PRP Records

Probable Primes Top 10000

(290751 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 ?
7501(3*2^328311+1)/598832Lelio R Paula11/2013
7502(2^328284+9)/132598821Lelio R Paula10/2013
7503(21*2^328258+1)/212598814Lelio R Paula11/2013
7504(28623^22171-1)/2862298806Serge Batalov06/2022
750524746^9825+9825^2474698795Hans Havermann07/2020
750626620^5143+5143^2662098793Hans Havermann07/2020
750765^54491+4898788Lelio R Paula04/2016
75083^207042+9898785Lelio R Paula08/2016
7509(2^328121+3110)/298774Stefano Morozzi09/2020
751010^98754+7338398755Patrick De Geest02/2021
75133^206977-11275698754Enzo Doria07/2014
751210^98754-4000000000198754Robert Price09/2020
751110^98754-16934398754Patrick De Geest02/2021
75147^116846-5098747Lelio R Paula08/2016
7515(19152^23059-1)/1915198740Serge Batalov06/2022
751623267^17512+17512^2326798730Hans Havermann04/2020
75172^327967-2863598728Lelio R Paula08/2016
7518707^34642+34642^70798710Norbert Schneider12/2017
7519(10771^24481-1)/1077098710Serge Batalov06/2022
75206^126850-4798709Lelio R Paula08/2016
7521(2^327886+2170)/298704Stefano Morozzi09/2020
7522(22*10^98697+47)/398698Robert Price06/2021
75238*6^126830-798694Lelio R Paula11/2014
752411^94770-27098693Enzo Doria08/2012
7525(2^327846+3250)/298692Stefano Morozzi01/2021
75262^327832+4398688Lelio R Paula12/2012
75272^327795+76198677Lelio R Paula02/2013
7528(2^327796+1522)/298677Stefano Morozzi09/2020
752910^98669+14741198670Patrick De Geest11/2016
753110^98669-9^(98669-1)98669Robert Price05/2016
753010^98669-10524998669Patrick De Geest11/2016
7532(7911^25309-1)/791098657Serge Batalov06/2022
75332^327671-10980198639Enzo Doria04/2014
753424398^11037+11037^2439898638Hans Havermann10/2019
75355^141090-1498618Lelio R Paula08/2016
753620^75799+4798617Lelio R Paula08/2016
7537(5452^26393-1)/545198616Serge Batalov06/2022
753828101^3226+3226^2810198597Hans Havermann07/2020
75392^327515-101798592Lelio R Paula08/2016
75406^126692+9768198586Mike Oakes04/2011
75412^327467-74198578Lelio R Paula08/2016
7542(2947^28411-1)/294698566Serge Batalov06/2022
754322713^21800+21800^2271398540Hans Havermann05/2020
7544(2^327329+9)/1998535Lelio R Paula10/2013
75457^116577-6698519Lelio R Paula08/2016
7546(3*2^327250+1)/798512Lelio R Paula11/2013
754723220^17479+17479^2322098512Hans Havermann03/2020
7548(2^327240+3798)/298509Stefano Morozzi02/2021
7549(28514^22111-1)/2851398502Serge Batalov06/2022
7550(19*2^327192+1)/27598494Lelio R Paula11/2013
75512^327162-6694598486Lelio R Paula08/2016
755230139^1852+1852^3013998484Hans Havermann02/2020
755323182^17703+17703^2318298479Hans Havermann01/2020
75544*10^98472-398473Erik Branger11/2013
755526167^5794+5794^2616798466Hans Havermann01/2020
7556(6883*2^327047-1)/7798453Lelio R Paula05/2015
7557(71*10^98446+1)/998447Serge Batalov11/2010
7558(2009^29803-1)/200898436Serge Batalov06/2022
755913^88363+9498432Lelio R Paula08/2016
756048^58543-47^5854398425Jean-Louis Charton11/2005
75616^126481+4198422Lelio R Paula08/2016
