Your Mother's suggestion of using a database is likely to be the best answer, but where you want to speed up a search for multiple records using the text file you can do something like:

use strict;
use warnings;

my @wanted = qw(1101077781172 1101077781180 1101077781183);
my %match = map {$_ => 1} @wanted;

while (<DATA>) {
    chomp;

    my (@fields) = split;

    next unless @fields >= 3;
    print "$_\n" if exists $match{$fields[0]};
}


__DATA__
1101077781160   1101077783656   bothChaff
1101077781161   1101077783657   bothChaff
1101077781162   1101077783658   bothChaff
...
[download]

Prints:

1101077781172   1101077783668   bothChaff
1101077781180   1101077783676   oneDegen
[download]