Primality proof for n = 12811352796235023217778801482819:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=726928914639303991.html>726928914639303991 is prime.</a>
<br>b^((n-1)/726928914639303991)-1 mod n = 6534906295293682835644564431795, which is a unit, inverse 2638829258957252504571109598233.
<p>(726928914639303991) divides n-1.
<p>(726928914639303991)^2 > n.
<p>n is prime by Pocklington's theorem.