Blum integer: Difference between revisions

Line 1,367:

<syntaxhighlight lang="perl" line>use v5.36;

use ntheory qw(is_square is_semiprime factor vecall);

use v5.36;

use enum <false true>;

use ntheory <is_prime gcd>;

sub comma { reverse ((reverse shift) =~ s/.{3}\K/,/gr) =~ s/^,//r }

sub comma { reverse((reverse shift) =~ s/.{3}\K/,/gr) =~ s/^,//r }

sub table ($c, @V) { my $t = $c * (my $w = 5); ( sprintf( ('%'.$w.'d')x@V, @V) ) =~ s/.{1,$t}\K/\n/gr }

sub table ($c, @V) { my $t = $c * (my $w = 5); (sprintf(('%' . $w . 'd') x @V, @V)) =~ s/.{1,$t}\K/\n/gr }

sub is_blum ($n) {

($n % 4) == 1 && is_semiprime($n) && !is_square($n) && vecall { ($_ % 4) == 3 } factor($n);

return false if $n < 2 or is_prime $n;

my $factor = find_factor($n);

my $div = int($n / $factor);

return true if is_prime($factor) && is_prime($div) && ($div != $factor) && ($factor%4 == 3) && ($div%4 == 3);

false;

}

sub find_factor ($n, $constant = 1) {

my($x, $rho, $factor) = (2, 1, 1);

while ($factor == 1) {

$rho *= 2;

my $fixed = $x;

for (0..$rho) {

$x = ( $x * $x + $constant ) % $n;

$factor = gcd(($x-$fixed), $n);

last if 1 < $factor;

}

$factor = find_factor($n, $constant+1) if $n == $factor;

$factor;

}

⚫

my~~($i,~~ @blum, %C);

my @nth = (26828, 1e5, 2e5, 3e5, 4e5);

⚫

my (@blum, %C);

while (++$i) {

for (my $i = 1 ; ; ++$i) {

push @blum, $i if is_blum $i;

last if $nth[-1] == ~~scalar~~ @blum;

last if $nth[-1] == @blum;

}

$C{~~substr~~ $_, ~~-1,~~ 1}++ for @blum;

$C{$_ % 10}++ for @blum;

say "The first fifty Blum integers:\n" . table 10, @blum[0..49];

say "The first fifty Blum integers:\n" . table 10, @blum[0 .. 49];

printf "The %7sth Blum integer: %9s\n", comma($_), comma $blum[$_-1] for @nth;

printf "The %7sth Blum integer: %9s\n", comma($_), comma $blum[$_ - 1] for @nth;

say '';

printf "$_: %6d (%.3f%%)\n", $C{$_}, 100*$C{$_}/scalar @blum for <1 3 7 9>;

printf "$_: %6d (%.3f%%)\n", $C{$_}, 100 * $C{$_} / scalar @blum for <1 3 7 9>;</syntaxhighlight>

</syntaxhighlight>

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