(8·104417-71)/9 is definitely prime proved by Primality proving program based on Pocklington's theorem on January 16, 2004.
input
88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888881 2 3 5 7 11 13 17 37 47 73 97 101 137 139 193 277 353 449 641 769 829 1289 1409 1657 2393 2531 9901 19841 31051 69857 136897 153089 176641 206209 976193 1404289 1569889 4970209 5882353 6187457 19708609 25687873 32620993 99990001 1469409649 5200544353 11266057249 66554101249 18371524594609 75118313082913 143574021480139 203864078068831 549797184491917 834427406578561 2128553705161057 9999999900000001 107297848804097377 536430531035337769 1253224535459902849 757108543129939106221 11111111111111111111111 23839779350937685860961 30942987586585490641217 24649445347649059192745899 1595352086329224644348978893 4181003300071669867932658901 38115215074391056784287931569 220080633974998351355221429249 275568764703416069789958894913 374531874959836692094017219169 19108466176791400681292709171992566565029 53763491189967221358575546107279034709697 107896522139513920752730643638401909724513 120553054891405588545727822543281066162803459003848166118314367809 41784371500167158378186418717091934768077726285039694944003301299623485206849143\ 75257 82951028565871011121512196630835144518774133555852877567503980614227065994320281\ 8322753067885238020768017585089 10776547730206021548358735954380169948015708115427100064296791127608890484017725\ 60028378495799359646781326368530020399986158679489264953 60540857450154303184251426233785900839891649570009594453019947075828557696548082\ 92021644588851350106701791000405671017580904574344888167840655585532966614126382\ 28437313050421607863292067456096593355205756948146818049307851471072877007436414\ 317133005835598894375059991594580587646655948884994805993941317793 0
output
Primality proving program based on Pocklington's theorem powered by GMP 4.1.2 version 0.2.1 by M.Kamada n=888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 88888888888888888888888888888888888888888888888888888888888888888888888888888888\ 8888888888888888881 f[0]=2 f[1]=3 f[2]=5 f[3]=7 f[4]=11 f[5]=13 f[6]=17 f[7]=37 f[8]=47 f[9]=73 f[10]=97 f[11]=101 f[12]=137 f[13]=139 f[14]=193 f[15]=277 f[16]=353 f[17]=449 f[18]=641 f[19]=769 f[20]=829 f[21]=1289 f[22]=1409 f[23]=1657 f[24]=2393 f[25]=2531 f[26]=9901 f[27]=19841 f[28]=31051 f[29]=69857 f[30]=136897 f[31]=153089 f[32]=176641 f[33]=206209 f[34]=976193 f[35]=1404289 f[36]=1569889 f[37]=4970209 f[38]=5882353 f[39]=6187457 f[40]=19708609 f[41]=25687873 f[42]=32620993 f[43]=99990001 f[44]=1469409649 f[45]=5200544353 f[46]=11266057249 f[47]=66554101249 f[48]=18371524594609 f[49]=75118313082913 f[50]=143574021480139 f[51]=203864078068831 f[52]=549797184491917 f[53]=834427406578561 f[54]=2128553705161057 f[55]=9999999900000001 f[56]=107297848804097377 f[57]=536430531035337769 f[58]=1253224535459902849 f[59]=757108543129939106221 f[60]=11111111111111111111111 f[61]=23839779350937685860961 f[62]=30942987586585490641217 f[63]=24649445347649059192745899 f[64]=1595352086329224644348978893 f[65]=4181003300071669867932658901 f[66]=38115215074391056784287931569 f[67]=220080633974998351355221429249 f[68]=275568764703416069789958894913 f[69]=374531874959836692094017219169 f[70]=19108466176791400681292709171992566565029 f[71]=53763491189967221358575546107279034709697 f[72]=107896522139513920752730643638401909724513 f[73]=120553054891405588545727822543281066162803459003848166118314367809 f[74]=41784371500167158378186418717091934768077726285039694944003301299623485206\ 84914375257 f[75]=82951028565871011121512196630835144518774133555852877567503980614227065994\ 3202818322753067885238020768017585089 f[76]=10776547730206021548358735954380169948015708115427100064296791127608890484\ 01772560028378495799359646781326368530020399986158679489264953 f[77]=60540857450154303184251426233785900839891649570009594453019947075828557696\ 54808292021644588851350106701791000405671017580904574344888167840655585532966614\ 12638228437313050421607863292067456096593355205756948146818049307851471072877007\ 436414317133005835598894375059991594580587646655948884994805993941317793 prime factor check f[0] is a definitely prime factor of n-1 f[1] is a definitely prime factor of n-1 f[2] is a definitely prime factor of n-1 f[3] is a definitely prime factor of n-1 f[4] is a definitely prime factor of n-1 f[5] is a definitely prime factor of n-1 f[6] is a definitely prime factor of n-1 f[7] is a definitely prime factor of n-1 f[8] is a definitely prime factor of n-1 f[9] is a definitely prime factor of n-1 f[10] is a definitely prime factor of n-1 f[11] is a definitely prime factor of n-1 f[12] is a definitely prime factor of n-1 f[13] is a definitely prime factor of n-1 f[14] is a definitely prime factor of n-1 f[15] is a definitely prime factor of n-1 f[16] is a definitely prime factor of n-1 f[17] is a definitely prime factor of n-1 f[18] is a definitely prime factor of n-1 f[19] is a definitely prime factor of n-1 f[20] is a definitely prime factor of n-1 f[21] is a definitely prime factor of n-1 f[22] is a definitely prime factor of n-1 f[23] is a definitely prime factor of n-1 f[24] is a definitely prime factor of n-1 f[25] is a definitely prime factor of n-1 f[26] is a definitely prime factor of n-1 f[27] is a definitely prime factor of n-1 f[28] is a definitely prime factor of n-1 f[29] is a definitely prime factor of n-1 f[30] is a definitely prime factor of n-1 f[31] is a definitely prime factor of n-1 f[32] is a definitely prime factor of n-1 f[33] is a definitely prime factor of n-1 f[34] is a definitely prime factor of n-1 f[35] is a probably prime factor of n-1 f[36] is a probably prime factor of n-1 f[37] is a probably prime factor of n-1 f[38] is a probably prime factor of n-1 f[39] is a probably prime factor of n-1 f[40] is a probably prime factor of n-1 f[41] is a probably prime factor of n-1 f[42] is a probably prime factor of n-1 f[43] is a probably prime factor of n-1 f[44] is a probably prime factor of n-1 f[45] is a probably prime factor of n-1 f[46] is a probably prime factor of n-1 f[47] is a probably prime factor of n-1 f[48] is a probably prime factor of n-1 f[49] is a probably prime factor of n-1 f[50] is a probably prime factor of n-1 f[51] is a probably prime factor of n-1 f[52] is a probably