756278*10^98413-798415Robert Price05/2017
756322634^22263+22263^2263498404Hans Havermann07/2020
7564(47*10^98386+241)/998387Robert Price06/2022
75657^116416+4698383Lelio R Paula08/2016
75667^116407-2498376Lelio R Paula07/2016
7567439^37228+37228^43998374Norbert Schneider08/2018
75682^326782-186067198372Enzo Doria03/2016
756917^79948+5898372Lelio R Paula08/2016
757022499^22602-22602^2249998368Norbert Schneider08/2020
75713^206143-9898356Lelio R Paula08/2016
75728*5^140705+798350Lelio R Paula11/2014
7573(2^326632+1662)/298326Stefano Morozzi09/2020
7574(638^35053-1)/63798315Serge Batalov06/2022
75752^326585+1198312Lelio R Paula12/2012
75762^326582-45916198311Enzo Doria05/2015
7577(1266^31687-1)/126598304Serge Batalov06/2022
7579(2^326548+9)/598301Lelio R Paula10/2013
7578(2^326549+18)/1098301Stefano Morozzi03/2020
75802^326538+7165998298Enzo Doria04/2016
7581(2^326520+2082)/298293Stefano Morozzi09/2020
7582(2^326521+1002)/298293Stefano Morozzi09/2020
758315^83575-5898292Lelio R Paula08/2016
758410^98288+398289Robert Price03/2011
758510^98288-11701798288Patrick De Geest11/2011
7586(44*10^98284-719)/998285Robert Price12/2017
7587(5985^26021-1)/598498280Serge Batalov06/2022
758823466^15419+15419^2346698277Hans Havermann02/2020
75892^326421-279757398263Enzo Doria04/2016
75902^326401+1609598257Lelio R Paula07/2016
7591(6494^25771-1)/649398249Serge Batalov06/2022
75927^116240-116240^798235Norbert Schneider05/2017
759317^79826-7898222Lelio R Paula08/2016
75942^326268-80998217Yves Minet04/2011
759522659^21590+21590^2265998210Hans Havermann10/2019
759622268^22587-22587^2226898202Norbert Schneider08/2020
7597(418*10^98199+23)/998201Robert Price08/2017
759812*10^98198-798200Robert Price11/2017
759915^83496-7698199Lelio R Paula08/2016
7600(10223*2^326179+1)/612598190Lelio R Paula07/2014
76019*5^140471-498186Lelio R Paula11/2014
7602(35103^21601-1)/3510298180Serge Batalov06/2022
760422774^20455+20455^2277498175Hans Havermann07/2020
7603(4516^26863-1)/451598175Serge Batalov06/2022
76052^326069-238398157Yves Minet10/2013
7606(9661^24631-1)/966098152Serge Batalov06/2022
7607(4175^27109-1)/417498149Serge Batalov06/2022
7608(57801^20611-1)/5780098144Serge Batalov06/2022
76092^325973+118598128Lelio R Paula07/2016
7610(25*2^325949-1)/1798121Lelio R Paula02/2014
76112^325945-184726998120Enzo Doria07/2015
76128*10^98111-6798112Robert Price10/2017
7613(2^325902+1138)/298106Stefano Morozzi09/2020
7614(215^42061-1)/21498103Serge Batalov06/2022
7615(6775^25609-1)/677498102Serge Batalov06/2022
7616(6718^25633-1)/671798100Serge Batalov06/2022
76172^325866+1598096Lelio R Paula12/2012
761822591^21952+21952^2259198079Hans Havermann02/2020
76192^325765+197430598066Enzo Doria06/2016
76202^325733-5869598056Lelio R Paula07/2016
7621(7*10^98055-529)/998055Robert Price08/2021
76222^325717-364598051Lelio R Paula07/2016
7623(2^325704+718)/298047Stefano Morozzi09/2020
7624(15679^23371-1)/1567898045Serge Batalov06/2022
7625(23342^22441-1)/2334198022Serge Batalov06/2022
