Primality proof for n = 13857381403312519376221497559214358876512960238914501360589056738895920081:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=9511259360250244436150360929400467.html>9511259360250244436150360929400467 is prime.</a>
<br>b^((n-1)/9511259360250244436150360929400467)-1 mod n = 403211022392273772999941116238478883042425153299917689318478805238989903, which is a unit, inverse 9812532048474059171616830744301303112839478413107047601920033622368327746.
<p><a href=12811352796235023217778801482819.html>12811352796235023217778801482819 is prime.</a>
<br>b^((n-1)/12811352796235023217778801482819)-1 mod n = 12154747181010635607082191656695992081257909299846558435145205032027007125, which is a unit, inverse 5966913861653582794804910290640872672398844798578400157830043186154427799.
<p>(12811352796235023217778801482819 * 9511259360250244436150360929400467) divides n-1.
<p>(12811352796235023217778801482819 * 9511259360250244436150360929400467)^2 > n.
<p>n is prime by Pocklington's theorem.