Primality proof for n = 547972593843380542316719287015009101629889568888367769396279985548530313239:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=392279121964710096549298451519713063.html>392279121964710096549298451519713063 is prime.</a>
<br>b^((n-1)/392279121964710096549298451519713063)-1 mod n = 336221319157242572228177339072647353154288379984914054482518363072156405583, which is a unit, inverse 29508012851988218349713389678529848695123681584555329922853405731746189058.
<p><a href=3591893631361984318311655378233263.html>3591893631361984318311655378233263 is prime.</a>
<br>b^((n-1)/3591893631361984318311655378233263)-1 mod n = 353838021808222323291506041974753204296743444283759922554764301383369955612, which is a unit, inverse 156266049811986714501327987784296339160016474664160184004592489710820989472.
<p>(3591893631361984318311655378233263 * 392279121964710096549298451519713063) divides n-1.
<p>(3591893631361984318311655378233263 * 392279121964710096549298451519713063)^2 > n.
<p>n is prime by Pocklington's theorem.