PRP Records

Probable Primes Top 10000

(292102 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 ?
87513*10^97205-6197206Robert Price04/2021
8752(7*2^322896-1)/5797201Lelio R Paula02/2014
8753(35*10^97194-341)/997195Robert Price08/2021
8754(4872^26357-1)/487197194Serge Batalov06/2022
8755(2^322897+5)/314610748997193Lelio R Paula10/2013
8756(796*10^97183-31)/997185Robert Price07/2022
8757(2^322789+2214)/297169Stefano Morozzi09/2020
87582^322725+7576197150Enzo Doria04/2016
8759(13*2^322686+1)/11997138Lelio R Paula11/2013
8760(2175^29101-1)/217497121Serge Batalov06/2022
876122402^21639+21639^2240297118Hans Havermann07/2020
876223399^14128+14128^2339997108Hans Havermann06/2020
8763(2892^28057-1)/289197108Serge Batalov06/2022
8764(9578^24391-1)/957797104Serge Batalov06/2022
8765(2^322525+2606)/297090Stefano Morozzi09/2020
8766(9563^24391-1)/956297087Serge Batalov06/2022
8767(41*10^97085+373)/997086Robert Price04/2017
8768(2^322473+854)/297074Stefano Morozzi02/2021
87692^322413+7797056Lelio R Paula12/2012
87702^322406+17797054Lelio R Paula12/2012
8771(349^38167-1)/34897050Serge Batalov06/2022
8772(14*10^97044+31)/997045Robert Price02/2015
87732^322302+25525597023Lelio R Paula07/2016
8774(1302^31147-1)/130197008Serge Batalov06/2022
87752^322196-11309396991Enzo Doria07/2014
8776(2^322169+2690)/296983Stefano Morozzi09/2020
8777(49*10^96980+221)/996981Robert Price02/2022
87789*10^96968-4796969Robert Price11/2021
8779(5895^25717-1)/589496962Serge Batalov06/2022
8780(27473^21841-1)/2747296946Serge Batalov06/2022
878123109^15668+15668^2310996943Hans Havermann07/2020
87822^322000-186146996932Enzo Doria03/2016
87832^321971-11274796923Enzo Doria06/2014
878423754^12023+12023^2375496917Hans Havermann07/2020
878511^93062-9296915Lelio R Paula06/2016
8786(37871^21169-1)/3787096914Serge Batalov06/2022
8787(2^321922+2214)/296908Stefano Morozzi09/2020
8788(2^321900+2086)/296902Stefano Morozzi09/2020
8789(11*2^321841-7)/1596884Renaud Lifchitz03/2011
87903^203051+3496880Lelio R Paula05/2016
87912*10^96867-5196868Robert Price11/2017
8792(2^321779+2618)/296865Stefano Morozzi09/2020
8793(64*10^96863-1)/2796864Serge Batalov05/2010
87942^321716-278693996847Enzo Doria03/2016
879522496^20181+20181^2249696844Hans Havermann03/2020
87962^321701-11305396842Enzo Doria07/2014
87972^321700-2863596842Lelio R Paula06/2016
8798(5*2^321691-1)/2796838Lelio R Paula02/2014
87996*10^96835+1396836Robert Price10/2021
88006^124433-12443396828Robert Price01/2014
88012^321631+6996821Lelio R Paula12/2012
8802(27109^21841-1)/2710896820Serge Batalov06/2022
8803(13*2^321606+1)/11996813Lelio R Paula11/2013
8804(5052^26141-1)/505196809Serge Batalov06/2022
8805(46*10^96798-1)/996799Serge Batalov10/2014
8806(59*10^96798+31)/996799Robert Price09/2015
8807(2^321536+2062)/296792Stefano Morozzi09/2020
8808223319#+23122396790Makoto Morimoto02/2016
88092^321519-2863596787Lelio R Paula06/2016
88102^321487-186723796778Enzo Doria03/2016
88112^321461-6396770Lelio R Paula12/2012
8812(16053^23011-1)/1605296770Serge Batalov06/2022
