Primality proof for n = 3167286967475404111215579779960013343298694729431415913444417037:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=9533836766459662372116970697.html>9533836766459662372116970697 is prime.</a>
<br>b^((n-1)/9533836766459662372116970697)-1 mod n = 154318801853022251295015190968958956314004248316389551849264740, which is a unit, inverse 1996320642578129881446866087629616338888490509704543666681665061.
<p><a href=22153296627978863.html>22153296627978863 is prime.</a>
<br>b^((n-1)/22153296627978863)-1 mod n = 741588322980934153901532593185948478864044125556208390474674811, which is a unit, inverse 2993177587335983237114720435137133936166162015115981714418626676.
<p>(22153296627978863 * 9533836766459662372116970697) divides n-1.
<p>(22153296627978863 * 9533836766459662372116970697)^2 > n.
<p>n is prime by Pocklington's theorem.