Primality proof for n = 3378892281805798826440512057402586184339:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=3752823319668658282198008768437.html>3752823319668658282198008768437 is prime.</a>
<br>b^((n-1)/3752823319668658282198008768437)-1 mod n = 184946080192435110328219018408549828350, which is a unit, inverse 659624996574668187614555563240690487199.
<p>(3752823319668658282198008768437) divides n-1.
<p>(3752823319668658282198008768437)^2 > n.
<p>n is prime by Pocklington's theorem.