Another Mersenne factorization

(Continuing Mersenne Factorization)

? ispseudoprime(2^4423-1)
%44 = 1

? print(factorint(2^4423-2))

[2, 1; 3, 2; 7, 1; 23, 1; 67, 2; 89, 1; 683, 1; 1609, 1; 2011, 1; 4423, 1; 9649, 1; 13267, 1; 20857, 1; 22111, 1; 39799, 1; 283009, 1; 599479, 1; 6324667, 1; 7327657, 1; 193707721, 1; 12148690313, 1; 12371522263, 1; 361859649163, 1; 761838257287, 1; 6713103182899, 1; 224134035919267, 1; 3556355492892313, 1; 5157050159173695487, 1; 17153597302151518561, 1; 17904041241938148871927, 1; 59151549118532676874448563, 1; 1647072866431538116058878617811, 1; 87449423397425857942678833145441, 1; 1963672214729590922916323781834466879, 1; 49929707724752567469731915956762751258933207272739486748238351859309991348433, 1; 40393566547943595749562506243285884534929026356774912763863482259566537671583290150415083011252727505582091, 1; 245646981125691497673324668265536334044341262452177697864695233686173498977525877540362298849614068695233671, 1; 29792282327632127192280512714312339494458105715740509816040019161219528270861465666941470299423164525021764760664757557501816665197191248140710453823079834899917278481203481942074120698987141443607970695192539694488469929529584413885826254451155851081784465332583575562462448913571987013144129130422035667076921, 1; 81306434126435390369376308017426816467338589074376606953450887738659949122190481971292960301001128628269985908910250733571484380927682097166969483636698401864705393738719321415525908871375830643489767976984133538274257006197857712319103629206245907496601803359738478994241731519997695185318284051254656008033048015655006605203258597365919579712675545019366698923697429439095730189943, 1]

? znprimroot(2^4423-1)
%45 = Mod(7, 285542542228279613901563566102164008326164238644702889199247456602284400390600653875954571505539843239754513915896150297878399377056071435169747221107988791198200988477531339214282772016059009904586686254989084815735422480409022344297588352526004383890632616124076317387416881148592486188361873904175783145696016919574390765598280188599035578448591077683677175520434074287726578006266759615970759521327828555662781678385691581844436444812511562428136742490459363212810180276096088111401003377570363545725120924073646921576797146199387619296560302680261790118132925012323046444438622308877924609373773012481681672424493674474488537770155783006880852648161513067144814790288366664062257274665275787127374649231096375001170901890786263324619578795731425693805073056119677580338084333381987500902968831935913095269821311141322393356490178488728982288156282600813831296143663845945431144043753821542871277745606447858564159213328443580206422714694913091762716447041689678070096773590429808909616750452927258000843500344831628297089902728649981994387647234574276263729694848304750917174186181130688518792748622612293341368928056634384466646326572476167275660839105650528975713899320211121495795311427946254553305387067821067601768750977866100460014602138408448021225053689054793742003095722096732954750721718115531871310231057902608580607)

This is the result of the factorization of 2^2211+1 noted earlier, and a fortuitously easy factorization of the primitive part of 2^2211-1 (and of course lots of hard work by others for 2^737+-1)