Primality proof for n = 23978163906116309806674273528410869974800147232588444606571758029980837570993229680578504611504832152780419:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=60934327561511008916380516463943361.html>60934327561511008916380516463943361 is prime.</a>
<br>b^((n-1)/60934327561511008916380516463943361)-1 mod n = 11812447637621105011990136366077363054541643115215895109050047163005230122594956738616456690630805216525598, which is a unit, inverse 15707691776359548128845948049708415014781359516190799618266348495125083559120120322089927011749517252538594.
<p><a href=138897064261279495097010689063.html>138897064261279495097010689063 is prime.</a>
<br>b^((n-1)/138897064261279495097010689063)-1 mod n = 3604104311998622633424938329680089752096116148420715153316535707949847892778673189848238571037569480210194, which is a unit, inverse 19824653008921734764485718537886316880116243609714975086937197569909560849414903788137829925059634629917943.
<p>(138897064261279495097010689063 * 60934327561511008916380516463943361) divides n-1.
<p>(138897064261279495097010689063 * 60934327561511008916380516463943361)^2 > n.
<p>n is prime by Pocklington's theorem.