Primality proof for n = 13374631042347059581:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=50711861.html>50711861 is prime.</a>
<br>b^((n-1)/50711861)-1 mod n = 4627580390468896301, which is a unit, inverse 4144201685379093368.
<p><a href=56783.html>56783 is prime.</a>
<br>b^((n-1)/56783)-1 mod n = 11606040753584551413, which is a unit, inverse 11462222911130846259.
<p>(56783 * 50711861) divides n-1.
<p>(56783 * 50711861)^2 > n.
<p>n is prime by Pocklington's theorem.