88132^321439+12396763Lelio R Paula12/2012
88142^321434+70996762Lelio R Paula02/2013
8815(2^321415+554)/296756Stefano Morozzi09/2020
881614^84413+8996749Lelio R Paula07/2016
8817(28*10^96743+71)/996744Serge Batalov12/2008
881813^86847+9696743Lelio R Paula06/2016
88199*2^321336-796733Lelio R Paula08/2014
8820(209*10^96722-17)/396724Robert Price05/2017
8821(54163^20431-1)/5416296710Serge Batalov06/2022
88222^321237-461596702Yves Minet05/2019
8823(27273^21799-1)/2727296691Serge Batalov06/2022
88242^321187-115996687Yves Minet11/2012
88252^321182-185008196686Enzo Doria08/2015
882723359^13768+13768^2335996680Hans Havermann06/2020
8826(65630^20071-1)/6562996680Serge Batalov06/2022
88282^321116-11282996666Enzo Doria06/2014
88292^321108-10949996664Enzo Doria04/2014
88302^321098+279385996661Enzo Doria03/2016
8831(2^321100+1170)/296661Stefano Morozzi09/2020
88322^321057+409796648Lelio R Paula06/2016
8833(4435*29^66081-4)/796640Curtis Bright05/2015
883422743^17750+17750^2274396640Hans Havermann04/2020
883522882^16679+16679^2288296612Hans Havermann02/2020
883623452^13163+13163^2345296608Hans Havermann02/2020
8837(1042^32009-1)/104196596Serge Batalov06/2022
8838(85*10^96594-373)/996595Robert Price05/2021
8839(2^320863+666)/296590Stefano Morozzi09/2020
8840p(19849)#/2-6496581Robert Price04/2017
88412^320817+18996576Lelio R Paula12/2012
88422^320816-468596576Yves Minet05/2019
8844(361*10^96567-163)/996569Robert Price10/2017
8843(19*10^96568+137)/396569Robert Price03/2022
88452^320788-11032796567Enzo Doria05/2014
8846(3065^27697-1)/306496561Serge Batalov06/2022
88472^320764+79396560Lelio R Paula02/2013
8848(2^320752+1842)/296556Stefano Morozzi02/2021
8849(48331^20611-1)/4833096542Serge Batalov06/2022
8850(50595^20521-1)/5059496529Serge Batalov06/2022
8851(9179*2^320652-1)/22196528Lelio R Paula05/2015
885223288^13947+13947^2328896517Hans Havermann07/2020
88542^320616-7879596516Lelio R Paula03/2016
8853(19*10^96520+287)/9/109/40996516Alfred Reich11/2022
88552^320612-46193996514Enzo Doria07/2015
8856(21245^22303-1)/2124496507Serge Batalov06/2022
885710^96504+98765432196505Robert Price12/2019
885810^96504+7188796505Patrick De Geest02/2020
885922654^18195+18195^2265496505Hans Havermann07/2020
886010^96504-13927796504Patrick De Geest02/2020
8861(218^41263-1)/21796490Serge Batalov06/2022
8862(47220^20641-1)/4721996474Serge Batalov06/2022
88635*2^320431+796461Lelio R Paula08/2014
886419^75431-9096458Lelio R Paula06/2016
8865(11853^23677-1)/1185296452Serge Batalov06/2022
8866(2^320386+2814)/296446Stefano Morozzi02/2021
8867(2^320370+3)/6796440Lelio R Paula10/2013
88683*10^96431-1796432Robert Price03/2021
88692^320309+187147796423Enzo Doria05/2016
8870(10412^24001-1)/1041196421Serge Batalov06/2022
8871tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
8872(29*10^96407-23)/396408Robert Price03/2022
8873(21*2^320252-1)/189596404Lelio R Paula02/2014
88742^320232-17396400Lelio R Paula12/2012
8875175^42975-296395Lelio R Paula10/2017
8876(2^320170+2718)/296381Stefano Morozzi09/2020
