Unrelated to the problem which you already fixed... here are some tips (which you might already know)
You can save yourself some typing by eliminating those quotes and commas. Use qw as a list constructor.
my @unsorted = qw(
864278_864377
864518_864703
851171_851270
855398_855579
856258_856357
861015_861139
866387_866549
791806_792296
1088806_1082296
);
Also, the Core Data::Dumper module is handy for printing arbitrary data structures:
use Data::Dumper;
print Dumper(\@sorted);
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