Primality proof for n = 1675975991242824637446753124775730765934920727574049172215445180465220503759171922590715015775614839398225846029626614843464365685435390161686550775636333:
Take b = 2.
b^(n-1) mod n = 1.
40207916671986113857497328863224192623039803613950016309508083637168042126527904219 is prime.
b^((n-1)/40207916671986113857497328863224192623039803613950016309508083637168042126527904219)-1 mod n = 1519508504640425356407876427755774431688609750335661102422215941094743589251673214781748275797159129127380366090199029984064703555257083587798213341948895, which is a unit, inverse 1629464261065123132682542367730643939009832020881874446259011541159262518069091127821185277602541120373978452319393144905581202745875984139021418017851059.
(40207916671986113857497328863224192623039803613950016309508083637168042126527904219) divides n-1.
(40207916671986113857497328863224192623039803613950016309508083637168042126527904219)^2 > n.
n is prime by Pocklington's theorem.