PRP Records

Probable Primes Top 10000

(291910 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 (> 50000) Who ? When ?
8751(5928^25537-1)/592796345Serge Batalov06/2022
87532^320043-10877596343Enzo Doria04/2014
875224989^7168+7168^2498996343Hans Havermann11/2019
875410^96338+42493996339Patrick De Geest03/2016
875510^96338-928196338Robert Price09/2015
8756(8527^24509-1)/852696336Serge Batalov06/2022
8757(3*2^320008+1)/796332Lelio R Paula09/2013
8758(2444^28433-1)/244396331Serge Batalov06/2022
8759(48690^20551-1)/4868996327Serge Batalov06/2022
8760(61935^20101-1)/6193496318Serge Batalov06/2022
876125699^5596+5596^2569996317Hans Havermann07/2020
8762(7*10^96312+83)/996312Tyler Busby01/2023
8763(11*10^96298+529)/996299Robert Price09/2021
876526502^4297+4297^2650296287Hans Havermann07/2020
8764(54180^20341-1)/5417996287Serge Batalov06/2022
87662^319838+425796281Lelio R Paula03/2016
87672^319830-1699596279Lelio R Paula03/2016
87686^123713+14396268Lelio R Paula05/2016
8769(28*10^96265-97)/396266Robert Price07/2016
8770(3799^26893-1)/379896265Serge Batalov06/2022
8772103^47825-10296264Norbert Schneider10/2016
8771(54041^20341-1)/5404096264Serge Batalov06/2022
8773(2^319777+2082)/296263Stefano Morozzi09/2020
8774(2^319771+3686)/296261Stefano Morozzi09/2020
87752^319713-8196244Lelio R Paula11/2012
8776(55459*2^319706+1)/2016796242Lelio R Paula07/2014
877722834^16393+16393^2283496238Hans Havermann05/2020
87788*10^96236+2796237Robert Price09/2021
877912^89153-4396213Lelio R Paula06/2016
8780(25048^21871-1)/2504796202Serge Batalov06/2022
8782(2*10^96195-59)/396195Robert Price05/2017
87819*10^96194-7796195Robert Price08/2020
87832^319545+14796193Lelio R Paula11/2012
878423357^13128+13128^2335796189Hans Havermann02/2020
8785(19838^22381-1)/1983796179Serge Batalov06/2022
8786(221^41023-1)/22096172Serge Batalov06/2022
878725952^5073+5073^2595296160Hans Havermann12/2019
8788(50891^20431-1)/5089096157Serge Batalov06/2022
8789(50^56597+1)/5196155Robert Price03/2014
879022313^20374+20374^2231396149Hans Havermann12/2019
879122279^20668+20668^2227996141Hans Havermann11/2019
8792(41*10^96137-59)/996138Robert Price10/2017
87932^319353-11034396135Enzo Doria05/2014
879411^92309-4296130Lelio R Paula05/2016
8795(21675^22171-1)/2167496129Serge Batalov06/2022
879614^83869-13^8386996125Jean-Louis Charton01/2009
8797(7*10^96112+143)/396113Robert Price04/2016
879826731^3940+3940^2673196112Hans Havermann07/2020
879922640^17583+17583^2264096109Hans Havermann07/2020
8800(19178^22441-1)/1917796107Serge Batalov06/2022
88012^319237+6583596100Lelio R Paula03/2016
88022^319194-184196087Yves Minet03/2013
880323949^10280+10280^2394996084Hans Havermann07/2020
8804(1927^29251-1)/192696083Serge Batalov06/2022
880520^73847-3196078Lelio R Paula05/2016
8806(60229^20101-1)/6022896075Serge Batalov06/2022
8807(28044^21601-1)/2804396074Serge Batalov06/2022
880850^56543-4996065Norbert Schneider09/2018
88092^319107-10955596061Enzo Doria04/2014
8810(3*2^319114-1)/262796060Lelio R Paula02/2014
88112^319098-11215796059Enzo Doria06/2014
