Primality proof for n = 18895059184283836713882776167547354480336145147521570807563207379026619142420663903487643611:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=8118493917152534667909188789691403.html>8118493917152534667909188789691403 is prime.</a>
<br>b^((n-1)/8118493917152534667909188789691403)-1 mod n = 5890375678678625228805743178373369137306852775923621680686929095793143567390997349081482251, which is a unit, inverse 7053463882840838248564049310190082487924912954143654742909108340704335599267648705066049803.
<p><a href=59180993314580506221962671096753.html>59180993314580506221962671096753 is prime.</a>
<br>b^((n-1)/59180993314580506221962671096753)-1 mod n = 13248616945087878941466497165349459792996369475884506487477018600907789870987926893346190094, which is a unit, inverse 16845568217948155236676762768198784138986692212578837378916190860260131688122253315977360076.
<p>(59180993314580506221962671096753 * 8118493917152534667909188789691403) divides n-1.
<p>(59180993314580506221962671096753 * 8118493917152534667909188789691403)^2 > n.
<p>n is prime by Pocklington's theorem.