Primality proof for n = 42307582002575910332922579714097346549017899709713998034217522897561970639123926132812109468141778230245837569601494931472367:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=582976264895657809930367649386427562549872079.html>582976264895657809930367649386427562549872079 is prime.</a>
<br>b^((n-1)/582976264895657809930367649386427562549872079)-1 mod n = 18184092559964583369174350771144450733973948876533608143226905643021515997719815917923852931742068469392016323473034204307382, which is a unit, inverse 16411477265794035800174959309329942051409882208743462389627338592328239931685470650522739865801896124699584497933278512418395.
<p><a href=9632869229268961407429404857.html>9632869229268961407429404857 is prime.</a>
<br>b^((n-1)/9632869229268961407429404857)-1 mod n = 25611224418357691995484527959307856113209491148926246693948643570735803992616578912988461338183994814036101929351803639622290, which is a unit, inverse 21009156840434952807899055352747850611695406636497727857429092089773106776725808115161396225549718036304086711902729110197377.
<p>(9632869229268961407429404857 * 582976264895657809930367649386427562549872079) divides n-1.
<p>(9632869229268961407429404857 * 582976264895657809930367649386427562549872079)^2 > n.
<p>n is prime by Pocklington's theorem.