732161
a(8) = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561
a(9) = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561 * 1095045121
</pre>
Pleasingly fast, note however that a(10) remains well out of reach / would probably need a complete rewrite.
 
=={{header|Sidef}}==
<langsyntaxhighlight lang="ruby">func chernick_carmichael_factors (n, m) {
[6*m + 1, 12*m + 1, {|i| 2**i * 9*m + 1 }.map(1 .. n-2)...]
}
Line 947 ⟶ 1,391:
for n in (3..9) {
chernick_carmichael_number(n, {|*f| say "a(#{n}) = #{f.join(' * ')}" })
}</langsyntaxhighlight>
 
{{out}}
Line 958 ⟶ 1,402:
a(8) = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561
a(9) = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561 * 1095045121
</pre>
=={{header|Wren}}==
{{trans|Go}}
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
Based on Go's 'more efficient' version. Reaches a(9) in just over 0.1 seconds but a(10) would still be out of reasonable reach for Wren so I've had to be content with that.
<syntaxhighlight lang="wren">import "./big" for BigInt, BigInts
import "./fmt" for Fmt
 
var min = 3
var max = 9
var prod = BigInt.zero
var fact = BigInt.zero
var factors = List.filled(max, 0)
var bigFactors = List.filled(max, null)
 
var init = Fn.new {
for (i in 0...max) bigFactors[i] = BigInt.zero
}
 
var isPrimePretest = Fn.new { |k|
if (k%3 == 0 || k%5 == 0 || k%7 == 0 || k%11 == 0 ||
(k%13 == 0) || k%17 == 0 || k%19 == 0 || k%23 == 0) return k <= 23
return true
}
 
var ccFactors = Fn.new { |n, m|
if (!isPrimePretest.call(6*m + 1)) return false
if (!isPrimePretest.call(12*m + 1)) return false
factors[0] = 6*m + 1
factors[1] = 12*m + 1
var t = 9 * m
var i = 1
while (i <= n-2) {
var tt = (t << i) + 1
if (!isPrimePretest.call(tt)) return false
factors[i+1] = tt
i = i + 1
}
for (i in 0...n) {
fact = BigInt.new(factors[i])
if (!fact.isProbablePrime(1)) return false
bigFactors[i] = fact
}
return true
}
 
var ccNumbers = Fn.new { |start, end|
for (n in start..end) {
var mult = 1
if (n > 4) mult = 1 << (n - 4)
if (n > 5) mult = mult * 5
var m = mult
while (true) {
if (ccFactors.call(n, m)) {
var num = BigInts.prod(bigFactors.take(n))
Fmt.print("a($d) = $i", n, num)
Fmt.print("m($d) = $d", n, m)
Fmt.print("Factors: $n\n", factors[0...n])
break
}
m = m + mult
}
}
}
 
init.call()
ccNumbers.call(min, max)</syntaxhighlight>
 
{{out}}
<pre>
a(3) = 1729
m(3) = 1
Factors: [7, 13, 19]
 
a(4) = 63973
m(4) = 1
Factors: [7, 13, 19, 37]
 
a(5) = 26641259752490421121
m(5) = 380
Factors: [2281, 4561, 6841, 13681, 27361]
 
a(6) = 1457836374916028334162241
m(6) = 380
Factors: [2281, 4561, 6841, 13681, 27361, 54721]
 
a(7) = 24541683183872873851606952966798288052977151461406721
m(7) = 780320
Factors: [4681921, 9363841, 14045761, 28091521, 56183041, 112366081, 224732161]
 
a(8) = 53487697914261966820654105730041031613370337776541835775672321
m(8) = 950560
Factors: [5703361, 11406721, 17110081, 34220161, 68440321, 136880641, 273761281, 547522561]
 
a(9) = 58571442634534443082821160508299574798027946748324125518533225605795841
m(9) = 950560
Factors: [5703361, 11406721, 17110081, 34220161, 68440321, 136880641, 273761281, 547522561, 1095045121]
</pre>
 
Line 965 ⟶ 1,507:
Using GMP (probabilistic primes),
because it is easy and fast to check primeness.
<langsyntaxhighlight lang="zkl">var [const] BI=Import("zklBigNum"); // libGMP
 
fcn ccFactors(n,m){ // not re-entrant
Line 992 ⟶ 1,534:
}
}
}</langsyntaxhighlight>
<syntaxhighlight lang ="zkl">ccNumbers(3,9);</langsyntaxhighlight>
{{out}}
<pre>
PureFox
9,476

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