Primality proof for n = 3572919677:

Take b = 2.

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

937 is prime.
b^((n-1)/937)-1 mod n = 690486337, which is a unit, inverse 2565679398.

383 is prime.
b^((n-1)/383)-1 mod n = 1168562122, which is a unit, inverse 602762945.

(383 * 937) divides n-1.

(383 * 937)^2 > n.

n is prime by Pocklington's theorem.