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The Armenian word for seven is "yotta", which sounds suspiciously similar to the Greek prefix for a factor of one septillion (though AIUI it comes from the ancient Greek word for eight, not seven). Is there evidence that these words are related, or is it just a coincidence?

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It is a coincidence.

The prefix "yotta-" is in no way Greek. It is a modern, invented, coinage, derived from Greek ὀκτώ (okto) by a very roundabout and idiosyncratic route.

Armenian յոթ (yot') derives from Old Armenian եօթն (eot'n), older եւթն (ewtʿn), ultimately from IndoEuropean *septḿ̥

See Wiktionary here and here

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