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Two short words and an ending. Eight at a time, because the good one is usually the fourth.
No hyphens and no digits. Both are legal in a domain and both cost you every time somebody has to say the address out loud.
The two words are picked so that the joins do not repeat a letter, because "newwork" is a domain people mistype forever.
Checking availability means asking a registrar, which means telling a company which domains you are interested in. This page asks nobody, so you have to check yourself.
Everything runs on your device; no lookup leaves this page.
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