I started to call the Princeton Medical Center. Here's what their contact page says:
Those letter-mnemonics are easier to remember, but harder to dial. I had dialed 1.888.PHCS4 when I noticed the numbers in parenthesis. Just in time, I resisted the urge to dial -496, because I realized that the two numbers are different!!! I'm sure they both work. But I've never before seen an all digit phone number paired with a "letter-heavy" phone number, where they weren't the same. I finished my dialing with -YOU. Weird.
By the way, I'm okay.