881215^81673+9496055Lelio R Paula07/2016
8813(85761^19471-1)/8576096052Serge Batalov06/2022
88142^319074+187174996051Enzo Doria05/2016
881525670^5517+5517^2567096050Hans Havermann06/2020
88166*10^96037+1996038Robert Price11/2021
88172^319007-11211196031Enzo Doria06/2014
8818(57987^20161-1)/5798696029Serge Batalov06/2022
88202^318946-142196013Yves Minet01/2013
8819(68310^19861-1)/6830996013Serge Batalov06/2022
8821(20294^22291-1)/2029396012Serge Batalov06/2022
8822(304^38669-1)/30396008Serge Batalov06/2022
8823(1840^29401-1)/183995986Serge Batalov06/2022
882422830^16003+16003^2283095982Hans Havermann02/2020
88252^318834-11041195979Enzo Doria05/2014
88262^318831-196595978Lelio R Paula03/2016
8827(5*10^95976+7)/395977Erik Branger03/2014
8828(12797^23369-1)/1279695975Serge Batalov06/2022
8829(10534^23857-1)/1053395963Serge Batalov06/2022
883022871^15696+15696^2287195962Hans Havermann01/2020
8831(2^318760+858)/295957Stefano Morozzi02/2021
883223167^13860+13860^2316795953Hans Havermann01/2020
8833(823^32911-1)/82295946Serge Batalov06/2022
88355*3^201089-895945Lelio R Paula08/2014
8834(81783^19531-1)/8178295945Serge Batalov06/2022
88362^318711-13995942Lelio R Paula11/2012
88372^318635-116795919Lelio R Paula03/2016
883815^81555+1695917Lelio R Paula07/2016
8839(37*10^95895+377)/995896Robert Price10/2017
8840(22699*2^318527+1)/2195890Lelio R Paula07/2014
88412^318496-9730595877Lelio R Paula03/2016
884222129^21496+21496^2212995871Hans Havermann07/2020
88442^318466+1501595868Lelio R Paula03/2016
884324847^7216+7216^2484795868Hans Havermann07/2020
884523706^11065+11065^2370695866Hans Havermann07/2020
8846(2863^27733-1)/286295865Serge Batalov06/2022
88476^123187-17312995859Mike Oakes04/2011
88482^318423-48795855Yves Minet03/2012
884910^95848+44370995849Patrick De Geest10/2022
885010^95848-500000000195848Robert Price09/2022
885110^95848-6197195848Patrick De Geest10/2022
8852(2^318359+678)/295836Stefano Morozzi09/2020
8853(10223*2^318350+1)/156395834Lelio R Paula07/2014
8854(8060^24533-1)/805995831Serge Batalov06/2022
8855(9853^23993-1)/985295814Serge Batalov06/2022
8857(2^318267+2550)/295808Stefano Morozzi09/2020
8856(5048^25873-1)/504795808Serge Batalov06/2022
88594*10^95799+1395800Robert Price02/2021
8858(65533^19891-1)/6553295800Serge Batalov06/2022
886045369!2+102495787Robert Price02/2015
88613^200758-8695786Lelio R Paula05/2016
8862(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
8863(2^318171+2030)/295779Stefano Morozzi09/2020
88643*10^95776-5995777Robert Price10/2017
8865(82970^19471-1)/8296995772Serge Batalov06/2022
8866193^41901-295768Lelio R Paula10/2017
8867(2^318124+2502)/295765Stefano Morozzi09/2020
8868(12900^23297-1)/1289995761Serge Batalov06/2022
88694*10^95752-7195753Robert Price11/2017
8870(16955^22639-1)/1695495743Serge Batalov06/2022
8871(81795^19489-1)/8179495740Serge Batalov06/2022
8872(2742^27847-1)/274195737Serge Batalov06/2022
8873(6072^25303-1)/607195726Serge Batalov06/2022
887423640^11197+11197^2364095721Hans Havermann12/2019
