If you don't want to risk races, use sysopen and loop until you can create the file yourself:
#!/usr/bin/perl -w
use strict; use warnings; use 5.010;
use Fcntl qw/ O_CREAT O_EXCL O_WRONLY /;
my $fh = open_next( "Results", ".txt" );
print $fh "Hello!\n";
sub open_next {
my ($prefix, $suffix) = @_;
my $number = 0;
my $FH;
until (sysopen($FH, ($prefix . ($number || "") .$suffix), O_WRONLY
+|O_EXCL|O_CREAT)) {
$number++;
}
return $FH;
}
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