Primality proof for n = 38916407753682983861283783766663832991809018999410768212336775108672551624633480899:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=3076403577923417822298560225319886961076812195845551214932221395885381.html>3076403577923417822298560225319886961076812195845551214932221395885381 is prime.</a>
<br>b^((n-1)/3076403577923417822298560225319886961076812195845551214932221395885381)-1 mod n = 24336299872481881868448029499484570397249177882860891882130102223308988187366917499, which is a unit, inverse 13916807670192045069570962952129734637741414345207972073932449349343359877098105899.
<p>(3076403577923417822298560225319886961076812195845551214932221395885381) divides n-1.
<p>(3076403577923417822298560225319886961076812195845551214932221395885381)^2 > n.
<p>n is prime by Pocklington's theorem.