887510^95712+8932995713Patrick De Geest09/2022
887710^95712-400000195712Robert Price07/2021
887610^95712-98931395712Patrick De Geest09/2022
8878(60657^20011-1)/6065695706Serge Batalov06/2022
8879((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
8880(509203*2^317881-1)/5280595693Lelio R Paula04/2015
8881(26161^21661-1)/2616095687Serge Batalov06/2022
8882(2^317853+1086)/295683Stefano Morozzi09/2020
88834*10^95672+9195673Robert Price11/2017
88846*10^95665+4395666Robert Price07/2020
8885(20819^22153-1)/2081895663Serge Batalov06/2022
8886(64464^19891-1)/6446395658Serge Batalov06/2022
8887(934^32203-1)/93395652Serge Batalov06/2022
8888(11*10^95641-113)/395642Robert Price01/2017
8889(72330^19681-1)/7232995632Serge Batalov06/2022
8890(13224^23203-1)/1322395624Serge Batalov06/2022
8891(18211^22441-1)/1821095602Serge Batalov06/2022
8892(71975^19681-1)/7197495590Serge Batalov06/2022
8893(13*10^95588+11)/395589Robert Price05/2015
8894Phi(191188,10)/19118995587Maksym Voznyy11/2015
8895(13368^23167-1)/1336795585Serge Batalov06/2022
8896(25874^21661-1)/2587395583Serge Batalov06/2022
88973^200325+7095580Lelio R Paula05/2016
8898(25*10^95574-7)/995575Robert Price12/2014
8899(2^317485-3)/2131395569Lelio R Paula06/2013
89002^317464+3195567Lelio R Paula11/2012
8901(2^317451+2114)/295562Stefano Morozzi09/2020
89027^113073+8295558Lelio R Paula04/2016
8903(24728^21751-1)/2472795552Serge Batalov06/2022
8904(49764^20341-1)/4976395536Serge Batalov06/2022
8905(36155^20959-1)/3615495531Serge Batalov06/2022
8906(7725^24571-1)/772495526Serge Batalov06/2022
8907(20546^22147-1)/2054595510Serge Batalov06/2022
89082^317251+46595503Lelio R Paula03/2016
890919^74684+5895503Lelio R Paula06/2016
8910(2^317250-7)/33995500Lelio R Paula07/2013
89115*10^95498-2195499Robert Price12/2021
8912(21615^22031-1)/2161495495Serge Batalov06/2022
89136^122718-7995494Lelio R Paula05/2016
891422168^20291+20291^2216895485Hans Havermann10/2019
8915(77427^19531-1)/7742695481Serge Batalov06/2022
8916(13026^23203-1)/1302595472Serge Batalov06/2022
89172^317141-11049195469Enzo Doria05/2014
8918(2^317097+3014)/295456Stefano Morozzi09/2020
89192^317094+7630995455Enzo Doria05/2016
89202^317085+9595453Lelio R Paula11/2012
8921(17*10^95451-377)/995452Robert Price11/2017
89222^317057-10955195444Enzo Doria04/2014
89233^200026+2895437Lelio R Paula05/2016
89242^317024+9395434Donovan Johnson06/2008
8925(86*10^95428-437)/995429Robert Price03/2021
892610^95427+19259195428Patrick De Geest05/2021
89292^316999+160595427Lelio R Paula03/2016
8928(2^317000+3210)/295427Stefano Morozzi09/2020
892710^95427-1000195427Robert Price02/2021
89302^316995-11042795426Enzo Doria05/2014
8931(69841^19699-1)/6984095420Serge Batalov06/2022
8932(59242^19993-1)/5924195415Serge Batalov06/2022
893422300^18987+18987^2230095410Hans Havermann06/2020
8933(9478^23993-1)/947795410Serge Batalov06/2022
89352^316937+17795408Lelio R Paula11/2012
89364*10^95407+9195408Robert Price11/2017
89372^316908+191595399Lelio R Paula03/2016
89382^316894+9995395Lelio R Paula11/2012
