If you're on a Sprint phone and are calling another Sprint phone, adding "11" to the 10 digit number will send you directly to their voicemail without ringing their phone. The sending and receiving phone can be any Sprint phone: Android, iPhone, dumbphone.
Example: Say the person you're calling is on Sprint, and their number is (212)555-1212. If you dial 11-212-555-1212 from your sprint cell phone, their voicemail will pick up without ringing their phone, and you can leave them a message.
This is an undocumented feature/bug of Sprint's internal call routing system, been there since the very start of their network, and ONLY works if both the calling phone and the called phone are on Sprint. And sadly, it'll most likely not be around for much longer. It'll probably go away as Sprint transitions from its somewhat antiquated ANSI SS7-type system to something that enables Voice over LTE.