prime factor of n-1 f[53] is a probably prime factor of n-1 f[54] is a probably prime factor of n-1 f[55] is a probably prime factor of n-1 f[56] is a probably prime factor of n-1 f[57] is a probably prime factor of n-1 f[58] is a probably prime factor of n-1 f[59] is a probably prime factor of n-1 f[60] is a probably prime factor of n-1 f[61] is a probably prime factor of n-1 f[62] is a probably prime factor of n-1 f[63] is a probably prime factor of n-1 f[64] is a probably prime factor of n-1 f[65] is a probably prime factor of n-1 f[66] is a probably prime factor of n-1 f[67] is a probably prime factor of n-1 f[68] is a probably prime factor of n-1 f[69] is a probably prime factor of n-1 f[70] is a probably prime factor of n-1 f[71] is a probably prime factor of n-1 f[72] is a probably prime factor of n-1 f[73] is a probably prime factor of n-1 f[74] is a probably prime factor of n-1 f[75] is a probably prime factor of n-1 f[76] is a probably prime factor of n-1 f[77] is a probably prime factor of n-1 F=f[0]^4*f[1]*f[2]*f[3]*f[4]*f[5]*f[6]*f[7]*f[8]*f[9]*f[10]*f[11]*f[12]*f[13]*f[\ 14]*f[15]*f[16]*f[17]*f[18]*f[19]*f[20]*f[21]*f[22]*f[23]*f[24]*f[25]*f[26]*f[27\ ]*f[28]*f[29]*f[30]*f[31]*f[32]*f[33]*f[34]*f[35]*f[36]*f[37]*f[38]*f[39]*f[40]*\ f[41]*f[42]*f[43]*f[44]*f[45]*f[46]*f[47]*f[48]*f[49]*f[50]*f[51]*f[52]*f[53]*f[\ 54]*f[55]*f[56]*f[57]*f[58]*f[59]*f[60]*f[61]*f[62]*f[63]*f[64]*f[65]*f[66]*f[67\ ]*f[68]*f[69]*f[70]*f[71]*f[72]*f[73]*f[74]*f[75]*f[76]*f[77] n-1=F*R F=555529112591486390273457304515672667416024177743152829532898996895813782413087\ 19682486659183935550875390732548779986715384342024044968880407501540752834711954\ 45815286279292525228594436294646154892660964530198097446006250461651742764010097\ 49756438250878036109467053292148046120202310725517787219220456165831819138642146\ 65315950862436013670157198300675075314651815721820162592910448216520085753653001\ 56180601720729831956565305311993806433591665022608847703601675757866281073342774\ 77601172138737469419770220871506417991569225712753856230630870207371277375162619\ 35341228568536785190404144469415673867613196837907577649672407768979269444720772\ 49804737787096123816578155158056155858822570828888386311819471841310072863596499\ 90713323769823849442352875407518027639320936215099399925064248892351383713376766\ 97708528842535794698418000748273111579127593411788667995128232464262169778625916\ 51259138319547122085138038737414143807223037202051177400570213646856922066041620\ 50149239026565691691022841578863055719961337451862054646435594114887944744621050\ 08348475280245200135071580423065299650946836599159135201485094484650407375621845\ 01465809130136651048606494593683471010136135467286023307500164405781896306499090\ 88003855933238918906549452792919724689644579516024867509744095391281043603579645\ 92953892915040473132543809812988147626252219725099279905346982875908901699425889\ 76873972219458941686192887957054285008851150861051080784409583777828035484719482\ 535659380307016675953342896842817168760880 R=160007615936150186351626687225816041155634538262432018023830099370942068263488\ 00073222411879096738690868638643448969987423852389629642121726155976005581814043\ 02740574757806739021030333353423269789992188731705729959752462957358106248671929\ 98026763044445429765123532301511368858318793071020409378466248579886055240518433\ 10448774644985683180859784423127862343949178392873473953273562295049818403867227\ 06668470893471771998312901323831144498736516983184661147464243027555183990644138\ 66816690503189060631299002913563827470299351330905515171702693857794183968188152\ 85751857680394076189447843418261426509589439665161781439143248037125881420772862\ 42125785352661172951941488562483772067309029037044756971496902354720370348040461\ 09093590646853198783444996753881038057157194776804078191541541774651233460178866\ 51286591607320255592999150554393876860970226471221672179783895176132376733095679\ 66831804536802725072809131448280870821737339729385655633177060715613448766158320\ 00616161373978937741840424819094963189321068918240329691703156286253992219894323\ 21782423353820172031485953607025124269201254936573071864314701037488409934073772\ 76642086143209465523525063111609319132400375600796662974354502668158975870070971\ 04257328939911820321681672348762336369534008319436880003398409708756434961695377\ 18819989853257018272555881892115956879200895677607642644879586434568458165758289\ 89472504676249425453212249086260248953840776905343019898238719511144551920111408\ 17393869796587803945854373397019255979912323485930418435302575036865472666695069\ 62897921758113164814981160387546111612972145569745799985893948291224172381357066\ 46721465276058653551554760627375179000106629215553587647748488562741135745308735\ 97659995690614601751859771487342494190658393754219080581907288356924395738879003\ 22210968942054582785648255237187586415043662708464574071864556824517108301450774\ 42310800489806495383497662036850274887661674763507814333737804772883852085376369\ 17225301882182980281579508030249513999872752363122524545934961541028230689274062\ 21377058689926471827794480705435566397976734894438303666718888410778801225619922\ 57381345686826502174266254808108759772883386339147874297444086606696946419456720\ 72907456646593504436784078037040055501283616423371554706750823123745777706136490\ 42918834251892264455313378226154368529405712610557653729307689292935727237183071\ 18389489319398351973674333217801417695124079105862733281815334343149346428687900\ 79182107864672117220623982120521405785748101145945839550232815238781293936528045\ 69745187861976517046935698795366694573042306724200631024475302066409386003127187\ 69389651431897311463260877693809242728602883385423657631764822643200692408465018\ 63838049427941179604062242975297748463434560518439583363743201834896249802262166\ 39495972902143914125755628799946183261921988361462759954791046317876232825645883\ 51176146949656458337707733658626324469702357161437207563712886777248195494812195\ 870949458678352901177974477139852311606499418231903554845601 F is not greater than R main proof 2^(n-1)=1 (mod n) gcd(2^((n-1)/f[0])-1,n)=n 3^(n-1)=1 (mod n) gcd(3^((n-1)/f[0])-1,n)=n 5^(n-1)=1 (mod n) gcd(5^((n-1)/f[0])-1,n)=n 7^(n-1)=1 (mod n) gcd(7^((n-1)/f[0])-1,n)=n 11^(n-1)=1 (mod n) gcd(11^((n-1)/f[0])-1,n)=n 13^(n-1)=1 (mod