Chernick's Carmichael numbers: Difference between revisions
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→{{header|Wren}}: Minor tidy
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<br><br>
=={{header|C}}==
{{libheader|GMP}}
<
#include <stdlib.h>
#include <gmp.h>
Line 106 ⟶ 105:
return 0;
}</
{{out}}
<pre>
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a(10) has m = 3208386195840
</pre>
=={{header|C++}}==
{{libheader|GMP}}
<
#include <iostream>
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return 0;
}</
{{out}}
<pre>
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</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#)]
<
// 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>
{{out}}
<pre>
Line 238 ⟶ 235:
cherCar(9): m=950560 primes -> [5703361; 11406721; 17110081; 34220161; 68440321; 136880641; 273761281; 547522561; 1095045121]
</pre>
===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===
<
import (
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func main() {
ccNumbers(3, 9)
}</
{{out}}
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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.
<
import (
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func main() {
ccNumbers(min, max)
}</
{{out}}
Line 449 ⟶ 492:
Factors: [19250317175041 38500634350081 57750951525121 115501903050241 231003806100481 462007612200961 924015224401921 1848030448803841 3696060897607681 7392121795215361]
</pre>
=={{header|J}}==
▲=={{header|j}}==
Brute force:
<
if.3=y do.1729 return.end.
m=. z=. 2^y-4
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m=.m+z
end.
}}</
Task examples:
<
1729
a 4
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53487697914261966820654105730041031613370337776541835775672321
a 9
58571442634534443082821160508299574798027946748324125518533225605795841</
=={{header|Java}}==
<
import java.math.BigInteger;
import java.util.ArrayList;
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}
</syntaxhighlight>
{{out}}
<pre>
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U(9, 950560) = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561 * 1095045121 = 58571442634534443082821160508299574798027946748324125518533225605795841
</pre>
=={{header|Julia}}==
<
function trial_pretest(k::UInt64)
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end
cc_numbers(3, 10)</
{{out}}
Line 813 ⟶ 853:
(takes ~6.5 minutes)
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<
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}]
Line 840 ⟶ 879:
FindFirstChernickCarmichaelNumber[7]
FindFirstChernickCarmichaelNumber[8]
FindFirstChernickCarmichaelNumber[9]</
{{out}}
<pre>{1,1729}
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{950560,53487697914261966820654105730041031613370337776541835775672321}
{950560,58571442634534443082821160508299574798027946748324125518533225605795841}</pre>
=={{header|Nim}}==
{{libheader|bignum}}
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With these optimizations, the program executes in 4-5 minutes.
<
import bignum
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s.addSep(" × ")
s.add($factor)
stdout.write s, '\n'</
{{out}}
Line 945 ⟶ 983:
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}}==
<
cherCar(n)={
my(C=vector(n));C[1]=6; C[2]=12; for(g=3,n,C[g]=2^(g-2)*9);
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printf("cherCar(%d): m = %d\n",n,m)}
for(x=3,9,cherCar(x))
</syntaxhighlight>
{{out}}
<pre>
Line 967 ⟶ 1,004:
cherCar(10): m = 3208386195840
</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<
use warnings;
use ntheory qw/:all/;
Line 993 ⟶ 1,029:
foreach my $n (3..9) {
chernick_carmichael_number($n, sub (@f) { say "a($n) = ", vecprod(@f) });
}</
{{out}}
Line 1,005 ⟶ 1,041:
a(9) = 58571442634534443082821160508299574798027946748324125518533225605795841
</pre>
=={{header|Phix}}==
{{libheader|Phix/mpfr}}
{{trans|Sidef}}
<!--<
<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>
Line 1,048 ⟶ 1,083:
<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>
<!--</
{{out}}
<pre style="font-size: 10px">
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{{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>
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...
<!--<
<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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</
{{out}}
<pre>
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"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)).
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?- main.
</syntaxhighlight>
isprime predicate:
<syntaxhighlight lang="prolog">
prime(N) :-
integer(N),
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succ(S0, S1), D1 is D0 >> 1,
factor_2s(S1, D1, S, D).
</syntaxhighlight>
{{Out}}
<pre>
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</pre>
=={{header|Python}}==
<
"""
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k += 1
</syntaxhighlight>
{{out}}
Line 1,301 ⟶ 1,335:
a(9) has m = 950560
</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{trans|Perl}}▼
Use the ntheory library from Perl 5 for primality testing since it is much, ''much'' faster than Rakus built-in .is-prime method.▼
▲Use the ntheory library from Perl
<lang perl6>use Inline::Perl5;▼
▲{{trans|Perl}}
{{libheader|ntheory}}
use ntheory:from<Perl5> <:all>;
sub chernick-factors ($n, $m) {
}
Line 1,318 ⟶ 1,351:
my $multiplier = 1 +< (($n-4) max 0);
my $iterator = $n < 5 ?? (1 .. *) !! (1 .. *).map: *
$multiplier
[&&] chernick-factors($n, $m
}
Line 1,329 ⟶ 1,362:
my $m = chernick-carmichael-number($n);
my @f = chernick-factors($n, $m);
say "U($n, $m): {[
}</
{{out}}
<pre>U(3, 1): 1729 = 7 ⨉ 13 ⨉ 19
Line 1,339 ⟶ 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|Sidef}}==
<
[6*m + 1, 12*m + 1, {|i| 2**i * 9*m + 1 }.map(1 .. n-2)...]
}
Line 1,359 ⟶ 1,391:
for n in (3..9) {
chernick_carmichael_number(n, {|*f| say "a(#{n}) = #{f.join(' * ')}" })
}</
{{out}}
Line 1,371 ⟶ 1,403:
a(9) = 5703361 * 11406721 * 17110081 * 34220161 * 68440321 * 136880641 * 273761281 * 547522561 * 1095045121
</pre>
=={{header|Wren}}==
{{trans|Go}}
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{{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.
<
import "./fmt" for Fmt
var min = 3
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init.call()
ccNumbers.call(min, max)</
{{out}}
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Using GMP (probabilistic primes),
because it is easy and fast to check primeness.
<
fcn ccFactors(n,m){ // not re-entrant
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}
}
}</
<syntaxhighlight lang
{{out}}
<pre>
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