Primality proof for n = 1890206079784759632867687927237221931415993:

Take b = 2.

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

143868846306805039381043 is prime.
b^((n-1)/143868846306805039381043)-1 mod n = 991889672936538679985176154967467539568962, which is a unit, inverse 1074257486403253704905773364364017704621796.

(143868846306805039381043) divides n-1.

(143868846306805039381043)^2 > n.

n is prime by Pocklington's theorem.