Primality proof for n = 19173790298027098165721053155794528970226934547887232785722672956982046098136719667167519737147526097:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=12397338596863679689524759770405177749801411.html>12397338596863679689524759770405177749801411 is prime.</a>
<br>b^((n-1)/12397338596863679689524759770405177749801411)-1 mod n = 2539117792220556006441845660179844080937154456605443202561962260010654127191785336148804255125174771, which is a unit, inverse 4965032846660451006894594672251535978686376798432297212367094385305698025297354036999309611502433574.
<p><a href=529709925838459440593.html>529709925838459440593 is prime.</a>
<br>b^((n-1)/529709925838459440593)-1 mod n = 18654722295080779974836048271850388944497961014241089788342851007261594700951844323631654696672060687, which is a unit, inverse 15575792314690497902928137703166167001597435883390653128097062667454861604445175549384151863819903606.
<p>(529709925838459440593 * 12397338596863679689524759770405177749801411) divides n-1.
<p>(529709925838459440593 * 12397338596863679689524759770405177749801411)^2 > n.
<p>n is prime by Pocklington's theorem.