887710^96377+19991196378Patrick De Geest12/2016
887810^96377-2000196377Robert Price11/2016
8879(18079^22639-1)/1807896374Serge Batalov06/2022
88812^320124-279044996367Enzo Doria03/2016
888010^96366+1919796367Patrick De Geest08/2021
888310^96366-1000000000196366Robert Price04/2021
888210^96366-28736796366Patrick De Geest08/2021
8884(26351^21799-1)/2635096365Serge Batalov06/2022
888522488^19255+19255^2248896351Hans Havermann11/2019
888623248^13939+13939^2324896346Hans Havermann11/2019
8887(5928^25537-1)/592796345Serge Batalov06/2022
88892^320043-10877596343Enzo Doria04/2014
888824989^7168+7168^2498996343Hans Havermann11/2019
889010^96338+42493996339Patrick De Geest03/2016
889110^96338-928196338Robert Price09/2015
8892(8527^24509-1)/852696336Serge Batalov06/2022
8893(3*2^320008+1)/796332Lelio R Paula09/2013
8894(2444^28433-1)/244396331Serge Batalov06/2022
8895(48690^20551-1)/4868996327Serge Batalov06/2022
8896(61935^20101-1)/6193496318Serge Batalov06/2022
889725699^5596+5596^2569996317Hans Havermann07/2020
8898(7*10^96312+83)/996312Tyler Busby01/2023
8899(11*10^96298+529)/996299Robert Price09/2021
890126502^4297+4297^2650296287Hans Havermann07/2020
8900(54180^20341-1)/5417996287Serge Batalov06/2022
89022^319838+425796281Lelio R Paula03/2016
89032^319830-1699596279Lelio R Paula03/2016
89046^123713+14396268Lelio R Paula05/2016
8905(28*10^96265-97)/396266Robert Price07/2016
8906(3799^26893-1)/379896265Serge Batalov06/2022
8908103^47825-10296264Norbert Schneider10/2016
8907(54041^20341-1)/5404096264Serge Batalov06/2022
8909(2^319777+2082)/296263Stefano Morozzi09/2020
8910(2^319771+3686)/296261Stefano Morozzi09/2020
89112^319713-8196244Lelio R Paula11/2012
8912(55459*2^319706+1)/2016796242Lelio R Paula07/2014
891322834^16393+16393^2283496238Hans Havermann05/2020
89148*10^96236+2796237Robert Price09/2021
891512^89153-4396213Lelio R Paula06/2016
8916(25048^21871-1)/2504796202Serge Batalov06/2022
8918(2*10^96195-59)/396195Robert Price05/2017
89179*10^96194-7796195Robert Price08/2020
89192^319545+14796193Lelio R Paula11/2012
892023357^13128+13128^2335796189Hans Havermann02/2020
8921(19838^22381-1)/1983796179Serge Batalov06/2022
8922(221^41023-1)/22096172Serge Batalov06/2022
892325952^5073+5073^2595296160Hans Havermann12/2019
8924(50891^20431-1)/5089096157Serge Batalov06/2022
8925(50^56597+1)/5196155Robert Price03/2014
892622313^20374+20374^2231396149Hans Havermann12/2019
892722279^20668+20668^2227996141Hans Havermann11/2019
8928(41*10^96137-59)/996138Robert Price10/2017
89292^319353-11034396135Enzo Doria05/2014
893011^92309-4296130Lelio R Paula05/2016
8931(21675^22171-1)/2167496129Serge Batalov06/2022
893214^83869-13^8386996125Jean-Louis Charton01/2009
8933(7*10^96112+143)/396113Robert Price04/2016
893426731^3940+3940^2673196112Hans Havermann07/2020
893522640^17583+17583^2264096109Hans Havermann07/2020
8936(19178^22441-1)/1917796107Serge Batalov06/2022
89372^319237+6583596100Lelio R Paula03/2016
89382^319194-184196087Yves Minet03/2013
