Primality proof for n = 39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=19173790298027098165721053155794528970226934547887232785722672956982046098136719667167519737147526097.html>19173790298027098165721053155794528970226934547887232785722672956982046098136719667167519737147526097 is prime.</a>
<br>b^((n-1)/19173790298027098165721053155794528970226934547887232785722672956982046098136719667167519737147526097)-1 mod n = 20589130545846038237401292368512872887777285501716675359660390814757880357128794021938900177283661979735628815822796, which is a unit, inverse 29383782265230260129358932694103216031094940221335538712016733030718368683237214395286358116911883279502983351240333.
<p>(19173790298027098165721053155794528970226934547887232785722672956982046098136719667167519737147526097) divides n-1.
<p>(19173790298027098165721053155794528970226934547887232785722672956982046098136719667167519737147526097)^2 > n.
<p>n is prime by Pocklington's theorem.