Primality proof for n = 37414057161322375957408148834323969:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=25136521679249.html>25136521679249 is prime.</a>
<br>b^((n-1)/25136521679249)-1 mod n = 6772492156945118320874071589113045, which is a unit, inverse 26360473500412185258572012786466916.
<p><a href=1255525949.html>1255525949 is prime.</a>
<br>b^((n-1)/1255525949)-1 mod n = 32200227004957829326855801306052441, which is a unit, inverse 22305879472907750984994263430620755.
<p>(1255525949 * 25136521679249) divides n-1.
<p>(1255525949 * 25136521679249)^2 > n.
<p>n is prime by Pocklington's theorem.