Primality proof for n = 3055465788140352002733946906144561090641249606160407884365391979704929268480326390471:

Take b = 2.

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

1059392654943455286185473617842338478315215895509773412096307 is prime.
b^((n-1)/1059392654943455286185473617842338478315215895509773412096307)-1 mod n = 5563581472304666537367698222031436414809456114137236663142714881049629858689529786, which is a unit, inverse 2712496454280912552189064744403578205633632341143601555674953748700913292982480842577.

(1059392654943455286185473617842338478315215895509773412096307) divides n-1.

(1059392654943455286185473617842338478315215895509773412096307)^2 > n.

n is prime by Pocklington's theorem.