{"items": [{"author": "Satvik", "source_link": "https://www.facebook.com/jefftk/posts/630234552782?comment_id=630235615652", "anchor": "fb-630235615652", "service": "fb", "text": "Another way to formulate that first pattern is (k+1)(k-1) = k^2 - 1, thus (2^n + 1)(2^n - 1) = 2^(2n) - 1. <br><br>You're not the first person to over-extrapolate Fermat numbers...Fermat himself calculated the first 5 numbers, and held on to the belief that all such numbers were prime for *18 years* (though he admitted he had no proof).", "timestamp": "1380824345"}, {"author": "Jeff&nbsp;Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/630234552782?comment_id=630236024832", "anchor": "fb-630236024832", "service": "fb", "text": "@Satvik: \"(k+1)(k-1) = k^2 - 1\" right!  I'd forgotten; this 2^(2^n) stuff is a special case of that.", "timestamp": "1380824603"}, {"author": "Stefano", "source_link": "https://www.facebook.com/jefftk/posts/630234552782?comment_id=711899081412", "anchor": "fb-711899081412", "service": "fb", "text": "\"though he admitted he had no proof \" that's SO FERMAT", "timestamp": "1425151181"}]}