Primality proof for n = 3617872258517821:

Take b = 2.

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

61292713 is prime.
b^((n-1)/61292713)-1 mod n = 3536708525250730, which is a unit, inverse 1111407430832800.

(61292713) divides n-1.

(61292713)^2 > n.

n is prime by Pocklington's theorem.