PRP Records

Probable Primes Top 10000

(172751 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
3251(50^56597+1)/5196155Robert Price03/2014
32522^319353-11034396135Enzo Doria05/2014
325311^92309-4296130Lelio R Paula05/2016
325414^83869-13^8386996125Jean-Louis Charton01/2009
3255(7*10^96112+143)/396113Robert Price04/2016
32562^319237+6583596100Lelio R Paula03/2016
32572^319194-184196087Yves Minet03/2013
325820^73847-3196078Lelio R Paula05/2016
32592^319107-10955596061Enzo Doria04/2014
3260(3*2^319114-1)/262796060Lelio R Paula02/2014
32612^319098-11215796059Enzo Doria06/2014
326215^81673+9496055Lelio R Paula07/2016
32632^319074+187174996051Enzo Doria05/2016
32642^319007-11211196031Enzo Doria06/2014
32652^318946-142196013Yves Minet01/2013
32662^318834-11041195979Enzo Doria05/2014
32672^318831-196595978Lelio R Paula03/2016
3268(5*10^95976+7)/395977Erik Branger03/2014
32695*3^201089-895945Lelio R Paula08/2014
32702^318711-13995942Lelio R Paula11/2012
32712^318635-116795919Lelio R Paula03/2016
327215^81555+1695917Lelio R Paula07/2016
3273(22699*2^318527+1)/2195890Lelio R Paula07/2014
32742^318496-9730595877Lelio R Paula03/2016
32752^318466+1501595868Lelio R Paula03/2016
32766^123187-17312995859Mike Oakes04/2011
32772^318423-48795855Yves Minet03/2012
3278(10223*2^318350+1)/156395834Lelio R Paula07/2014
327945369!2+102495787Robert Price02/2015
32803^200758-8695786Lelio R Paula05/2016
3281(509203*2^317881-1)/5280595693Lelio R Paula04/2015
3282(11*10^95641-113)/395642Robert Price01/2017
3283(13*10^95588+11)/395589Robert Price05/2015
3284Phi(191188,10)/19118995587Maksym Voznyy11/2015
32853^200325+7095580Lelio R Paula05/2016
3286(25*10^95574-7)/995575Robert Price12/2014
3287(2^317485-3)/2131395569Lelio R Paula06/2013
32882^317464+3195567Lelio R Paula11/2012
32897^113073+8295558Lelio R Paula04/2016
32902^317251+46595503Lelio R Paula03/2016
329119^74684+5895503Lelio R Paula06/2016
3292(2^317250-7)/33995500Lelio R Paula07/2013
32936^122718-7995494Lelio R Paula05/2016
32942^317141-11049195469Enzo Doria05/2014
32952^317094+7630995455Enzo Doria05/2016
32962^317085+9595453Lelio R Paula11/2012
32972^317057-10955195444Enzo Doria04/2014
32983^200026+2895437Lelio R Paula05/2016
32992^317024+9395434Donovan Johnson06/2008
33002^316999+160595427Lelio R Paula03/2016
33012^316995-11042795426Enzo Doria05/2014
33022^316937+17795408Lelio R Paula11/2012
33032^316908+191595399Lelio R Paula03/2016
33042^316894+9995395Lelio R Paula11/2012
33056^122547+1195361Lelio R Paula05/2016
33062^316771+8287595358Lelio R Paula03/2016
3307(23*10^95326+1)/395327Serge Batalov05/2009
33081*10^95326+5795327Robert Price03/2011
330910^95326-39368795326Patrick De Geest09/2013
3310(3^199803+4)/47953995325Lelio R Paula04/2013
33112^316654-10948195323Enzo Doria04/2014
3312(50^56099+43^56099)/9395309Serge Batalov12/2016
3313(23*2^316559+1)/392595292Lelio R Paula09/2013
331419^74503-5695271Lelio R Paula06/2016
331511^91475-438095262Enzo Doria01/2013
3316(2^316321-509203)/6937795218Lelio R Paula06/2013
3317(79*10^95214-43)/995215Erik Branger11/2013
3318(9*2^316233-1)/175195194Lelio R Paula02/2014
33195*2^316213+995191Lelio R Paula08/2014
33202^316205-184816395188Enzo Doria07/2015
33212^316185-278791395182Enzo Doria04/2016
3322(9787*2^316142-1)/395172Lelio R Paula04/2015
33232^316140-595168Henri Lifchitz02/2006
3324(15185*2^316117-1)/395165Lelio R Paula04/2015
3325(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
33262^316069+7681795147Enzo Doria05/2016
3327(199*10^95134-7)/395136Robert Price02/2017
33282^316027-9730595134Lelio R Paula03/2016
33292^316006-279805195128Enzo Doria04/2016
33302^315921-279760395102Enzo Doria04/2016
33312^315857+129995083Lelio R Paula03/2016
333214^82955-4395078Lelio R Paula06/2016
