As of 10/4/2015, no live official trademarks were found on USPTO.gov for the exact term/number
8883838888 (asymmetrical version)
In the West, a 10-number domain may seem too long and mean little to average Occidentals; heck, we don't fully understand the premise, either. However...
In the Chinese market, "8" is the luckiest number.
In addition, the number "38" represents triple prosperity.
We cannot even fathom what 8.com, 88.com, 888.com, and 8888.com are worth -- probably much more than the average investor could afford.
Long repeating 8's are prized as well. In fact, 5, 6, 7, 8, 9, and even 10+ repeating 8's are commanding excellent prices these days.
Evidently, every possible string of 8's have been registered in .com, all the way up to the longest one.
Finally, repeating 8's with other lucky numerals are becoming rare as hand registrations (fresh from the registrar) and are also highly prized.
The Chinese market for numerals is HUGE.
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