Primality proof for n = 40042367836462537109954173483078259560889892167509224859669902483113168741:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=3378892281805798826440512057402586184339.html>3378892281805798826440512057402586184339 is prime.</a>
<br>b^((n-1)/3378892281805798826440512057402586184339)-1 mod n = 27166613964756521151742149789247743004762583635390999898002554002616997308, which is a unit, inverse 37003065831909544219710482755234969409920878679158111530191644276923272846.
<p>(3378892281805798826440512057402586184339) divides n-1.
<p>(3378892281805798826440512057402586184339)^2 > n.
<p>n is prime by Pocklington's theorem.