Primality proof for n = 726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018365439:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=37414057161322375957408148834323969.html>37414057161322375957408148834323969 is prime.</a>
<br>b^((n-1)/37414057161322375957408148834323969)-1 mod n = 540366568130778135898441510835856455534389914303085338364659337135897003548076429119005429909235469480789211561903941233448506771974658, which is a unit, inverse 519518080572253603367051247665846755713605907580011593346876370765869096000338358463558345755733082510164841518241698999535429907019721.
<p><a href=596242599987116128415063.html>596242599987116128415063 is prime.</a>
<br>b^((n-1)/596242599987116128415063)-1 mod n = 190003410667075674092982632203727792856127504982081000771883257365242547555534483515426075207288243150997979464781148373943997064249656, which is a unit, inverse 622143034522204649195295391496844845148580674104142999054667679714261380717200767300452778319734914841204185644938301518028430773008897.
<p><a href=167773885276849215533569.html>167773885276849215533569 is prime.</a>
<br>b^((n-1)/167773885276849215533569)-1 mod n = 55525769416912324234359085335631801563531687326947362005607509724730022900672777197089304749607041703088011799398802938442416997100247, which is a unit, inverse 501788639088368826987400606481767918276057647070744111966357515498496197208259609929578546273395592909823544835784940147559659365465460.
<p>(167773885276849215533569 * 596242599987116128415063 * 37414057161322375957408148834323969) divides n-1.
<p>(167773885276849215533569 * 596242599987116128415063 * 37414057161322375957408148834323969)^2 > n.
<p>n is prime by Pocklington's theorem.