n) gcd(13^((n-1)/f[0])-1,n)=n 17^(n-1)=1 (mod n) gcd(17^((n-1)/f[0])-1,n)=n 19^(n-1)=1 (mod n) gcd(19^((n-1)/f[0])-1,n)=n 23^(n-1)=1 (mod n) gcd(23^((n-1)/f[0])-1,n)=1 gcd(2^((n-1)/f[1])-1,n)=1 gcd(2^((n-1)/f[2])-1,n)=1 gcd(2^((n-1)/f[3])-1,n)=1 gcd(2^((n-1)/f[4])-1,n)=1 gcd(2^((n-1)/f[5])-1,n)=1 gcd(2^((n-1)/f[6])-1,n)=1 gcd(2^((n-1)/f[7])-1,n)=1 gcd(2^((n-1)/f[8])-1,n)=1 gcd(2^((n-1)/f[9])-1,n)=1 gcd(2^((n-1)/f[10])-1,n)=1 gcd(2^((n-1)/f[11])-1,n)=1 gcd(2^((n-1)/f[12])-1,n)=1 gcd(2^((n-1)/f[13])-1,n)=1 gcd(2^((n-1)/f[14])-1,n)=1 gcd(2^((n-1)/f[15])-1,n)=1 gcd(2^((n-1)/f[16])-1,n)=1 gcd(2^((n-1)/f[17])-1,n)=1 gcd(2^((n-1)/f[18])-1,n)=1 gcd(2^((n-1)/f[19])-1,n)=1 gcd(2^((n-1)/f[20])-1,n)=1 gcd(2^((n-1)/f[21])-1,n)=1 gcd(2^((n-1)/f[22])-1,n)=1 gcd(2^((n-1)/f[23])-1,n)=1 gcd(2^((n-1)/f[24])-1,n)=1 gcd(2^((n-1)/f[25])-1,n)=1 gcd(2^((n-1)/f[26])-1,n)=1 gcd(2^((n-1)/f[27])-1,n)=1 gcd(2^((n-1)/f[28])-1,n)=1 gcd(2^((n-1)/f[29])-1,n)=1 gcd(2^((n-1)/f[30])-1,n)=1 gcd(2^((n-1)/f[31])-1,n)=1 gcd(2^((n-1)/f[32])-1,n)=1 gcd(2^((n-1)/f[33])-1,n)=1 gcd(2^((n-1)/f[34])-1,n)=1 gcd(2^((n-1)/f[35])-1,n)=1 gcd(2^((n-1)/f[36])-1,n)=1 gcd(2^((n-1)/f[37])-1,n)=1 gcd(2^((n-1)/f[38])-1,n)=1 gcd(2^((n-1)/f[39])-1,n)=1 gcd(2^((n-1)/f[40])-1,n)=1 gcd(2^((n-1)/f[41])-1,n)=1 gcd(2^((n-1)/f[42])-1,n)=1 gcd(2^((n-1)/f[43])-1,n)=1 gcd(2^((n-1)/f[44])-1,n)=1 gcd(2^((n-1)/f[45])-1,n)=1 gcd(2^((n-1)/f[46])-1,n)=1 gcd(2^((n-1)/f[47])-1,n)=1 gcd(2^((n-1)/f[48])-1,n)=1 gcd(2^((n-1)/f[49])-1,n)=1 gcd(2^((n-1)/f[50])-1,n)=1 gcd(2^((n-1)/f[51])-1,n)=1 gcd(2^((n-1)/f[52])-1,n)=1 gcd(2^((n-1)/f[53])-1,n)=1 gcd(2^((n-1)/f[54])-1,n)=1 gcd(2^((n-1)/f[55])-1,n)=1 gcd(2^((n-1)/f[56])-1,n)=1 gcd(2^((n-1)/f[57])-1,n)=1 gcd(2^((n-1)/f[58])-1,n)=1 gcd(2^((n-1)/f[59])-1,n)=1 gcd(2^((n-1)/f[60])-1,n)=1 gcd(2^((n-1)/f[61])-1,n)=1 gcd(2^((n-1)/f[62])-1,n)=1 gcd(2^((n-1)/f[63])-1,n)=1 gcd(2^((n-1)/f[64])-1,n)=1 gcd(2^((n-1)/f[65])-1,n)=1 gcd(2^((n-1)/f[66])-1,n)=1 gcd(2^((n-1)/f[67])-1,n)=1 gcd(2^((n-1)/f[68])-1,n)=1 gcd(2^((n-1)/f[69])-1,n)=1 gcd(2^((n-1)/f[70])-1,n)=1 gcd(2^((n-1)/f[71])-1,n)=1 gcd(2^((n-1)/f[72])-1,n)=1 gcd(2^((n-1)/f[73])-1,n)=1 gcd(2^((n-1)/f[74])-1,n)=1 gcd(2^((n-1)/f[75])-1,n)=1 gcd(2^((n-1)/f[76])-1,n)=1 gcd(2^((n-1)/f[77])-1,n)=1 R=2Fs+r, 1<=r<2F s=144013709011334304803826637085022876204979883924960814688550071625812463816481\ 86733282448423996945943268856363646153240732329419147014490681170715492978657110\ 43049883712218300377467011089892079259494744951909730085973958473312118089916511\ 42496815169681630670667694488937497231834713585449751964050089701775123822933310\ 29050406832078883561407822100810616679930909977983455317603793964161237668718711\ 99022430968429612949126392695510687551812708384836874045862009626729610933361968\ 81435211984978334821135058951289460356457499277199570417653596288300504536790733\ 30248694658533709460229989728230789742235481654996720392538097430655191665302048\ 11693202720574091928075382404108033420124874373509919617903066703044231824283371\ 24144519657140894702870604602981258234052650738681707532301136162376948368643622\ 73408555412843913898364253716526737105251467979850322735201131874291408436362493\ 94254925044727405382455869661880464732976649707499955124665084179949305592761399\ 93604645502320078940720172714213172052496851214731389244242049136761411083602430\ 64472462446909179800378449614606678592356794230947881815589949430944999316921736\ 36541778091373785925382296555665550321306542103518207881976538089402067061777126\ 43818590145647924595526116959560141341327430577255170503273210760864244662831527\ 69404997873517570814365196192868917028959679046932917206844966278215738909017017\ 03977193476347611384831859757875995220068717237374286769291894413624546902590676\ 41290615173547140353 r=843244129676189461254435257797570473387490076022834221407386128856632884976743\ 47294387471714985272136902438605036365781854379664263272005293794323553502674157\ 70322256985553115518769873188177634138480710047232846180683149847640396469292988\ 31502489025708101867699630022799631197994556752695370872217755783813019354421760\ 89988729570936484845310680346231311975281337265597598768053734486291402105489390\ 53448393975428033302168205805655759116963265586676032653145916721512264401820735\ 94460962154089936189899352736180005329408988534712820547992521142259421095741303\ 09365125522168925115171129373236897615004130788922400262394951338847057277077756\ 63003984800873878005630714745915089602522375942509196179305011264542782937792912\ 64740435552406597849884291689666201030123120897597497096279980370275258097647003\ 50974487749579865258205903745026291026749425442519389819295818005577589391964937\ 97926271065220461736977992719622550081563226628473945062216469468996359068618646\ 96664327893667439793714954291760517013401824760123249070791899892509601110523797\ 24832465975788570568752463394341551631954594224159147458421637178910059984080356\ 67232167049567147136231508345009719902636306293595850990998776370290917564466907\ 36560403670662215266977611666467397868309841213143165797856225222771076485021241\ 48819418799943302723152858073595365651850913673775077849496683200337604054591214\ 33973809653592582909118197665422042196823569875968144883314799491990774109756003\ 833643527970501943407469602106846643264321 let D be discriminant of (mF+1)(2F^2+(r-m)F+1)>=N+1 D=F^2((F(2F+r))^2-4(N-F(2F+r)))=363756534117327480250379671760860774463379367240\ 35561415099635771072882934629953530405148661745461631036280579172030498578726528\ 28781662145841516035426553192187687929130624209598406996984121493178833891356847\ 88691779041856669000824795108320129051182976859030171352126956287779409389402648\ 62959718310530573364220538404547059120075729915369845598032928329617633084373485\ 85250328561164445721168503547693220036472632542438790964798529468976954337014340\ 03909106357358024106949171569741133238659800225196906871766989539081888657673088\ 66069380023508813150008570978649319270852235165305822168008281697681326469919321\ 39907079447238048409906768566744560356987842522372398870575216831014649271725087\ 33626306422475651843085216212726193117008376323308320951141849597185433019582114\ 39824978135278007809203431815606606374163951136656871839793508438819429898657608\ 89622797998603407667748144131292536724144144705449957614663125966038926333083464\ 