Here are some ways to do it:

#!perl -w
use strict;
use File::stat;

# Method 1: 
my $input_directory_lowest = "pridir";
opendir (LOWEST, $input_directory_lowest) 
  or die "Error opening directory: $!"; 
my @files;
while (my $fname = readdir LOWEST) {
 if ($fname =~ /^Flat_file.*\.txt$/) {
   push @files,
    [stat("$input_directory_lowest/$fname")->ctime, $fname];
 }
}
closedir(LOWEST);

my @low1 = 
  map { $_->[1] } 
    sort {$a->[0] <=> $b->[0]} @files;

print join("\n  ", "low1=", @low1), "\n";


# Method 2: same as 1, but without explicit loop
opendir (LOWEST, $input_directory_lowest) 
  or die "Error opening directory: $!"; 
my @low2 =
  map { $_->[1] }
   sort {$a->[0] <=> $b->[0]}
     map { [ stat("$input_directory_lowest/$_")->ctime, $_ ] }
       grep /^Flat_file.*txt$/,
         readdir(LOWEST);

closedir(LOWEST);
print join("\n  ", "low2=", @low2), "\n";


# Method 3: outputs file names with directory; uses 'glob'
my @low3 = 
  map { $_->[1] }
   sort {$a->[0] <=> $b->[0]}
     map { [ stat($_)->ctime, $_ ] }
       glob("$input_directory_lowest/Flat_file*.txt");
print join("\n  ", "low3=", @low3), "\n";
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