762623968^12293+12293^2396898021Hans Havermann11/2019
7627(23*2^325583-1)/2198011Lelio R Paula02/2014
7628(7*10^98007-13)/398008Robert Price06/2016
7629(2^325544+1110)/297999Stefano Morozzi09/2020
76302^325512-45995997989Enzo Doria05/2015
7631(2^325492+682)/297983Stefano Morozzi09/2020
7632(3^205354-8)/1797978Lelio R Paula09/2013
76332^325433+7681797966Enzo Doria05/2016
76345*10^97963+8197964Robert Price08/2017
7635(13208^23773-1)/1320797961Serge Batalov06/2022
76362^325390-10906197953Enzo Doria04/2014
7637(55*10^97940+323)/997941Robert Price10/2021
763813^87921+2497940Lelio R Paula08/2016
763910^97930-700000197930Robert Price06/2021
7640961^32831-960^3283197926Jean-Louis Charton02/2011
7641(17968^23017-1)/1796797922Serge Batalov06/2022
7642(3337^27793-1)/333697922Serge Batalov06/2022
764422600^21499+21499^2260097913Hans Havermann05/2020
7643(18703^22921-1)/1870297913Serge Batalov06/2022
76452^325215+1290997900Lelio R Paula07/2016
764622619^21286+21286^2261997898Hans Havermann04/2020
7647(85*10^97876-49)/997877Robert Price12/2020
76487*10^97874-6997875Robert Price01/2017
76495*10^97869-6397870Robert Price04/2021
7651(17^79537+5^79537)/2297865Robert Price06/2013
765015^83212+2297865Lelio R Paula08/2016
76522^325087-10905797861Enzo Doria04/2014
76532^325074+187065797858Enzo Doria05/2016
76552^325066-211197855Yves Minet08/2013
7654CopelandErdos(97855)97855Eric W. Weisstein10/2015
7656(8694^24841-1)/869397851Serge Batalov06/2022
7657(21159^22621-1)/2115897843Serge Batalov06/2022
765826660^4677+4677^2666097842Hans Havermann12/2019
765918^77944-8997841Lelio R Paula07/2016
7660119^47136+11897833Norbert Schneider09/2018
76616^125720-1766397830Enzo Doria02/2013
7662(73640^20101-1)/7363997829Serge Batalov06/2022
76632^324972-206997827Yves Minet05/2013
76642^324958-469197823Yves Minet05/2019
7665(8087^25033-1)/808697820Serge Batalov06/2022
76662^324944-278831997818Enzo Doria03/2016
766722845^19112+19112^2284597807Hans Havermann10/2019
7668(2^324898+1270)/297804Stefano Morozzi09/2020
76704*10^97799-997800Erik Branger11/2013
76692^324882+57729457597800Lelio R Paula09/2016
76712^324863-186792197794Enzo Doria04/2016
76726^125662-1847397785Enzo Doria03/2013
767312^90604+1197779Lelio R Paula07/2016
7674(29*10^97751+49)/397752Robert Price09/2021
7675(37108^21391-1)/3710797741Serge Batalov06/2022
76765^139830+2497737Lelio R Paula04/2016
7677(2^324672+1198)/297736Stefano Morozzi09/2020
7678(101*10^97724+7)/997726Robert Price02/2022
76792^324612+115597718Lelio R Paula07/2016
7680(2^324597+3542)/297714Stefano Morozzi09/2020
768119^76404-4497702Lelio R Paula07/2016
7682(5939^25889-1)/593897694Serge Batalov06/2022
76842^324505-298397686Yves Minet04/2011
7683(7740^25121-1)/773997686Serge Batalov06/2022
7685(144^45259+1)/14597684Paul Bourdelais08/2019
7686(31*2^324496-1)/4597683Lelio R Paula02/2014
7687(11234^24109-1)/1123397651Serge Batalov06/2022
76886^125488-1784397649Enzo Doria02/2013
7689(2^324350+3198)/297639Stefano Morozzi09/2020
