Primality proof for n = 6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=173308343918874810521923841.html>173308343918874810521923841 is prime.</a>
<br>b^((n-1)/173308343918874810521923841)-1 mod n = 6757709552787258283224292191130684403894131589762095923502462941530245153069290375851876247496322657786424190818591301735358207324248587433958854421908561003, which is a unit, inverse 6184049710182637047250982257292669555953986533094740368460765621820197314631113605032171456158958339938932905268956511189366980706880035796547580014208313570.
<p><a href=145295143558111.html>145295143558111 is prime.</a>
<br>b^((n-1)/145295143558111)-1 mod n = 3918415953319283151208477086007404346654576509226865903312798514180220402469210473811465761777842924051569397787348621256045827427164265273775342708072438779, which is a unit, inverse 2993322874796537353731467333582375797958073529922232752616946095831926375581587344784699133534860493190113741338619836859914977989256923056099316018242836782.
<p><a href=108140989558681.html>108140989558681 is prime.</a>
<br>b^((n-1)/108140989558681)-1 mod n = 5544264574857850964197733731661996467755052040950199944180374754841464329009999810703863617519207144860949817044524829625784502045225800019021018185516947149, which is a unit, inverse 4374077595673420886762068079357869289326809148373269480754169543646888573509121731683323598051276712974842721007895036085644341756342083332907981138641674646.
<p><a href=65427463921.html>65427463921 is prime.</a>
<br>b^((n-1)/65427463921)-1 mod n = 6512740200978147221820528467633942643040181066780047388147181964537846353846469052317558538489073912329794774901895899237559116951420139188716322281368423489, which is a unit, inverse 1554052947962961277781815108872592295246480335993777250639421559043146779205075052366887913834776440259864705519770785678635752467793428942740474029957265698.
<p><a href=2400573761.html>2400573761 is prime.</a>
<br>b^((n-1)/2400573761)-1 mod n = 1380874192327717388082288631309116191900933214983527487372909874424674266874074700692801808154649700940917111200136259256360265846213945449743250295990946286, which is a unit, inverse 2520606218608634882394832217569255465844393423080553407771326579875311935204639994713364075901884872585910111680317334894480474606167798483794081571649727564.
<p><a href=308761441.html>308761441 is prime.</a>
<br>b^((n-1)/308761441)-1 mod n = 1623889643233634573993602058016407655328141090820326818495641584970893961220942206555491516809574561195117209027502533998765179014195862801239601346069015352, which is a unit, inverse 3590915639602655421865563483278719321598691171293266075397271533086042121463415156115812969724264260988861276334225204706359713808824787011530785631557331685.
<p>(308761441 * 2400573761 * 65427463921 * 108140989558681 * 145295143558111 * 173308343918874810521923841) divides n-1.
<p>(308761441 * 2400573761 * 65427463921 * 108140989558681 * 145295143558111 * 173308343918874810521923841)^2 > n.
<p>n is prime by Pocklington's theorem.