Chernick's Carmichael numbers: Difference between revisions
Rename Perl 6 -> Raku, alphabetize, minor clean-up
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a(10) has m = 3208386195840
</pre>
=={{header|C++}}==
Line 841 ⟶ 840:
a(9) = 58571442634534443082821160508299574798027946748324125518533225605795841
</pre>
=={{header|Perl 6}}==▼
{{works with|Rakudo|2019.03}}▼
{{trans|Perl}}▼
Use the ntheory library from Perl 5 for primality testing since it is much, ''much'' faster than Perl 6s built-in .is-prime method.▼
<lang perl6>use Inline::Perl5;▼
use ntheory:from<Perl5> <:all>;▼
sub chernick-factors ($n, $m) {▼
6*$m + 1, 12*$m + 1, |((1 .. $n-2).map: { (1 +< $_) * 9*$m + 1 } )▼
}▼
sub chernick-carmichael-number ($n) {▼
my $multiplier = 1 +< (($n-4) max 0);▼
my $iterator = $n < 5 ?? (1 .. *) !! (1 .. *).map: * * 5;▼
$multiplier * $iterator.first: -> $m {▼
[&&] chernick-factors($n, $m * $multiplier).map: { is_prime($_) }▼
}▼
}▼
for 3 .. 9 -> $n {▼
my $m = chernick-carmichael-number($n);▼
my @f = chernick-factors($n, $m);▼
say "U($n, $m): {[*] @f} = {@f.join(' ⨉ ')}";▼
}</lang>▼
{{out}}▼
<pre>U(3, 1): 1729 = 7 ⨉ 13 ⨉ 19▼
U(4, 1): 63973 = 7 ⨉ 13 ⨉ 19 ⨉ 37▼
U(5, 380): 26641259752490421121 = 2281 ⨉ 4561 ⨉ 6841 ⨉ 13681 ⨉ 27361▼
U(6, 380): 1457836374916028334162241 = 2281 ⨉ 4561 ⨉ 6841 ⨉ 13681 ⨉ 27361 ⨉ 54721▼
U(7, 780320): 24541683183872873851606952966798288052977151461406721 = 4681921 ⨉ 9363841 ⨉ 14045761 ⨉ 28091521 ⨉ 56183041 ⨉ 112366081 ⨉ 224732161▼
U(8, 950560): 53487697914261966820654105730041031613370337776541835775672321 = 5703361 ⨉ 11406721 ⨉ 17110081 ⨉ 34220161 ⨉ 68440321 ⨉ 136880641 ⨉ 273761281 ⨉ 547522561▼
U(9, 950560): 58571442634534443082821160508299574798027946748324125518533225605795841 = 5703361 ⨉ 11406721 ⨉ 17110081 ⨉ 34220161 ⨉ 68440321 ⨉ 136880641 ⨉ 273761281 ⨉ 547522561 ⨉ 1095045121</pre>▼
=={{header|Phix}}==
Line 931 ⟶ 893:
</pre>
Pleasingly fast, note however that a(10) remains well out of reach / would probably need a complete rewrite.
(formerly Perl 6)
▲{{works with|Rakudo|2019.03}}
▲{{trans|Perl}}
▲Use the ntheory library from Perl 5 for primality testing since it is much, ''much'' faster than Perl 6s built-in .is-prime method.
▲<lang perl6>use Inline::Perl5;
▲use ntheory:from<Perl5> <:all>;
▲sub chernick-factors ($n, $m) {
▲ 6*$m + 1, 12*$m + 1, |((1 .. $n-2).map: { (1 +< $_) * 9*$m + 1 } )
▲}
▲sub chernick-carmichael-number ($n) {
▲ my $multiplier = 1 +< (($n-4) max 0);
▲ my $iterator = $n < 5 ?? (1 .. *) !! (1 .. *).map: * * 5;
▲ $multiplier * $iterator.first: -> $m {
▲ [&&] chernick-factors($n, $m * $multiplier).map: { is_prime($_) }
▲ }
▲}
▲for 3 .. 9 -> $n {
▲ my $m = chernick-carmichael-number($n);
▲ my @f = chernick-factors($n, $m);
▲ say "U($n, $m): {[*] @f} = {@f.join(' ⨉ ')}";
▲}</lang>
▲{{out}}
▲<pre>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>
=={{header|Sidef}}==
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