My style with the '..' operator:

use strict;
use warnings;

my %numbers = ( '2345678923' => 1,
                '2121212121' => 1,
                '4424352424' => 1,
                '2323232323' => 1 );

while (<DATA>) {
   chomp;
   if (/<BEGIN Transaction/ .. /<END Transaction>/) {
      if (/(?:^|\D)(\d+)(?:\D|$)/ && exists $numbers{$_}) {
         print "<BEGIN Transaction>$_<END Transaction>\n";
      }
   }
}

__DATA__
<BEGIN Transaction>
2345678923
</END Transaction>
<BEGIN Transaction>
1
</END Transaction>
junk
<BEGIN Transaction>
12345678923
</END Transaction>
<BEGIN Transaction>
2121212121
</END Transaction>
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