Primality proof for n = 60591682859247895515955060045153912202093072202746374731848221245220210313:

Take b = 2.

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

220355754737793598754693970385959669739 is prime.
b^((n-1)/220355754737793598754693970385959669739)-1 mod n = 20522829539963940785389210484797258588320722092216073939684967089296670202, which is a unit, inverse 15879151061902106919384613243397619218531910602569957455775705214159112534.

(220355754737793598754693970385959669739) divides n-1.

(220355754737793598754693970385959669739)^2 > n.

n is prime by Pocklington's theorem.