51101405928338946561729290860853506205867869561395804280548103617251123653618883\ 21473757283605004254354861960614861489761557358702352964921771731844772430216849\ 42720220014124789299250933652990140035722646488373207876477324291365082813499736\ 07382261230819476586061131180198830472456738982340529578740446782978633912260255\ 76109204910408442103909587436292440619104792782960549898186676799825870044671417\ 67327492929674320466350332277032157521027251087305171997981700389016568352089444\ 65509934786645947486798942825952734290833438443095787863103181887087863317976433\ 76969681068919639262422670295644902582248454756067777215316769312700812000085990\ 07920974349664940577357449981884928341587812226530924700971893986480384809071702\ 24270378802008490860923856082894754500143952658480942531833278096916330499161842\ 68227346214994235825545240769582195035798262340365840394815619699222824419004062\ 50873389387432867011263905545309377118188895616239523179837434239757256215338184\ 46244010053787567449061576746814476386149445858484093879435013939882185186215730\ 73394615814841005703441891619628538886338705042738007494075759632203094308905218\ 34548876004761546688757921946177374869608339238100170992426946087820364241283920\ 80138859707435716689253610922932232158126520689133412967552563512788663112897481\ 79010987226734372033143206093469651049023821463887633339788282085084750098025027\ 76401678347732304295769113003102609559044570972526327323378889403644719432698284\ 38848999813658739163949863979437851491594869241616798449711830395283877778863260\ 15111145864424639508456623961968498490498248616083046209107121068934815400632025\ 98026105692786753940901266622441022458484761807699814037927511699494153306804931\ 87251450655217859592514302817041878899662042029428669139528126521832961909369078\ 06650820108974985170233302893652621096660485876147918768629510628387175037415387\ 48673141382577074795245356951153531466287242671957197807105812406778571804676478\ 84386214869824495250066731956194618837653828870764929452656213106568181714766127\ 37204181859701441508693584690696025929672981243521985344402318551290020234330226\ 45717942838454342053105364309319412304678000324536204423143850366886711905960891\ 47562334360426197364308425574652616418760118444736699606804562144897308875653387\ 87229984373371858141299641352417435478663075035215234783709664646898517788126928\ 81347417777002161158418334313342069162555477604844583003915585770953741461341236\ 72767096544092580191945474442149501805335294883746291616332692239529833076199056\ 05704692210829697845138355927726537760507331971410483449184940494440241858014009\ 44244190868236221791628150758939528835201999171214733997105522661548837010708290\ 70998616022617069783791712400692650394356229502854239736172875226490677834902649\ 92254907128952653853274213567475044172799227209049257210102002040214438595410572\ 03891330327946537831684306035568207844524892125910972306529158124189030341941236\ 22338674584745952018116235418453760588478069778117332647061721742076307094530189\ 88649306958758357982587392398058681928900886973536131999420822735815087949293663\ 42792905669000782439351430396282252295577723888055531088699455193729487580070110\ 85199722027566811246210071413596815061533241574823635268928146805137759115932184\ 38931181931261270187936046652436427446544642219368008268255509039382586653907731\ 90460994716553702350206462150188921053088802129788156936943820362945854265428946\ 21587241589840712196563373382248563394455159581072314972251686378669256469593647\ 04208915670599075872667033254785934891331246495295046567820290329069784239646612\ 30933337606624386525825233394332538242153257344344143368825265369238624479487061\ 22655921968889141989995491640335709035529937722657930902281703929610913256100747\ 20642217591875237008411866999904411253153259149766242222307389489640450868106691\ 67116353228816023332807273830109025696715237651154570414273800418293929291995270\ 56735636630412779433013416960152948480148473393313074977226519433668833901361446\ 65857010343388099907082142282292663801015612207051041152074744192471336453253448\ 74477659222444175379556720334727604931493119713320113524677464085656317547340187\ 97445952611757943797528340844622434304607066210063848688333246674376991334828298\ 30740758121227447094727719595064309024688664946016504497327921973043265015789979\ 19207583147880442926482761664536291906305130807473715635474667682001584580649103\ 85073160078291153836190914824476859625753769350309821880509588018551646941868039\ 48660526427790053341069977894454401262741610729281563450209731529959573672237688\ 15870063581509358565769169044952395131673432402799243844175952588289157098715337\ 82485989193709090350348607310503187458433755499212313917789823337137736918057931\ 20410121341331391928459928602419018059246109044336773512845736887474486737831553\ 43955339507677437866281212165922672039215155167635279889974928242883775560540713\ 35179971497753387567610985335403444504047780126163841681685016652237714159304558\ 30208622598331397461230602433514872645130502837032602214127477805218680633793126\ 63419707548940050990034096484800795519470863531852526352893090540516044628202856\ 85876146308108502465166401557795497477995218823114582120877613697920890166339680\ 29845408600367324945118176060666148585934890842124119288477954417694294531894440\ 31076078322016794721197377708324415937482134867761223257522610226162539723650115\ 78553372465825771490628454559860251257899512028485870332969160673094469341131806\ 26317263174098083187030787605642103099232874810355329104664377131752361562580816\ 19990580353020089582229064210518163073818863201451090397237991150454817897049250\ 40330462171815432647643739886751073006109796327484861235410133047922228558368530\ 85279932092710381898985215370398412498499272812290863610619733568061234252550673\ 30931066453945491022440417901335488753911634130281256802290029775058470246469618\ 40365925341670289183111035233151806241277780063913394593824908086691918401831692\ 23005151544113725266385495904336068103613383008879357081172383108788206994617643\ 68316303453376648713717487223073228035024390871013047578323864006583179713642411\ 37098163410705485097069703624651798606389015062515984031475100061156139942713003\ 51937326707782546570274364556683703713881689968523634277747777646203163746853096\ 