This is a really basic regex question but since I can't seem to figure out why the match is failing in certain circumstances I figured I'd post it to see if anyone else can point out what I'm missing.

I'm trying to pull out the 2 sets of digits from strings of the form:

12309123098_102938120938120938
1321312_103810312032123
123123123_10983094854905490
38293827_1293120938129308

I'm using the following code to process each string:

if($string && $string =~ /^(\d)+_(\d)+$/) {
    if(IsInteger($1) && IsInteger($2)) { print "success ('$1','$2')"; }
    else { print "fail"; }
}

Where the IsInterger() function is as follows:

sub IsInteger {
    my $integer = shift;
    if($integer && $integer =~ /^\d+$/) { return 1; }
    return;
}

This function seems to work most of the time but fails on the following for some reason:

1287123437_1268098784380
1287123437_1267589971660

Any ideas on why these fail while others succeed? Thanks in advance for your help!