Primality proof for n = 54727285665848639308835362515367564072984674823934369078600661778098011196929:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=112356767778179104648003230782815205059434761578340093581.html>112356767778179104648003230782815205059434761578340093581 is prime.</a>
<br>b^((n-1)/112356767778179104648003230782815205059434761578340093581)-1 mod n = 39773397674325257635700014225351136671628121202858137108871592231307367934478, which is a unit, inverse 46179359197893443383741766101026531495918353779093219391480829967062338389048.
<p>(112356767778179104648003230782815205059434761578340093581) divides n-1.
<p>(112356767778179104648003230782815205059434761578340093581)^2 > n.
<p>n is prime by Pocklington's theorem.