Primality proof for n = 13823233105879:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=3499799.html>3499799 is prime.</a>
<br>b^((n-1)/3499799)-1 mod n = 8394433416340, which is a unit, inverse 6370809299365.
<p><a href=43.html>43 is prime.</a>
<br>b^((n-1)/43)-1 mod n = 12948309279233, which is a unit, inverse 2156286549676.
<p>(43 * 3499799) divides n-1.
<p>(43 * 3499799)^2 > n.
<p>n is prime by Pocklington's theorem.