Primality proof for n = 351209660225850764954644159:

Take b = 2.

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

2291581 is prime.
b^((n-1)/2291581)-1 mod n = 116002226738860544040725983, which is a unit, inverse 52112169542952434812978563.

962161 is prime.
b^((n-1)/962161)-1 mod n = 220193262975906730524207967, which is a unit, inverse 79131288168169884235299646.

15137 is prime.
b^((n-1)/15137)-1 mod n = 18418084680925879693246707, which is a unit, inverse 186812079661992554363942192.

(15137 * 962161 * 2291581) divides n-1.

(15137 * 962161 * 2291581)^2 > n.

n is prime by Pocklington's theorem.