Primality proof for n = 17942392077136950785977011829:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1495199339761412565498084319.html>1495199339761412565498084319 is prime.</a>
<br>b^((n-1)/1495199339761412565498084319)-1 mod n = 4095, which is a unit, inverse 2808564913661730269550980362.
<p>(1495199339761412565498084319) divides n-1.
<p>(1495199339761412565498084319)^2 > n.
<p>n is prime by Pocklington's theorem.