It looks like the max value is 9999999999.
"unix": 9999999999, "utc": "2286-11-20T17:46:39Z"
edit: No, I was very wrong. Adding another 9 seems to work. However, moving up one to 10000000000 does not.
edit2: Okay I wasn't wrong. It just was changed by the OP very quickly. Which I guess makes this entire post wrong now. But let the record reflect for a very brief period in my life I was correct.