The Story of the World's Most Popular Superstition (Avalon, 2004), author Nathaniel Lachenmeyer argues that the commingling of "unlucky Friday" and "unlucky 13" took place in the pages of a specific literary work, a novel published in 1907 titled — what else? — Friday, the Thirteenth.
The book, all but forgotten now, concerned dirty dealings in the stock market and sold quite well in its day. Both the titular phrase and the phobic premise behind it — namely that superstitious people regard Friday the 13th as a supremely unlucky day — were instantly adopted and popularized by the press.
It seems unlikely that the novelist, Thomas W. Lawson, literally invented that premise himself — he treats it within the story, in fact, as a notion that already existed in the public consciousness — but he most certainly lent it gravitas and set it on a path to becoming the most widespread superstition in modern times.
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