893923949^10280+10280^2394996084Hans Havermann07/2020
8940(1927^29251-1)/192696083Serge Batalov06/2022
894120^73847-3196078Lelio R Paula05/2016
8942(60229^20101-1)/6022896075Serge Batalov06/2022
8943(28044^21601-1)/2804396074Serge Batalov06/2022
894450^56543-4996065Norbert Schneider09/2018
89452^319107-10955596061Enzo Doria04/2014
8946(3*2^319114-1)/262796060Lelio R Paula02/2014
89472^319098-11215796059Enzo Doria06/2014
894815^81673+9496055Lelio R Paula07/2016
8949(85761^19471-1)/8576096052Serge Batalov06/2022
89502^319074+187174996051Enzo Doria05/2016
895125670^5517+5517^2567096050Hans Havermann06/2020
89526*10^96037+1996038Robert Price11/2021
89532^319007-11211196031Enzo Doria06/2014
8954(57987^20161-1)/5798696029Serge Batalov06/2022
89562^318946-142196013Yves Minet01/2013
8955(68310^19861-1)/6830996013Serge Batalov06/2022
8957(20294^22291-1)/2029396012Serge Batalov06/2022
8958(304^38669-1)/30396008Serge Batalov06/2022
8959(1840^29401-1)/183995986Serge Batalov06/2022
896022830^16003+16003^2283095982Hans Havermann02/2020
89612^318834-11041195979Enzo Doria05/2014
89622^318831-196595978Lelio R Paula03/2016
8963(5*10^95976+7)/395977Erik Branger03/2014
8964(12797^23369-1)/1279695975Serge Batalov06/2022
8965(10534^23857-1)/1053395963Serge Batalov06/2022
896622871^15696+15696^2287195962Hans Havermann01/2020
8967(2^318760+858)/295957Stefano Morozzi02/2021
896823167^13860+13860^2316795953Hans Havermann01/2020
8969(823^32911-1)/82295946Serge Batalov06/2022
89715*3^201089-895945Lelio R Paula08/2014
8970(81783^19531-1)/8178295945Serge Batalov06/2022
89722^318711-13995942Lelio R Paula11/2012
89732^318635-116795919Lelio R Paula03/2016
897415^81555+1695917Lelio R Paula07/2016
8975(37*10^95895+377)/995896Robert Price10/2017
8976(22699*2^318527+1)/2195890Lelio R Paula07/2014
89772^318496-9730595877Lelio R Paula03/2016
897822129^21496+21496^2212995871Hans Havermann07/2020
89802^318466+1501595868Lelio R Paula03/2016
897924847^7216+7216^2484795868Hans Havermann07/2020
898123706^11065+11065^2370695866Hans Havermann07/2020
8982(2863^27733-1)/286295865Serge Batalov06/2022
89836^123187-17312995859Mike Oakes04/2011
89842^318423-48795855Yves Minet03/2012
898510^95848+44370995849Patrick De Geest10/2022
898610^95848-500000000195848Robert Price09/2022
898710^95848-6197195848Patrick De Geest10/2022
8988(2^318359+678)/295836Stefano Morozzi09/2020
8989(10223*2^318350+1)/156395834Lelio R Paula07/2014
8990(8060^24533-1)/805995831Serge Batalov06/2022
8991(9853^23993-1)/985295814Serge Batalov06/2022
8993(2^318267+2550)/295808Stefano Morozzi09/2020
8992(5048^25873-1)/504795808Serge Batalov06/2022
89954*10^95799+1395800Robert Price02/2021
8994(65533^19891-1)/6553295800Serge Batalov06/2022
899645369!2+102495787Robert Price02/2015
89973^200758-8695786Lelio R Paula05/2016
8998(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
8999(2^318171+2030)/295779Stefano Morozzi09/2020
90003*10^95776-5995777Robert Price10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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