PRP Records

Probable Primes Top 10000

(291192 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 ?
8251(2^319777+2082)/296263Stefano Morozzi09/2020
8252(2^319771+3686)/296261Stefano Morozzi09/2020
82532^319713-8196244Lelio R Paula11/2012
8254(55459*2^319706+1)/2016796242Lelio R Paula07/2014
825522834^16393+16393^2283496238Hans Havermann05/2020
82568*10^96236+2796237Robert Price09/2021
825712^89153-4396213Lelio R Paula06/2016
8258(25048^21871-1)/2504796202Serge Batalov06/2022
8260(2*10^96195-59)/396195Robert Price05/2017
82599*10^96194-7796195Robert Price08/2020
82612^319545+14796193Lelio R Paula11/2012
826223357^13128+13128^2335796189Hans Havermann02/2020
8263(19838^22381-1)/1983796179Serge Batalov06/2022
8264(221^41023-1)/22096172Serge Batalov06/2022
826525952^5073+5073^2595296160Hans Havermann12/2019
8266(50891^20431-1)/5089096157Serge Batalov06/2022
8267(50^56597+1)/5196155Robert Price03/2014
826822313^20374+20374^2231396149Hans Havermann12/2019
826922279^20668+20668^2227996141Hans Havermann11/2019
8270(41*10^96137-59)/996138Robert Price10/2017
82712^319353-11034396135Enzo Doria05/2014
827211^92309-4296130Lelio R Paula05/2016
8273(21675^22171-1)/2167496129Serge Batalov06/2022
827414^83869-13^8386996125Jean-Louis Charton01/2009
8275(7*10^96112+143)/396113Robert Price04/2016
827626731^3940+3940^2673196112Hans Havermann07/2020
827722640^17583+17583^2264096109Hans Havermann07/2020
8278(19178^22441-1)/1917796107Serge Batalov06/2022
82792^319237+6583596100Lelio R Paula03/2016
82802^319194-184196087Yves Minet03/2013
828123949^10280+10280^2394996084Hans Havermann07/2020
8282(1927^29251-1)/192696083Serge Batalov06/2022
828320^73847-3196078Lelio R Paula05/2016
8284(60229^20101-1)/6022896075Serge Batalov06/2022
8285(28044^21601-1)/2804396074Serge Batalov06/2022
828650^56543-4996065Norbert Schneider09/2018
82872^319107-10955596061Enzo Doria04/2014
8288(3*2^319114-1)/262796060Lelio R Paula02/2014
82892^319098-11215796059Enzo Doria06/2014
829015^81673+9496055Lelio R Paula07/2016
8291(85761^19471-1)/8576096052Serge Batalov06/2022
82922^319074+187174996051Enzo Doria05/2016
829325670^5517+5517^2567096050Hans Havermann06/2020
82946*10^96037+1996038Robert Price11/2021
82952^319007-11211196031Enzo Doria06/2014
8296(57987^20161-1)/5798696029Serge Batalov06/2022
82982^318946-142196013Yves Minet01/2013
8297(68310^19861-1)/6830996013Serge Batalov06/2022
8299(20294^22291-1)/2029396012Serge Batalov06/2022
8300(304^38669-1)/30396008Serge Batalov06/2022
8301(1840^29401-1)/183995986Serge Batalov06/2022
830222830^16003+16003^2283095982Hans Havermann02/2020
83032^318834-11041195979Enzo Doria05/2014
83042^318831-196595978Lelio R Paula03/2016
8305(5*10^95976+7)/395977Erik Branger03/2014
8306(12797^23369-1)/1279695975Serge Batalov06/2022
8307(10534^23857-1)/1053395963Serge Batalov06/2022
830822871^15696+15696^2287195962Hans Havermann01/2020
8309(2^318760+858)/295957Stefano Morozzi02/2021
831023167^13860+13860^2316795953Hans Havermann01/2020
8311(823^32911-1)/82295946Serge Batalov06/2022
