Regex replace any number of matches at the start of the line

I have text with this structure:

1.  Text1
2.  Text 2. It has a number with a dot.
3.  1.   Text31

I want to get this text:

# Text1
# Text 2. It has a number with a dot. (notice that this number did not get replaced)
## Text31

I tried doing the following but it does not work

var pattern = @"^(\s*\d+\.\s*)+";
var replaced = Regex.Replace(str, pattern, "#", RegexOptions.Multiline);

Basically, it should start matching at the start of every line and replace every matched group with # symbol. Currently, if more than one group is matched, everything is replaced by a single # symbol. Pattern I am using is probably incorrect, can anyone come up with a solution?