3333(2*10^95072-17)/395072Robert Price08/2014
33342^315727+6595044Lelio R Paula11/2012
33352^315725+188575795043Enzo Doria03/2017
33361*10^94983+2194984Robert Price03/2011
333710^94983-71794983Patrick De Geest08/2013
333817^77187-8294975Lelio R Paula07/2016
3339(2^315481-1017)/2062728594962Lelio R Paula06/2013
33402^315423-11032994952Enzo Doria05/2014
334111^91169-723094943Enzo Doria02/2013
33427*10^94938+6194939Robert Price02/2017
33432^315351+102594931Lelio R Paula03/2016
33442^315350-11225394930Enzo Doria06/2014
3347((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
33462^315268+794906Lelio R Paula10/2012
334511^91133+6294906Lelio R Paula05/2016
334830^64244+4194897Lelio R Paula08/2012
33494^157583+2214794875Mike Oakes01/2011
33502^315098+12394854Lelio R Paula11/2012
33513^198791-3494848Robert Price11/2013
33523*2^315067+794846Lelio R Paula08/2014
3353(9*2^315057+1)/7394841Lelio R Paula09/2013
3354(16*10^94822+53)/394823Robert Price12/2016
33558*6^121849-794818Lelio R Paula10/2014
3356(85*10^94802+473)/994803Robert Price03/2017
33572^314870-10876194786Enzo Doria03/2014
33585*2^314841-394778Lelio R Paula08/2014
33596^121772+11394758Lelio R Paula05/2016
33606^121756-1625394745Enzo Doria02/2013
33612^314718-11279394740Enzo Doria06/2014
33622^314697-184729394734Enzo Doria07/2015
33632^314548-24994689Yves Minet02/2012
33645^135469+4294689Lelio R Paula04/2016
3365gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
33663*2^314152+594570Lelio R Paula08/2014
33672*6^121530-594570Lelio R Paula10/2014
33687*10^94563+8794564Robert Price11/2016
33692^314114-10967794558Enzo Doria04/2014
33702^314059+7658394542Enzo Doria05/2016
33712^314041-403594536Lelio R Paula03/2016
3372(7*2^314003-11)/1594524Renaud Lifchitz03/2011
337311^90760-471094517Enzo Doria01/2013
3374(7*2^313926-1)/14882194497Lelio R Paula02/2014
337594*10^94493-394495Robert Price11/2016
3376(1000547^15749+1)/100054894492Faysal YAtim12/2008
33777^111792-3294476Lelio R Paula04/2016
337811^90680-585094434Enzo Doria01/2013
33792^313675-11012594426Enzo Doria04/2014
3380(2999*29^64556-2427)/494410Curtis Bright05/2015
33812^313609-11222594406Enzo Doria06/2014
33822^313584+7290194399Enzo Doria04/2016
33832^313510-11286594376Enzo Doria06/2014
33847*10^94373+8794374Robert Price11/2016
3385(9^98897+8^98897)/1794371Robert Price12/2012
33862^313453-11470394359Enzo Doria04/2015
33872^313344-313344+194326Robert Price10/2014
338820^72481-4994300Lelio R Paula05/2016
338944725!2+12894289Robert Price03/2015
33904*10^94286+994287Robert Price05/2015
339117^76621+2494279Lelio R Paula07/2016
33922^313156-11285994270Enzo Doria06/2014
33936^121130-5994258Lelio R Paula05/2016
33943^197542+2894252Robert Price11/2013
3395(3^197521+2)/5165594237Lelio R Paula04/2013
33962^313045-595594236Lelio R Paula03/2016
3397(67*10^94212+23)/994213Ray Chandler02/2011
33982^312909-186520394195Enzo Doria03/2016
33992^312848-14994177Lelio R Paula11/2012
34004^156403-7759794164Mike Oakes04/2011
340118^75004-8594151Lelio R Paula06/2016
340219^73622-4894145Lelio R Paula06/2016
3403(11^90397-3^90397)/894138Robert Price04/2011
3404(3^197287+5)/1694129Lelio R Paula04/2013
340512^87212-3794118Lelio R Paula06/2016
340611^90376+7694117Lelio R Paula05/2016
3407(6^120946-11)/594114Paul Bourdelais11/2011
34082^312562-11268594091Enzo Doria06/2014
34092^312404-86968810594043Lelio R Paula09/2016
34102^312387+279353394038Enzo Doria03/2016
341210^94016+9194017Robert Price04/2011
3411(15*2^312325-1)/720194017Lelio R Paula02/2014
341310^94016-18896394016Patrick De Geest08/2013
3414(17*2^312315-1)/4594016Lelio R Paula02/2014
34156^120802+766194003Mike Oakes04/2011
3416(67607*2^312254+1)/17794001Lelio R Paula06/2014
3417(11*2^312207+1)/1993984Lelio R Paula09/2013
34182^312201+5193982Lelio R Paula11/2012
