Have you tried use re 'debug';

Yes. But it didn't help. It shows that matches do occur; but doesn't explain why the newlines are never inserted.

It seems your example data miss a digit at the end of each number.

My mistake trying to simplify the data. Two corrections are possible:

1. Remove one \d from each side of the regex:

   while( <DATA> ) {
       s[\s(\d+)\d\K\s(?=(\d+)\d\s)]{
           print "$1:$2";
           $1 + 1 == $2 ? "\n" : ' '
       }ge;
       print;
   }
   [download]

2. Add a digit to the end of each number in the data:

   1051 1061 1071 1081 1091 1101 1111 1121 1131
   11151 11161 11171 11181 11191 11201 11211 11221 11231
   123451 123461 123471 123481 123491 123501 123511 123531
   [download]

as you know what the regex should do

The idea of the regex is to match each pair of numbers in a line and capture the first d-2 digits of each number.

Eg. Match the pair and capture the first two digits of each:  (10)91 (11)01.

Then if $1+1 (10+1) == $2 (11) replace the space between them with a newline.

The \K prevents the number before the replaced space being replaced. And the lookahead prevents the number after ebing replaced.