Primality proof for n = 7545728982901378757453953508051:

Take b = 2.

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

1840314809 is prime.
b^((n-1)/1840314809)-1 mod n = 6764467150662333179018001652598, which is a unit, inverse 5437872333199248690383253769644.

3055649 is prime.
b^((n-1)/3055649)-1 mod n = 3639999861318539854536547017519, which is a unit, inverse 7484414399815812994562953968091.

(3055649 * 1840314809) divides n-1.

(3055649 * 1840314809)^2 > n.

n is prime by Pocklington's theorem.