Try:

push @ten_digit_numbers, $1 while ($string =~ /(\d{10})/g);
print "found: @ten_digit_numbers\n";
[download]

The "push ... while" is not needed:

   my $string = "this 12345567890 is a 1029384756 test";

   my @results = $string =~ /\d{10}/g;

   print "@results\n";
[download]

In other words, instead of trying to remove stuff, flip it around and try to get stuff. If all you want is the 10-digit numbers, zenfargoyle's answer is the appropriate one.

------
We are the carpenters and bricklayers of the Information Age.

Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.

What you wrote means, "do s/\d{10}//g and then return success if it failed." Although that sounds a little funny and is not what you intended, it could actually be useful. Perhaps this will help you conceptualize what is happening:

if ($string !~ s/\d{10}//g) {
   print "String unchanged: couldn't find 10 digits.\n";
   # do stuff to deal with regex failure
}
else {
   print "All cases of 10 digits have been deleted.\n";
}
[download]

if (not $string =~ s/\d{10}//g) {
unless ($string =~ s/\d{10}//g) {
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------------------------------------------------------------
"Perl is a mess and that's good because the
problem space is also a mess." - Larry Wall

$string =~ s/\d{1,9}//g;
$string =~ s/\d{11,}//g;
$string =~ s/\D//g;
[download]

Note: If your $string starts with 3 10 digit numbers, you will end up with one thirty digit number when you are done. Probably not such a big deal since you know the exact size of each number