Primality proof for n = 30461532566489734432033897907025322605647670983785646081730729521647935009277217:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=11165728476386063307853657259304797238595952598104253398091264650988917.html>11165728476386063307853657259304797238595952598104253398091264650988917 is prime.</a>
<br>b^((n-1)/11165728476386063307853657259304797238595952598104253398091264650988917)-1 mod n = 4591665778645111823285309638972316729903666303295021943357682181467002615307631, which is a unit, inverse 1709904931675066487327128912428503550333667001559745729281955830457788293027520.
<p>(11165728476386063307853657259304797238595952598104253398091264650988917) divides n-1.
<p>(11165728476386063307853657259304797238595952598104253398091264650988917)^2 > n.
<p>n is prime by Pocklington's theorem.