Primality proof for n = 419614160145355971032988144925355006655173:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=24286359868392659038129333.html>24286359868392659038129333 is prime.</a>
<br>b^((n-1)/24286359868392659038129333)-1 mod n = 135097614486614224040845948467476714133015, which is a unit, inverse 192435052585548997709206578265134792049850.
<p>(24286359868392659038129333) divides n-1.
<p>(24286359868392659038129333)^2 > n.
<p>n is prime by Pocklington's theorem.