8939(2^316887+2546)/295393Stefano Morozzi09/2020
89402*10^95374-2195375Robert Price09/2020
89416^122547+1195361Lelio R Paula05/2016
89422^316771+8287595358Lelio R Paula03/2016
8943(15609^22741-1)/1560895358Serge Batalov06/2022
8944(2^316765+3102)/295356Stefano Morozzi09/2020
8945(2267^28411-1)/226695329Serge Batalov06/2022
8946(824^32693-1)/82395328Serge Batalov06/2022
8947(23*10^95326+1)/395327Serge Batalov05/2009
89481*10^95326+5795327Robert Price03/2011
894910^95326-39368795326Patrick De Geest09/2013
8950(3^199803+4)/47953995325Lelio R Paula04/2013
89512^316654-10948195323Enzo Doria04/2014
89528*10^95316+5195317Robert Price05/2017
8953(50^56099+43^56099)/9395309Serge Batalov12/2016
8954(23*2^316559+1)/392595292Lelio R Paula09/2013
8956(71*10^95277-539)/995278Robert Price11/2017
895523422^11691+11691^2342295278Hans Havermann10/2019
895719^74503-5695271Lelio R Paula06/2016
8958(5038^25733-1)/503795267Serge Batalov06/2022
895911^91475-438095262Enzo Doria01/2013
8960(62*10^95251-611)/995252Robert Price05/2017
8961(160090^18301-1)/16008995240Serge Batalov06/2022
8962(173205^18181-1)/17320495238Serge Batalov06/2022
8963(158710^18313-1)/15870995234Serge Batalov06/2022
8964(9979^23813-1)/997895227Serge Batalov06/2022
8965(57376^20011-1)/5737595223Serge Batalov06/2022
8966(2^316321-509203)/6937795218Lelio R Paula06/2013
896726541^3868+3868^2654195216Hans Havermann07/2020
8968(79*10^95214-43)/995215Erik Branger11/2013
8969(7176^24691-1)/717595202Anonymous11/2020
8970(9*2^316233-1)/175195194Lelio R Paula02/2014
89715*2^316213+995191Lelio R Paula08/2014
89722*10^95188-9195189Robert Price04/2020
89732^316205-184816395188Enzo Doria07/2015
89742^316185-278791395182Enzo Doria04/2016
8975(2^316174+3538)/295178Stefano Morozzi09/2020
8976(9787*2^316142-1)/395172Lelio R Paula04/2015
89772^316140-595168Henri Lifchitz02/2006
8978(15185*2^316117-1)/395165Lelio R Paula04/2015
8979(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
89802^316069+7681795147Enzo Doria05/2016
8981(199*10^95134-7)/395136Robert Price02/2017
89822^316027-9730595134Lelio R Paula03/2016
89832^316006-279805195128Enzo Doria04/2016
898424994^6397+6397^2499495127Hans Havermann02/2020
89862^315921-279760395102Enzo Doria04/2016
8985(2^315921+1314)/295102Stefano Morozzi02/2021
89872*10^95095+6395096Robert Price10/2017
89882^315857+129995083Lelio R Paula03/2016
8989(2^315858+2598)/295083Stefano Morozzi09/2020
899114^82955-4395078Lelio R Paula06/2016
8990(8*10^95078-269)/995078Robert Price09/2021
8992(23*10^95074-101)/395075Robert Price04/2021
89932^315827-93307595074Paul Bourdelais04/2021
8994(2*10^95072-17)/395072Robert Price08/2014
8995(286*10^95059-1)/395061Robert Price11/2020
8996(2^315779+1610)/295059Stefano Morozzi09/2020
89972^315775-11154643595058Paul Bourdelais10/2021
899821938^21513+21513^2193895051Hans Havermann09/2020
89992^315727+6595044Lelio R Paula11/2012
90002^315725+188575795043Enzo Doria03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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