Primality proof for n = 276602624281642239937218680557139826668747:

Take b = 2.

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

19757330305831588566944191468367130476339 is prime.
b^((n-1)/19757330305831588566944191468367130476339)-1 mod n = 16383, which is a unit, inverse 94074944912245044309966580483695483989395.

(19757330305831588566944191468367130476339) divides n-1.

(19757330305831588566944191468367130476339)^2 > n.

n is prime by Pocklington's theorem.