83135*3^201089-895945Lelio R Paula08/2014
8312(81783^19531-1)/8178295945Serge Batalov06/2022
83142^318711-13995942Lelio R Paula11/2012
83152^318635-116795919Lelio R Paula03/2016
831615^81555+1695917Lelio R Paula07/2016
8317(37*10^95895+377)/995896Robert Price10/2017
8318(22699*2^318527+1)/2195890Lelio R Paula07/2014
83192^318496-9730595877Lelio R Paula03/2016
832022129^21496+21496^2212995871Hans Havermann07/2020
83222^318466+1501595868Lelio R Paula03/2016
832124847^7216+7216^2484795868Hans Havermann07/2020
832323706^11065+11065^2370695866Hans Havermann07/2020
8324(2863^27733-1)/286295865Serge Batalov06/2022
83256^123187-17312995859Mike Oakes04/2011
83262^318423-48795855Yves Minet03/2012
832710^95848-500000000195848Robert Price09/2022
8328(2^318359+678)/295836Stefano Morozzi09/2020
8329(10223*2^318350+1)/156395834Lelio R Paula07/2014
8330(8060^24533-1)/805995831Serge Batalov06/2022
8331(9853^23993-1)/985295814Serge Batalov06/2022
8333(2^318267+2550)/295808Stefano Morozzi09/2020
8332(5048^25873-1)/504795808Serge Batalov06/2022
83354*10^95799+1395800Robert Price02/2021
8334(65533^19891-1)/6553295800Serge Batalov06/2022
833645369!2+102495787Robert Price02/2015
83373^200758-8695786Lelio R Paula05/2016
8338(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
8339(2^318171+2030)/295779Stefano Morozzi09/2020
83403*10^95776-5995777Robert Price10/2017
8341(82970^19471-1)/8296995772Serge Batalov06/2022
8342193^41901-295768Lelio R Paula10/2017
8343(2^318124+2502)/295765Stefano Morozzi09/2020
8344(12900^23297-1)/1289995761Serge Batalov06/2022
83454*10^95752-7195753Robert Price11/2017
8346(16955^22639-1)/1695495743Serge Batalov06/2022
8347(81795^19489-1)/8179495740Serge Batalov06/2022
8348(2742^27847-1)/274195737Serge Batalov06/2022
8349(6072^25303-1)/607195726Serge Batalov06/2022
835023640^11197+11197^2364095721Hans Havermann12/2019
835110^95712+8932995713Patrick De Geest09/2022
835310^95712-400000195712Robert Price07/2021
835210^95712-98931395712Patrick De Geest09/2022
8354(60657^20011-1)/6065695706Serge Batalov06/2022
8355((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
8356(509203*2^317881-1)/5280595693Lelio R Paula04/2015
8357(26161^21661-1)/2616095687Serge Batalov06/2022
8358(2^317853+1086)/295683Stefano Morozzi09/2020
83594*10^95672+9195673Robert Price11/2017
83606*10^95665+4395666Robert Price07/2020
8361(20819^22153-1)/2081895663Serge Batalov06/2022
8362(64464^19891-1)/6446395658Serge Batalov06/2022
8363(934^32203-1)/93395652Serge Batalov06/2022
8364(11*10^95641-113)/395642Robert Price01/2017
8365(72330^19681-1)/7232995632Serge Batalov06/2022
8366(13224^23203-1)/1322395624Serge Batalov06/2022
8367(18211^22441-1)/1821095602Serge Batalov06/2022
8368(71975^19681-1)/7197495590Serge Batalov06/2022
8369(13*10^95588+11)/395589Robert Price05/2015
8370Phi(191188,10)/19118995587Maksym Voznyy11/2015
8371(13368^23167-1)/1336795585Serge Batalov06/2022
8372(25874^21661-1)/2587395583Serge Batalov06/2022
83733^200325+7095580Lelio R Paula05/2016
