I did things a bit differently. I would advise having some clear code that talks about the BREAK line rather than using some trick to skip it. Striving for the absolute shortest code is often meaningless. Update: I went ahead and took it the redo loop trick.

I put in way more comments than normal to try to help Op understand how it works.

#!/usr/bin/perl -w
use strict;

my $last_num=0;
my @data =();

while ( my $line=<DATA>)
{

   #  Output CASE 1:
   #  A BREAK line just causes the output to be dumped
   
   if ($line =~ m/BREAK\s*$/)
   {  
      output_data(); 
      next;
   }
   
   my ($seq_num, $data) = split(/\s+/,$line); #no need for chomp
   
   #  Output CASE 2:
   #  when numbers go to far, also a signal to dump output
   #  but we've already read one line too far! 
   
   if ( ($last_num != 0) and ($seq_num > $last_num+1) )
   {
      output_data();
   }
   
   #
   #  This is the normal data processing
   
   push (@data, $data);
   $last_num = $seq_num;
   
   #print "seq_num = $seq_num data = $data\n"; #debug statement

}

#Output CASE 4:
output_data();  #last record may be here!

sub output_data
{
   
   #Output CASE 3:
   #won't print anything if data set is less than 2
   print "$data[0] $data[-1] ".@data, "\n" if @data>1;
   
   @data =();     #erase current data;
   $last_num =0;  #set up for next set
}

=prints
3DKG000004283 3DKG000004543 4
3DiKG000004569 3DiKG000004879 5
3DiKG000005165 3DiKG000005193 2
3DKG000007633 3DKG000007769 5
3DKG000008189 3DKG000008261 3
=cut

__DATA__
10000058        3DKG000004283       290.48
10000059        3DKG000004315       290.48
10000060        3DKG000004421       1693.9
10000061        3DKG000004543       3118.77
 THIS   IS      A      BREAK
10000062        3DiKG000004569      2372.94
10000063        3DiKG000004681      528.87
10000064        3DiKG000004741      187.54
10000065        3DiKG000004773      327.84
10000066        3DiKG000004879      1301.43
10000071        3DiKG000005165      17.94
10000072        3DiKG000005193      13.45
10000074        3DiKG000005261      14.33
10000076        3DiKG000005331      144 
 THIS   IS      A       BREAK
10000145        3DKG000007633       10.43
10000146        3DKG000007663       10.43
10000147        3DKG000007693       1224.8
10000148        3DKG000007727       1224.8
10000149        3DKG000007769       1359.73
10000162        3DKG000008189       307.62
10000163        3DKG000008231       307.62
10000164        3DKG000008261       14.69
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