Primality proof for n = 21659270770119316173069236842332604979796116387017648600081618503821089934025961822236561982844534088440708417973331:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=13857381403312519376221497559214358876512960238914501360589056738895920081.html>13857381403312519376221497559214358876512960238914501360589056738895920081 is prime.</a>
<br>b^((n-1)/13857381403312519376221497559214358876512960238914501360589056738895920081)-1 mod n = 2576712927685190635873226528266519214685615654347412061207568284991870799176527348532866724401353967980592629254508, which is a unit, inverse 12325936529042679658713994173734649238400972111135330401608774966279305827886618979237823800795648634878579568808946.
<p>(13857381403312519376221497559214358876512960238914501360589056738895920081) divides n-1.
<p>(13857381403312519376221497559214358876512960238914501360589056738895920081)^2 > n.
<p>n is prime by Pocklington's theorem.