Primality proof for n = 125972502705620325124785968921221517:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=168233516889622588559.html>168233516889622588559 is prime.</a>
<br>b^((n-1)/168233516889622588559)-1 mod n = 83502151627756640504099316019809415, which is a unit, inverse 83728809698945167079696810615893670.
<p>(168233516889622588559) divides n-1.
<p>(168233516889622588559)^2 > n.
<p>n is prime by Pocklington's theorem.