Primality proof for n = 26662209338045324627822402579758961857427012457827101:

Take b = 2.

b^(n-1) mod n = 1.

419614160145355971032988144925355006655173 is prime.
b^((n-1)/419614160145355971032988144925355006655173)-1 mod n = 11854262717827283296765183007971426279078579223152857, which is a unit, inverse 22912777519750553734509558013554391359522547795969214.

(419614160145355971032988144925355006655173) divides n-1.

(419614160145355971032988144925355006655173)^2 > n.

n is prime by Pocklington's theorem.