Primality proof for n = 61292713:

Take b = 2.

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

1301 is prime.
b^((n-1)/1301)-1 mod n = 34554112, which is a unit, inverse 36003754.

151 is prime.
b^((n-1)/151)-1 mod n = 42273170, which is a unit, inverse 30294922.

(151 * 1301) divides n-1.

(151 * 1301)^2 > n.

n is prime by Pocklington's theorem.