99436164971135640672454281484662538419691963547489418819010230735827553247711440\ 99723429355067712547533699838184766837011202854768930400071282585286569980180668\ 19744944157266982521454821920428412359947336693407276108065330423444879027737382\ 02575724166768526991577178727932459005932556805869950468493748084617853123927054\ 87950591994298919759919014744763719433432180795022179976084084188216404391147440\ 22353087124413888690235079641229401250658107530778318839490913464790717542247271\ 09913504721554025249233025927455693859117295246602796219660318781068711583105334\ 51314530895881026529681959954820115776162917522732296587842838481387866769643380\ 77963431353395899993698863187839748905967734321147571531370779343713739246446747\ 35878153704218682152341132888240611936797969485971858745983075666746331699897016\ 22188218908730628132896572553935786218205457902092239782874163781392073391366212\ 42375695112834878399355097881065039307280522090081297915495180853478685108478152\ 17057895779120049563338786228689154099649793789590753035359793225090934788178197\ 68539257093575220615292307809195153088394912085731552526349143094217805217312789\ 38923742318553767445665829469573810160905328369061812991236804886696929759105623\ 69713411905715608369481225038946380936527754554003973139842407326923936501484930\ 01139496099540122895803494978136534454416108411686103265452108766648813796042508\ 91639470067965080102302734941509191098911480204485175905382047002466156375610152\ 86575202806213506557737329402164242389050715617705783022867024163623381141617666\ 83288518584434512366707096271933534388905332844433418441731516328523427646252152\ 28358687237901936114071908209834489949462476727921374045021002705193921267308583\ 65969096912219313366265789889544157375647837685702839640923728225013260094867374\ 09203025554299603484682569702400 m=max(1,ceil((F^2(2F+r)-isqrt(D))/2F^2))=1 (mF+1)(2F^2+(r-m)F+1)=6031223210239590197904527870487664028534230474469038371372\ 72568232721815056991981219012553821236693980336100745346301117845572750332765167\ 31996021306252785677337686638591833860212501899638092871765009311277804946721111\ 89380200215236510261420195555573768471906982673910554971547409364729049959313614\ 12336765644717150727670414534549583883737545090085289436765800101511414296410680\ 91006251231560215099463646413266903396497027349416363637340428040465193302984558\ 08995805888131905384846194053002371019131168169855872520725067044127771338385843\ 32274194322762549225805498351193715954020792557066804990441598787822246683393519\ 67956254917874402393549536997766708440160702114619678130358330593263834969828926\ 41409573506670477316291344564371267232816401480052553743760385389416092914541356\ 03070608681518825875741859919498073677562447054889143415375332716073576290534663\ 51873585945698101094467086866370501717161518900933433676692903100514058372239929\ 85625392958863865291902766307502382549605458399280445983501433380627661872863646\ 36434218805446347052940503328822357354629714899418292690318418587891468279221096\ 14714478340878577968179267841976502897139178149216655380733053176632877914844498\ 55305664270708140450368811130899549634822867598130468157741898726966477096813161\ 79604423764455788532781837197071462563332649471691801254382982232331563133937465\ 49428211195676408399906573302289853081171563762142894617481251718081271899717877\ 53348134169906652496594106837852208263895102801123554375417746771736274114701642\ 56368523973422568474563426593852488469297432989474697995555718296938574992330829\ 32653105210716108637799749086528556741270120033804300936155401121574246138237600\ 40846053021318812525447098053514599187399108326437907943982528661858548648661380\ 04803382635507099215119714338327216521779095501866341653414001352084841864202578\ 93484415951548586126430686017948864563915619226517797631958507921546156515830151\ 09178925039124715206328264958162049168195930195323068816139774477535659347549578\ 07986068140000418293355233607205132538974072922357582504132840591769858759730128\ 60559435884652804139264222812174006241683101446750758655851476847801152748410845\ 38158789646737315907535158198413794662507668526752292988728698689250378508390409\ 63343261105210322385379131455084741536603805151380582050023776857398974366587794\ 41790933050049628139511154333432405146839026635328206062365807388680281340525713\ 41171727153251423457887780921077378011330591281267835578245641207599311423235764\ 54160428732200022051276660961869083697572648940956106286497278135077017692434475\ 88678039186789701306143431935218253547632502146655678645874422425913051437998024\ 54219026265408662361753159134197377693033950461314387586201574533299779788574839\ 79700530323905550232990043987235688131708547568868494865270697102762658114664298\ 91502459783900368375383428375661800493983284170121372055140447814228822229712449\ 74516852095582226703131117621214244075199850162712454930065474899907302741378384\ 46262246981695669010471668472458541048087263052061449889796510209442427271669423\ 48856440071639574106887563847694925806781542072573704779301026307280670422645633\ 28937815783792401976434852380691972773916029782642242501768627252599551204773700\ 68199087626560322990279557868807666829862226486424617520852595897902944492005452\ 20109313296619179498603565412383513179685088055231068924734983845551510669390705\ 72214037372592712685748054839072780948584040217623789223029102409348058693189682\ 75701716959490400714696237402172133603072023923388766739305154752056633213503348\ 25683717330843883871728971208794235265462130357926898097706419137960584726720674\ 02237642375927269113316308044600298194809269956997374620112942112977975576162569\ 95854853716997230212987903977664537869811822638234357616145106920516884982513690\ 78154429528553255850158560526649098206899481321365223329218611162513478336542843\ 33705747554149740634667497060666398350983308059217397555412416872963178509896782\ 37284275250810941036402499049103733914483361306624502607589513072447013967387757\ 93679253328445115310002258153260521397757774664111265394995615978581671718296994\ 64995145293101218290679924030486298002309254443139749601809971855975392695904945\ 07048846607401539275305812103022035591763011945684119765857869557193773368903542\ 13416225825577248392614247454676220183397778057975372895170914675734251704076383\ 79775941964636802880520028245083759331571217334697832902227878806648935778519489\ 