Primality proof for n = 5288447750321988791615322464262168318627237463714249754277190328831105466135348245791335989419337099796002495788978276839289:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=7005507114193524029414407471112866694107408372181827430432047949693881095742546770048184168812214569007093.html>7005507114193524029414407471112866694107408372181827430432047949693881095742546770048184168812214569007093 is prime.</a>
<br>b^((n-1)/7005507114193524029414407471112866694107408372181827430432047949693881095742546770048184168812214569007093)-1 mod n = 661563047981040585557407863195166961183607641784545938928010334314512434124566303658480370479028636593741435630344833767232, which is a unit, inverse 5211483174855046129801522737876397850093939475525233568229828182535655425388954208273327453581840875921046089638966788403885.
<p>(7005507114193524029414407471112866694107408372181827430432047949693881095742546770048184168812214569007093) divides n-1.
<p>(7005507114193524029414407471112866694107408372181827430432047949693881095742546770048184168812214569007093)^2 > n.
<p>n is prime by Pocklington's theorem.