Primality proof for n = 380059961:

Take b = 2.

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

7583 is prime.
b^((n-1)/7583)-1 mod n = 284000832, which is a unit, inverse 32291158.

179 is prime.
b^((n-1)/179)-1 mod n = 190086705, which is a unit, inverse 117268543.

(179 * 7583) divides n-1.

(179 * 7583)^2 > n.

n is prime by Pocklington's theorem.