Primality proof for n = 274641681901431937:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=27869213.html>27869213 is prime.</a>
<br>b^((n-1)/27869213)-1 mod n = 101106520766935027, which is a unit, inverse 226249110964769897.
<p><a href=313.html>313 is prime.</a>
<br>b^((n-1)/313)-1 mod n = 37174037842747943, which is a unit, inverse 267650764067605571.
<p>(313 * 27869213) divides n-1.
<p>(313 * 27869213)^2 > n.
<p>n is prime by Pocklington's theorem.