If you're happy to slurp the file

my @data = do {
  open(my $fh, '<', 'yourfile') or die("ack: $!");
  local $/ = '>gb|';
  scalar <$fh>;      # first read will be useless
  <$fh>; 
};
my @nums = qw( 456-3210 4670-5490 );

for my $n (@nums) {
  print map  { '>gb|' . substr($_, 0, -4) }
        grep { $_ =~ /^$n/ } @data;
}
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So that will create an array consisting of chunks of the file delimited by >gb|, and then print any chunk that matches any of thenumber sequences in @nums.