LEGO Digital Designer Part Numbers
The two different number systems are:


Element ID: 6-7 digits, uniquely identifies a piece by shape and color
Part number: usually 4-5 digits, uniquely identifies a piece shape, stamped on many bricks


(Unfortunately an element ID is not simply a few numbers added onto a part number)

In LDD regular mode (not extended mode), you can search by both numbers. I was able to find the 3L blue pins by searching both element ID 4514553 and part number 6558. When in extended mode however you can only search by part number (many of those pieces listed are only in extended mode).

Generally, you can also search for an element ID on BrickLink and find the part number. Not sure about going the other way.