45256882164331059212316051792974421597048578300432222869663281 (mF+1)(2F^2+(r-m)F+1) is greater than n s is not zero r^2-8s=7110606622333542280461832002083689450193112487333569179616215886956002432\ 78019383073461950343356062871270910042805055841357455097277461758659625209411484\ 17065716083535904841559927041072210488481640921827048555828904666636419261912528\ 62092751237460946773517068674428187091120575763511325078158248310841690222377581\ 59469193193014063220421790362493057514256212675195028438839709500014779092074358\ 92253008181430367269137397233098022536171489074697251150924530395920870528166504\ 51256863021607565175442366146160757996190065411443138869124333587953411613940609\ 64831362179753217345070336263071445021468073774552941229226230860367764653397029\ 28341068727306947588569060051659235131377758945432674310193811095464014127192145\ 83570167140749947638474756553129981861846977117616653792702134237550556818205533\ 83273510174289036860955522873117317384032823874075096862720951145716488214936829\ 03329159615696197630093909148975902652725150883309210061392733032155720032229414\ 19613227605108604153654337174131750355193856465989680697272548015845079137804677\ 79329866402141337419901846713002485955612142223620979563798810854000878635641541\ 18173972313973011808829311093733350204440776431002031514455334309508279179163134\ 13879119411951711673443068661752277259239529055380652824189843796611552818449374\ 95417256227727018341344943748328465785929573461753737577569397385086425705818936\ 09827465986621853187608396017138435285025004257092555763298758968850741987879778\ 58705755212310120472221496203629054944234030013649365531037585683286351889328468\ 98600265534139828052291417698100285258899794895071936585420870062876900774897969\ 87231209069003485818311832347702004574826700550441451186536403743053860353945645\ 77982018192683534226409488740539671304037589312945720764588925399901456055591069\ 83116354942973352112777126589541466624706163047153031777520478686526755536736080\ 42695930979063220202066109095980235608451010045497028929640108022894209481095857\ 06557109477706554635401740809859399496639763702303136628252860845773590055503272\ 86698786920467481151046124429933488454316858324600761899914819608645456906644374\ 34088687619928417057801531026223340881255412568598499585742746273190013962858122\ 54985802407137600815640888519650863492313917078317763140997324053843654861733933\ 90869563545257010597104336322576086769346885555194771295497898679438934937440600\ 42498913178485170577767512548944012936973917409659721879090070432646517330287826\ 12499010524303527731058590978153436416409544695642794408127529505894245881438398\ 89716391473706731074251617409736601749894073581043636605578427844349923418671228\ 77182539057851989387874954328767669538539946093056414419026947909024581526570857\ 73502419560424835024534422798057430245391942817582228966276446235442068861426056\ 09769048474772769288569398065696687317303591796317924248361779539378362166410941\ 79769084341602375071644790001813553877063470379394263276448063641800698091509982\ 08442819954220726022504421784660527792488274578629264907105264738138701215073029\ 4468217 r^2-8s=x^2+y, 0<=y<2x+1 x=843244129676189461254435257797570473387490076022834221407386128856632884976743\ 47294387471714985272136902438605036365781854379664263272005293794323553502674157\ 70322256985553115518769873188177634138480710047232846180683149847640396469292988\ 31502489025708101867699630022799631197994556752695370872217755783813019354421760\ 89988729570936484845310680346231311975281337265597598768053734486291402105489390\ 53448393975428033302168205805655759116963265586676032653145916721512264401820735\ 94460962154089936189899352736180005329408988534712820547992521142259421095741303\ 09365125522168925115171129373236897615004130788922400262394951338847057277077756\ 63003984800873878005630714745915089602522375942509196179305011264542782937792912\ 64740435552406597849884291689666201030123120897597497096279980370275258097647003\ 50974487749579865258205903745026291026749425442519389819295818005577589391964937\ 97926271065220461736977992719622550081563226628473945062216469468996359068618646\ 96664327893667439793714954291760517013401824760123249070791899892509601110523797\ 24832465975788570568752463394341551631954594224159147458421637178910059984080356\ 67232167049567147136231508345009719902636306293595850990998776370290917564466907\ 36560403670662215266977611666467397868309841213143165797856225222771076485021241\ 48819418799943302723152858073595365651850913673775077849496683200337604054591214\ 33973809653592582909118197665422042196823569875968144883314799491990774109756003\ 833643527970501943407469602106846643264320 y=168648825935237892250875530462793187933113709073600042451380827380612580130173\ 61058304487843286522572441825125133353400695414424343562708799500278357168773672\ 28615085673166793846870530646938549363665944648559377869795870389931926515451719\ 74632711308196901041448526259346351709145257934979959174665004379675767890727228\ 17280131713196713502579812036699696084371354827351454904276352424460041744672469\ 80337965505184256910737719366653677454356723005919565675625038327631665930440478\ 22815178593930520342229355730277202799096106902226460952769987628509708253514848\ 33102718700397490697167805979074696826244007758606221589299611429237011717784148\ 27821351718641453184741207492965371993150229157909510593187392262958675793989150\ 28414462756626725303006926776360668934448394531151260918597271861995957082926816\ 61105598534329023902659308064572230692238015948206555824890743483677129852574171\ 50530259881776601447444058149920931823882048856121838575264655761822671817313756\ 18659425984288745867543502486711917796365107338207512760394180230404741710965220\ 08573399103869045294305334881872557592006888568862660957396938892243536166270824\ 13850985849918894053355378326754634077653230674994716954174050750689902056262823\ 35007365517595948836384016846081827739694326153271868348263938850108034883363986\ 44077796846031357892409019214889191724705033519059586056537019865743766177541695\ 27064536204807244445687321357606300630453927426412998897045354401019164879009657\ 4151756156303481814273808879292304909405817 r^2-8s is not a square n is definitely prime 692.875 sec.
