Primality proof for n = 181709681073901722637330951972001133588410340171829515070372549795160160121825800627002436557645897001734148521830156375752993149532941:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=134209075623850670257907127035661234387627594536271696043327.html>134209075623850670257907127035661234387627594536271696043327 is prime.</a>
<br>b^((n-1)/134209075623850670257907127035661234387627594536271696043327)-1 mod n = 74326894691175361330958554382656397001526766611051882230885260345718120802344379862730246703215694766003391436830484106708820805961156, which is a unit, inverse 123660310982692495056751896204138444868139190147315283652707553374773230934709756159951840567437204524615577881738785611399858686697002.
<p><a href=1671380110708512442103829423217.html>1671380110708512442103829423217 is prime.</a>
<br>b^((n-1)/1671380110708512442103829423217)-1 mod n = 27169729379448434579414636669065613746997482918109272394931468489201118318914202342387014624818347576127164961297355367846290588513621, which is a unit, inverse 156985120146607436686718971250774696805293084320259825575459856469898329911844521513558929674155448990638930538753036529744656622303588.
<p>(1671380110708512442103829423217 * 134209075623850670257907127035661234387627594536271696043327) divides n-1.
<p>(1671380110708512442103829423217 * 134209075623850670257907127035661234387627594536271696043327)^2 > n.
<p>n is prime by Pocklington's theorem.