Primality proof for n = 471155737497642486266649722911997034941785580633861408520357030668404527002692877857903580176417856629449583072727858932500851:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1046598874349470040812238544166825597307092300404591085307326405812564486341.html>1046598874349470040812238544166825597307092300404591085307326405812564486341 is prime.</a>
<br>b^((n-1)/1046598874349470040812238544166825597307092300404591085307326405812564486341)-1 mod n = 309351804148255816433002698876812438068416132985732538566264070025732484833250407620211562424793698447908419383421777318940292, which is a unit, inverse 30193543290499120249254615871486836599207520820553011019781295503775949012169096547952231899921317341177144535699288269427382.
<p>(1046598874349470040812238544166825597307092300404591085307326405812564486341) divides n-1.
<p>(1046598874349470040812238544166825597307092300404591085307326405812564486341)^2 > n.
<p>n is prime by Pocklington's theorem.