8374(25*10^95574-7)/995575Robert Price12/2014
8375(2^317485-3)/2131395569Lelio R Paula06/2013
83762^317464+3195567Lelio R Paula11/2012
8377(2^317451+2114)/295562Stefano Morozzi09/2020
83787^113073+8295558Lelio R Paula04/2016
8379(24728^21751-1)/2472795552Serge Batalov06/2022
8380(49764^20341-1)/4976395536Serge Batalov06/2022
8381(36155^20959-1)/3615495531Serge Batalov06/2022
8382(7725^24571-1)/772495526Serge Batalov06/2022
8383(20546^22147-1)/2054595510Serge Batalov06/2022
83842^317251+46595503Lelio R Paula03/2016
838519^74684+5895503Lelio R Paula06/2016
8386(2^317250-7)/33995500Lelio R Paula07/2013
83875*10^95498-2195499Robert Price12/2021
8388(21615^22031-1)/2161495495Serge Batalov06/2022
83896^122718-7995494Lelio R Paula05/2016
839022168^20291+20291^2216895485Hans Havermann10/2019
8391(77427^19531-1)/7742695481Serge Batalov06/2022
8392(13026^23203-1)/1302595472Serge Batalov06/2022
83932^317141-11049195469Enzo Doria05/2014
8394(2^317097+3014)/295456Stefano Morozzi09/2020
83952^317094+7630995455Enzo Doria05/2016
83962^317085+9595453Lelio R Paula11/2012
8397(17*10^95451-377)/995452Robert Price11/2017
83982^317057-10955195444Enzo Doria04/2014
83993^200026+2895437Lelio R Paula05/2016
84002^317024+9395434Donovan Johnson06/2008
8401(86*10^95428-437)/995429Robert Price03/2021
840210^95427+19259195428Patrick De Geest05/2021
84052^316999+160595427Lelio R Paula03/2016
8404(2^317000+3210)/295427Stefano Morozzi09/2020
840310^95427-1000195427Robert Price02/2021
84062^316995-11042795426Enzo Doria05/2014
8407(69841^19699-1)/6984095420Serge Batalov06/2022
8408(59242^19993-1)/5924195415Serge Batalov06/2022
841022300^18987+18987^2230095410Hans Havermann06/2020
8409(9478^23993-1)/947795410Serge Batalov06/2022
84112^316937+17795408Lelio R Paula11/2012
84124*10^95407+9195408Robert Price11/2017
84132^316908+191595399Lelio R Paula03/2016
84142^316894+9995395Lelio R Paula11/2012
8415(2^316887+2546)/295393Stefano Morozzi09/2020
84162*10^95374-2195375Robert Price09/2020
84176^122547+1195361Lelio R Paula05/2016
84182^316771+8287595358Lelio R Paula03/2016
8419(15609^22741-1)/1560895358Serge Batalov06/2022
8420(2^316765+3102)/295356Stefano Morozzi09/2020
8421(2267^28411-1)/226695329Serge Batalov06/2022
8422(824^32693-1)/82395328Serge Batalov06/2022
8423(23*10^95326+1)/395327Serge Batalov05/2009
84241*10^95326+5795327Robert Price03/2011
842510^95326-39368795326Patrick De Geest09/2013
8426(3^199803+4)/47953995325Lelio R Paula04/2013
84272^316654-10948195323Enzo Doria04/2014
84288*10^95316+5195317Robert Price05/2017
8429(50^56099+43^56099)/9395309Serge Batalov12/2016
8430(23*2^316559+1)/392595292Lelio R Paula09/2013
8432(71*10^95277-539)/995278Robert Price11/2017
843123422^11691+11691^2342295278Hans Havermann10/2019
843319^74503-5695271Lelio R Paula06/2016
8434(5038^25733-1)/503795267Serge Batalov06/2022
843511^91475-438095262Enzo Doria01/2013
8436(62*10^95251-611)/995252Robert Price05/2017
8437(160090^18301-1)/16008995240Serge Batalov06/2022
