Primality proof for n = 31937378989:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=3460921.html>3460921 is prime.</a>
<br>b^((n-1)/3460921)-1 mod n = 27018183262, which is a unit, inverse 23875014899.
<p>(3460921) divides n-1.
<p>(3460921)^2 > n.
<p>n is prime by Pocklington's theorem.