Primality proof for n = 490812343031:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=49081234303.html>49081234303 is prime.</a>
<br>b^((n-1)/49081234303)-1 mod n = 1023, which is a unit, inverse 443794151812.
<p>(49081234303) divides n-1.
<p>(49081234303)^2 > n.
<p>n is prime by Pocklington's theorem.