7690(75638^20011-1)/7563797624Serge Batalov06/2022
76917^115515-297622Lelio R Paula09/2013
7692(15672^23269-1)/1567197613Serge Batalov06/2022
7693(89^50069-1)/8897603Paul Bourdelais08/2017
76946^125418-597595Lelio R Paula11/2014
7695(2^324193+3522)/297592Stefano Morozzi09/2020
7696(2422^28837-1)/242197587Serge Batalov06/2022
7697(2^324172+666)/297586Stefano Morozzi09/2020
76982^324091+11154643597562Paul Bourdelais10/2021
76992^324076+115597557Lelio R Paula07/2016
7700(2^324074+9)/1397555Lelio R Paula10/2013
7701(11*10^97539-71)/397540Robert Price04/2022
7702(55459*2^323993+1)/2197536Lelio R Paula07/2014
770313^87557-12^8755797534Jean-Louis Charton12/2008
77042^323946+7393997518Enzo Doria04/2016
77052^323937+186694797515Enzo Doria03/2016
7706(98339^19531-1)/9833897508Serge Batalov06/2022
77086^125290-1853397495Enzo Doria03/2013
7707(2^323870+1650)/297495Stefano Morozzi09/2020
77092^323845+10197488Lelio R Paula12/2012
771018^77662+6597487Lelio R Paula07/2016
771122634^20265+20265^2263497479Hans Havermann04/2020
7712(5533^26041-1)/553297467Serge Batalov06/2022
77132^323772+7677197466Enzo Doria05/2016
77142^323765-11221397463Enzo Doria06/2014
771522730^19389+19389^2273097457Hans Havermann02/2020
77162^323720-655597450Lelio R Paula07/2016
77172^323694-186040197442Enzo Doria03/2016
771820^74886+397429Lelio R Paula06/2016
771924476^9561+9561^2447697427Hans Havermann01/2020
7720(2^323623+1766)/297420Stefano Morozzi09/2020
7721(3250^27739-1)/324997413Serge Batalov06/2022
77233*10^97399+7397400Robert Price04/2016
77227^115252-5097400Lelio R Paula07/2016
7724(4715^26513-1)/471497392Serge Batalov06/2022
7725224737#+39358197389Nicolas PALAU12/2016
7726(2^323468+3186)/297374Stefano Morozzi09/2020
7727(2^323456+538)/297370Stefano Morozzi09/2020
772823277^15236+15236^2327797365Hans Havermann07/2020
7730(26*10^97353+31)/397354Robert Price07/2016
7729(2^323403+3510)/297354Stefano Morozzi09/2020
773123756^12519+12519^2375697342Hans Havermann07/2020
773210^97335-400000197335Robert Price07/2021
7733(637*10^97331+11)/997333Robert Price10/2021
773423991^11402+11402^2399197332Hans Havermann07/2020
773561^54517-60^5451797331Jean-Louis Charton09/2005
7736(38*10^97329+187)/997330Robert Price11/2017
7737(31147^21661-1)/3114697328Serge Batalov06/2022
773886455!4+897319Robert Price09/2019
773922591^20310+20310^2259197316Hans Havermann06/2020
77402^323261-43117397312Harrison Mesh06/2022
7741(3996^27017-1)/399597302Serge Batalov06/2022
774225101^7520+7520^2510197297Hans Havermann05/2020
7743(233*10^97294+7)/397296Robert Price03/2022
7744p(19982)#/2-102497293Robert Price09/2017
7745(65*10^97288+277)/997289Robert Price08/2021
77466^125021-8597286Lelio R Paula08/2016
77472^323164-4735597283Lelio R Paula07/2016
7748(3^203902+4)/3605101515797276Lelio R Paula09/2013
77492^323054-655597249Lelio R Paula07/2016
775022822^18247+18247^2282297249Hans Havermann02/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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