ppsiqs input
1404289 1569889 4970209 5882353 6187457 19708609 25687873 32620993 99990001 1469409649 5200544353 11266057249 66554101249 18371524594609 75118313082913 143574021480139 203864078068831 549797184491917 834427406578561 2128553705161057 9999999900000001 107297848804097377 536430531035337769 1253224535459902849 757108543129939106221 11111111111111111111111 23839779350937685860961 30942987586585490641217 24649445347649059192745899 1595352086329224644348978893 4181003300071669867932658901 38115215074391056784287931569 220080633974998351355221429249 275568764703416069789958894913 374531874959836692094017219169 19108466176791400681292709171992566565029 53763491189967221358575546107279034709697 107896522139513920752730643638401909724513 120553054891405588545727822543281066162803459003848166118314367809 41784371500167158378186418717091934768077726285039694944003301299623485206849143\ 75257 82951028565871011121512196630835144518774133555852877567503980614227065994320281\ 8322753067885238020768017585089 10776547730206021548358735954380169948015708115427100064296791127608890484017725\ 60028378495799359646781326368530020399986158679489264953 60540857450154303184251426233785900839891649570009594453019947075828557696548082\ 92021644588851350106701791000405671017580904574344888167840655585532966614126382\ 28437313050421607863292067456096593355205756948146818049307851471072877007436414\ 317133005835598894375059991594580587646655948884994805993941317793 0
ppsiqs output
Input number ( input 0 to exit ) 1404289 is probably prime t et 12 5040 Input number ( input 0 to exit ) 1569889 is probably prime t et 12 5040 Input number ( input 0 to exit ) 4970209 is probably prime t et 12 5040 Input number ( input 0 to exit ) 5882353 is probably prime t et 12 5040 Input number ( input 0 to exit ) 6187457 is probably prime t et 12 5040 Input number ( input 0 to exit ) 19708609 is probably prime t et 12 5040 Input number ( input 0 to exit ) 25687873 is probably prime t et 12 65520 Input number ( input 0 to exit ) 32620993 is probably prime t et 12 65520 Input number ( input 0 to exit ) 99990001 is probably prime t et 12 65520 Input number ( input 0 to exit ) 1469409649 is probably prime t et 12 65520 Input number ( input 0 to exit ) 5200544353 is probably prime t et 60 327600 Input number ( input 0 to exit ) 11266057249 is probably prime t et 60 327600 Input number ( input 0 to exit ) 66554101249 is probably prime t et 60 327600 Input number ( input 0 to exit ) 18371524594609 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 for P=3 Q=7 13 31 for P=5 Q=11 31 final test Input number ( input 0 to exit ) 75118313082913 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 for P=3 Q=7 13 31 for P=5 Q=11 31 final test Input number ( input 0 to exit ) 143574021480139 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 retry 61 for P=3 Q=7 13 31 61 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 203864078068831 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 for P=3 Q=7 13 31 for P=5 Q=11 31 final test Input number ( input 0 to exit ) 549797184491917 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 for P=3 Q=7 13 31 for P=5 Q=11 31 final test Input number ( input 0 to exit ) 834427406578561 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 for P=3 Q=7 13 31 for P=5 Q=11 31 final test Input number ( input 0 to exit ) 2128553705161057 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 for P=3 Q=7 13 31 for P=5 Q=11 31 final test Input number ( input 0 to exit ) 9999999900000001 is probably prime t et 60 111711600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 for P=3 Q=7 13 31 for P=5 Q=11 31 final test Input number ( input 0 to exit ) 107297848804097377 is probably prime t et 60 6814407600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 for P=3 Q=7 13 31 61 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 536430531035337769 is probably prime t et 60 6814407600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 for P=3 Q=7 13 31 61 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 1253224535459902849 is probably prime t et 60 6814407600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 for P=3 Q=7 13 31 61 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 757108543129939106221 is probably prime t et 180 388421233200 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 for P=3 Q=7 13 31 61 19 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 11111111111111111111111 is probably prime t et 180 388421233200 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 for P=3 Q=7 13 31 61 19 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 23839779350937685860961 is probably prime t et 180 388421233200 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 for P=3 Q=7 13 31 61 19 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 30942987586585490641217 is probably prime t et 180 388421233200 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 for P=3 Q=7 13 31 61 19 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 24649445347649059192745899 is probably prime t et 180 14371585628400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 for P=3 Q=7 13 31 61 19 37 for P=5 Q=11 31 61 final test Input number ( input 0 to exit ) 1595352086329224644348978893 is probably prime t et 180 2601256998740400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 for P=3 Q=7 13 31 61 19 37 181 for P=5 Q=11 31 61 181 final test Input number ( input 0 to exit ) 4181003300071669867932658901 is probably prime t et 180 2601256998740400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 for P=3 Q=7 13 31 61 19 37 181 for P=5 Q=11 31 61 181 final test Input number ( input 0 to exit ) 38115215074391056784287931569 is probably prime t et 180 2601256998740400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 for P=3 Q=7 13 31 61 19 37 181 for P=5 Q=11 31 61 181 final test Input number ( input 0 to exit ) 220080633974998351355221429249 is probably prime t et 180 2601256998740400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 for P=3 Q=7 13 31 61 19 37 181 for P=5 Q=11 31 61 181 final test Input number ( input 0 to exit ) 275568764703416069789958894913 is probably prime t et 180 2601256998740400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 for P=3 Q=7 13 31 61 19 37 181 for P=5 Q=11 31 61 181 final test Input number ( input 0 to exit ) 374531874959836692094017219169 is probably prime t et 180 2601256998740400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 for P=3 Q=7 13 31 61 19 37 181 for P=5 Q=11 31 61 181 final test Input number ( input 0 to exit ) 19108466176791400681292709171992566565029 is probably prime t et 1260 1612152436282351563600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 for P=3 Q=7 13 31 61 19 37 181 43 for P=5 Q=11 31 61 181 71 for P=7 Q=29 43 71 final test Input number ( input 0 to exit ) 53763491189967221358575546107279034709697 is probably prime t et 1260 1612152436282351563600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 for P=3 Q=7 13 31 61 19 37 181 43 for P=5 Q=11 31 61 181 71 for P=7 Q=29 43 71 final test Input number ( input 0 to exit ) 107896522139513920752730643638401909724513 is probably prime t et 1260 1612152436282351563600 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 for P=3 Q=7 13 31 61 19 37 181 43 for P=5 Q=11 31 61 181 71 for P=7 Q=29 43 71 final test Input number ( input 0 to exit ) 120553054891405588545727822543281066162803459003848166118314367809 is probably p\ rime t et 2520 941060592898327214975750763074400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 127 211 421 631 41 for P=3 Q=7 13 31 61 19 37 181 43 127 211 421 631 for P=5 Q=11 31 61 181 71 211 421 631 41 for P=7 Q=29 43 71 127 211 421 631 final test Input number ( input 0 to exit ) 41784371500167158378186418717091934768077726285039694944003301299623485206849143\ 75257 is probably prime t et 5040 186972172311057523116686181723948752936030400 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 127 211 421 631 41 73 281 2521 17\ 113 for P=3 Q=7 13 31 61 19 37 181 43 127 211 421 631 73 2521 for P=5 Q=11 31 61 181 71 211 421 631 41 281 2521 for P=7 Q=29 43 71 127 211 421 631 281 2521 113 final test Input number ( input 0 to exit ) 82951028565871011121512196630835144518774133555852877567503980614227065994320281\ 8322753067885238020768017585089 is probably prime t et 25200 1168378102584095572671947534158028685782695433121182856000 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 127 211 421 631 41 73 281 2521 17\ 113 241 337 1009 101 151 for P=3 Q=7 13 31 61 19 37 181 43 127 211 421 631 73 2521 241 337 1009 151 for P=5 Q=11 31 61 181 71 211 421 631 41 281 2521 241 101 151 for P=7 Q=29 43 71 127 211 421 631 281 2521 113 337 1009 final test Input number ( input 0 to exit ) 10776547730206021548358735954380169948015708115427100064296791127608890484017725\ 60028378495799359646781326368530020399986158679489264953 is probably prime t et 25200 207454561048856791275050095904987030401052160061082013736736636856000 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 127 211 421 631 41 73 281 2521 17\ 113 241 337 1009 101 151 401 601 701 1051 for P=3 Q=7 13 31 61 19 37 181 43 127 211 421 631 73 2521 241 337 1009 151 601 1\ 051 for P=5 Q=11 31 61 181 71 211 421 631 41 281 2521 241 101 151 401 601 701 1051 for P=7 Q=29 43 71 127 211 421 631 281 2521 113 337 1009 701 1051 final test Input number ( input 0 to exit ) 60540857450154303184251426233785900839891649570009594453019947075828557696548082\ 92021644588851350106701791000405671017580904574344888167840655585532966614126382\ 28437313050421607863292067456096593355205756948146818049307851471072877007436414\ 317133005835598894375059991594580587646655948884994805993941317793 is probably p\ rime t et 1058400 8303211261569213624192214496508606810064538400837792276227356335260\ 68601187648242841480880458339435691287354556678080121881146945460635693071833178\ 288000 Jacobi Sum Test ( APR-CL ) for P=2 Q=3 5 7 13 11 31 61 19 37 181 29 43 71 127 211 421 631 41 73 281 2521 17\ 113 241 337 1009 101 151 401 601 701 1051 1201 1801 2801 4201 6301 12601 109 27\ 1 379 433 541 757 2161 7561 15121 97 673 2017 3361 21601 30241 197 491 883 1471 \ 2647 for P=3 Q=7 13 31 61 19 37 181 43 127 211 421 631 73 2521 241 337 1009 151 601 1\ 051 1201 1801 4201 6301 12601 109 271 379 433 541 757 2161 7561 15121 97 673 201\ 7 3361 21601 30241 883 1471 2647 for P=5 Q=11 31 61 181 71 211 421 631 41 281 2521 241 101 151 401 601 701 1051 1\ 201 1801 2801 4201 6301 12601 271 541 2161 7561 15121 3361 21601 30241 491 1471 for P=7 Q=29 43 71 127 211 421 631 281 2521 113 337 1009 701 1051 2801 4201 6301\ 12601 379 757 7561 15121 673 2017 3361 30241 197 491 883 1471 2647 final test Input number ( input 0 to exit )
SIQS.LOG
========================= 1404289 is prime ========================= 1569889 is prime ========================= 4970209 is prime ========================= 5882353 is prime ========================= 6187457 is prime ========================= 19708609 is prime ========================= 25687873 is prime ========================= 32620993 is prime ========================= 99990001 is prime ========================= 1469409649 is prime ========================= 5200544353 is prime ========================= 11266057249 is prime ========================= 66554101249 is prime ========================= 18371524594609 is prime ========================= 75118313082913 is prime ========================= 143574021480139 is prime ========================= 203864078068831 is prime ========================= 549797184491917 is prime ========================= 834427406578561 is prime ========================= 2128553705161057 is prime ========================= 9999999900000001 is prime ========================= 107297848804097377 is prime ========================= 536430531035337769 is prime ========================= 1253224535459902849 is prime ========================= 757108543129939106221 is prime ========================= 11111111111111111111111 is prime ========================= 23839779350937685860961 is prime ========================= 30942987586585490641217 is prime ========================= 24649445347649059192745899 is prime ========================= 1595352086329224644348978893 is prime ========================= 4181003300071669867932658901 is prime ========================= 38115215074391056784287931569 is prime ========================= 220080633974998351355221429249 is prime ========================= 275568764703416069789958894913 is prime ========================= 374531874959836692094017219169 is prime ========================= 19108466176791400681292709171992566565029 is prime ========================= 53763491189967221358575546107279034709697 is prime ========================= 107896522139513920752730643638401909724513 is prime ========================= 120553054891405588545727822543281066162803459003848166118314367809 is prime ========================= 41784371500167158378186418717091934768077726285039694944003301299623485206849143\ 75257 is prime ========================= 82951028565871011121512196630835144518774133555852877567503980614227065994320281\ 8322753067885238020768017585089 is prime ========================= 10776547730206021548358735954380169948015708115427100064296791127608890484017725\ 60028378495799359646781326368530020399986158679489264953 is prime ========================= 60540857450154303184251426233785900839891649570009594453019947075828557696548082\ 92021644588851350106701791000405671017580904574344888167840655585532966614126382\ 28437313050421607863292067456096593355205756948146818049307851471072877007436414\ 317133005835598894375059991594580587646655948884994805993941317793 is prime