3419(4*6^120749+1)/593961Serge Batalov10/2014
34203^196892+5893942Lelio R Paula05/2016
34212^312060+1891593940Lelio R Paula03/2016
34222^311992-1620993919Enzo Doria04/2013
34232^311965-3993911Lelio R Paula11/2012
34242^311920-11168993898Enzo Doria05/2014
34257*10^93887-4793888Robert Price02/2017
342612^86965-1393851Lelio R Paula06/2016
34272^311705+1609593833Lelio R Paula03/2016
34282^311665-8193821Lelio R Paula11/2012
342911^90073+9293802Lelio R Paula05/2016
34306*10^93792+4193793Robert Price01/2017
3431(2^311580+7)/59132993790Lelio R Paula06/2013
343212^86900-7793781Lelio R Paula06/2016
34332^311508-10976993774Enzo Doria04/2014
34342^311486-185962193767Enzo Doria03/2016
3435Phi(93811,10)/968129521/2109997013/3280113810431/63963778254583193765Kurt Beschorner04/2015
34362^311471+31146993763Renaud Lifchitz01/2003
34372^311426+7945993749Enzo Doria06/2016
34382^311294+577593709Lelio R Paula03/2016
34392^311252-101793697Lelio R Paula03/2016
34402^311247-11204193695Enzo Doria06/2014
34412^311205-10964593683Enzo Doria04/2014
34425^134027-8493681Lelio R Paula04/2016
3443(2^311148-1017)/55793663Lelio R Paula06/2013
3444(2^311027-2^155514+1)/59362811/2006
34453^196192-2893608Robert Price12/2013
3446216091#+26143393606Makoto Morimoto12/2015
34475^133917+6893604Lelio R Paula04/2016
34482^310924-170993598Yves Minet03/2013
3449(266*10^93577-11)/393579Robert Price09/2016
3450(16*10^93577+161)/393578Robert Price05/2016
34513^196113-5693570Lelio R Paula04/2016
34522^310806-11034593562Enzo Doria05/2014
34533^196093+8693561Lelio R Paula04/2016
34542^310780-232793555Yves Minet10/2013
345530^63332+4193550Lelio R Paula08/2012
3456(21181*2^310707+1)/2193536Lelio R Paula06/2014
34578*5^133807+793528Lelio R Paula10/2014
34582^310686+819393526Lelio R Paula03/2016
34592^310646+6393514Lelio R Paula11/2012
3460(77*10^93508+31)/993509Robert Price10/2015
3461(1000907^15583+1)/100090893499Faysal YAtim04/2009
3462(2*10^93497+7)/993497Erik Branger03/2011
34633^195958-11285293496Enzo Doria07/2014
34642^310583+1638593495Lelio R Paula03/2016
3465(9913*2^310557-1)/3593490Lelio R Paula04/2015
34669*7^110614+293481Lelio R Paula11/2014
34672^310469-829593461Lelio R Paula03/2016
34682^310459-115993458Yves Minet11/2012
34696^120075-9593437Lelio R Paula05/2016
34702^310289+9832793407Yves Minet11/2010
34712^310217-11314393385Enzo Doria07/2014
34727^110494-6893379Lelio R Paula04/2016
34732^310184-11309393375Enzo Doria07/2014
34742^310180-11041793374Enzo Doria05/2014
3475gcd(V(1124905),5*F(224981)*(F(224981)-1)+1)93372Serge Batalov04/2015
34763^195669+6893358Lelio R Paula04/2016
347710^93356+9193357Robert Price04/2011
347810^93356-2831393356Patrick De Geest08/2013
3479(85*10^93346+23)/993347Robert Price11/2015
3480(3^195648-5)/315827693342Lelio R Paula04/2013
34813^195556+868093304Lelio R Paula04/2016
34822^309942-10999193302Enzo Doria04/2014
34832^309926-186730193298Enzo Doria03/2016
34842^309924+8595193297Yves Minet03/2011
3485(86*10^93263-77)/993264Robert Price05/2016
34866^119836-12593251Lelio R Paula05/2016
34873^195430-293244Theodore Burton02/2007
3488(13*10^93236+47)/393237Robert Price01/2017
34892^309637-1632993211Enzo Doria04/2013
3490(41*10^93207+49)/993208Robert Price04/2016
349114^81312-5793194Lelio R Paula06/2016
349241^57783-4093192Theodore Burton02/2007
34935*7^110252-493175Lelio R Paula11/2014
34942^309380-2793133Lelio R Paula11/2012
349523*10^93116-793118Robert Price03/2016
3496(29*10^93082+1)/393083Robert Price11/2015
3497(58*10^93062-13)/993063Robert Price09/2015
34982^309131+186938393058Enzo Doria05/2016
34992^309066-9393039Lelio R Paula11/2012
35002^309063-11326993038Enzo Doria07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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