8438(173205^18181-1)/17320495238Serge Batalov06/2022
8439(158710^18313-1)/15870995234Serge Batalov06/2022
8440(9979^23813-1)/997895227Serge Batalov06/2022
8441(57376^20011-1)/5737595223Serge Batalov06/2022
8442(2^316321-509203)/6937795218Lelio R Paula06/2013
844326541^3868+3868^2654195216Hans Havermann07/2020
8444(79*10^95214-43)/995215Erik Branger11/2013
8445(7176^24691-1)/717595202Anonymous11/2020
8446(9*2^316233-1)/175195194Lelio R Paula02/2014
84475*2^316213+995191Lelio R Paula08/2014
84482*10^95188-9195189Robert Price04/2020
84492^316205-184816395188Enzo Doria07/2015
84502^316185-278791395182Enzo Doria04/2016
8451(2^316174+3538)/295178Stefano Morozzi09/2020
8452(9787*2^316142-1)/395172Lelio R Paula04/2015
84532^316140-595168Henri Lifchitz02/2006
8454(15185*2^316117-1)/395165Lelio R Paula04/2015
8455(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
84562^316069+7681795147Enzo Doria05/2016
8457(199*10^95134-7)/395136Robert Price02/2017
84582^316027-9730595134Lelio R Paula03/2016
84592^316006-279805195128Enzo Doria04/2016
846024994^6397+6397^2499495127Hans Havermann02/2020
84622^315921-279760395102Enzo Doria04/2016
8461(2^315921+1314)/295102Stefano Morozzi02/2021
84632*10^95095+6395096Robert Price10/2017
84642^315857+129995083Lelio R Paula03/2016
8465(2^315858+2598)/295083Stefano Morozzi09/2020
846714^82955-4395078Lelio R Paula06/2016
8466(8*10^95078-269)/995078Robert Price09/2021
8468(23*10^95074-101)/395075Robert Price04/2021
84692^315827-93307595074Paul Bourdelais04/2021
8470(2*10^95072-17)/395072Robert Price08/2014
8471(286*10^95059-1)/395061Robert Price11/2020
8472(2^315779+1610)/295059Stefano Morozzi09/2020
84732^315775-11154643595058Paul Bourdelais10/2021
847421938^21513+21513^2193895051Hans Havermann09/2020
84752^315727+6595044Lelio R Paula11/2012
84762^315725+188575795043Enzo Doria03/2017
847723277^12058+12058^2327795000Hans Havermann09/2020
84781*10^94983+2194984Robert Price03/2011
847910^94983-71794983Patrick De Geest08/2013
848017^77187-8294975Lelio R Paula07/2016
84813*10^94964+3794965Robert Price10/2017
8482(2^315481-1017)/2062728594962Lelio R Paula06/2013
84832^315423-11032994952Enzo Doria05/2014
848411^91169-723094943Enzo Doria02/2013
84857*10^94938+6194939Robert Price02/2017
84862^315351+102594931Lelio R Paula03/2016
84872^315350-11225394930Enzo Doria06/2014
8488(2^315343+1766)/294928Stefano Morozzi09/2020
8489(2^315343+3066)/294928Stefano Morozzi09/2020
8492((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
84912^315268+794906Lelio R Paula10/2012
849011^91133+6294906Lelio R Paula05/2016
8493(2^315264+1558)/294904Stefano Morozzi09/2020
849430^64244+4194897Lelio R Paula08/2012
8495(151*10^94885-7)/994887Robert Price07/2017
84964^157583+2214794875Mike Oakes01/2011
84972^315098+12394854Lelio R Paula11/2012
84983^198791-3494848Robert Price11/2013
84993*2^315067+794846Lelio R Paula08/2014
8500(9*2^315057+1)/7394841Lelio R Paula09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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