Primality proof for n = 181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=547972593843380542316719287015009101629889568888367769396279985548530313239.html>547972593843380542316719287015009101629889568888367769396279985548530313239 is prime.</a>
<br>b^((n-1)/547972593843380542316719287015009101629889568888367769396279985548530313239)-1 mod n = 13995993571918153025736360650318956434327835245585226838198420867415647141113543606157090355023190097782870659400805051055600910483491, which is a unit, inverse 151206335236078112364174442497238138328346587776066277356501210072100520604335529866549970650721051305665642246799060090783851727146302.
<p>(547972593843380542316719287015009101629889568888367769396279985548530313239) divides n-1.
<p>(547972593843380542316719287015009101629889568888367769396279985548530313239)^2 > n.
<p>n is prime by Pocklington's theorem.