PRP Records

Probable Primes Top 10000

(294613 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 ?
950120^75799+4798617Lelio R Paula08/2016
9502(5452^26393-1)/545198616Serge Batalov06/2022
950328101^3226+3226^2810198597Hans Havermann07/2020
95042^327515-101798592Lelio R Paula08/2016
95056^126692+9768198586Mike Oakes04/2011
95062^327467-74198578Lelio R Paula08/2016
9507(2947^28411-1)/294698566Serge Batalov06/2022
950822713^21800+21800^2271398540Hans Havermann05/2020
9509(2^327329+9)/1998535Lelio R Paula10/2013
95107^116577-6698519Lelio R Paula08/2016
9511(3*2^327250+1)/798512Lelio R Paula11/2013
951223220^17479+17479^2322098512Hans Havermann03/2020
9513(2^327240+3798)/298509Stefano Morozzi02/2021
9514(28514^22111-1)/2851398502Serge Batalov06/2022
9515(19*2^327192+1)/27598494Lelio R Paula11/2013
95162^327162-6694598486Lelio R Paula08/2016
951730139^1852+1852^3013998484Hans Havermann02/2020
951823182^17703+17703^2318298479Hans Havermann01/2020
95194*10^98472-398473Erik Branger11/2013
952026167^5794+5794^2616798466Hans Havermann01/2020
9521(6883*2^327047-1)/7798453Lelio R Paula05/2015
9522(71*10^98446+1)/998447Serge Batalov11/2010
9523(2009^29803-1)/200898436Serge Batalov06/2022
952413^88363+9498432Lelio R Paula08/2016
952548^58543-47^5854398425Jean-Louis Charton11/2005
95266^126481+4198422Lelio R Paula08/2016
952778*10^98413-798415Robert Price05/2017
952822634^22263+22263^2263498404Hans Havermann07/2020
9529(47*10^98386+241)/998387Robert Price06/2022
95307^116416+4698383Lelio R Paula08/2016
95317^116407-2498376Lelio R Paula07/2016
9532439^37228+37228^43998374Norbert Schneider08/2018
95332^326782-186067198372Enzo Doria03/2016
953417^79948+5898372Lelio R Paula08/2016
953522499^22602-22602^2249998368Norbert Schneider08/2020
95363^206143-9898356Lelio R Paula08/2016
95378*5^140705+798350Lelio R Paula11/2014
9538(2^326632+1662)/298326Stefano Morozzi09/2020
9539(638^35053-1)/63798315Serge Batalov06/2022
95402^326585+1198312Lelio R Paula12/2012
95412^326582-45916198311Enzo Doria05/2015
9542(1266^31687-1)/126598304Serge Batalov06/2022
9544(2^326548+9)/598301Lelio R Paula10/2013
9543(2^326549+18)/1098301Stefano Morozzi03/2020
95452^326538+7165998298Enzo Doria04/2016
9546(2^326520+2082)/298293Stefano Morozzi09/2020
9547(2^326521+1002)/298293Stefano Morozzi09/2020
954815^83575-5898292Lelio R Paula08/2016
954910^98288+398289Robert Price03/2011
955010^98288-11701798288Patrick De Geest11/2011
9551(44*10^98284-719)/998285Robert Price12/2017
9552(5985^26021-1)/598498280Serge Batalov06/2022
955323466^15419+15419^2346698277Hans Havermann02/2020
95542^326421-279757398263Enzo Doria04/2016
95552^326401+1609598257Lelio R Paula07/2016
9556(6494^25771-1)/649398249Serge Batalov06/2022
95577^116240-116240^798235Norbert Schneider05/2017
955817^79826-7898222Lelio R Paula08/2016
95592^326268-80998217Yves Minet04/2011
956022659^21590+21590^2265998210Hans Havermann10/2019
956122268^22587-22587^2226898202Norbert Schneider08/2020
9562(418*10^98199+23)/998201Robert Price08/2017
956312*10^98198-798200Robert Price11/2017
956415^83496-7698199Lelio R Paula08/2016
9565(10223*2^326179+1)/612598190Lelio R Paula07/2014
95669*5^140471-498186Lelio R Paula11/2014
9567(35103^21601-1)/3510298180Serge Batalov06/2022
956922774^20455+20455^2277498175Hans Havermann07/2020
9568(4516^26863-1)/451598175Serge Batalov06/2022
95702^326069-238398157Yves Minet10/2013
9571(9661^24631-1)/966098152Serge Batalov06/2022
9572(4175^27109-1)/417498149Serge Batalov06/2022
9573(57801^20611-1)/5780098144Serge Batalov06/2022
95742^325973+118598128Lelio R Paula07/2016
9575(25*2^325949-1)/1798121Lelio R Paula02/2014
95762^325945-184726998120Enzo Doria07/2015
95778*10^98111-6798112Robert Price10/2017
9578(2^325902+1138)/298106Stefano Morozzi09/2020
9579(215^42061-1)/21498103Serge Batalov06/2022
9580(6775^25609-1)/677498102Serge Batalov06/2022
9581(6718^25633-1)/671798100Serge Batalov06/2022
95822^325866+1598096Lelio R Paula12/2012
958322591^21952+21952^2259198079Hans Havermann02/2020
95842^325765+197430598066Enzo Doria06/2016
95852^325733-5869598056Lelio R Paula07/2016
9586(7*10^98055-529)/998055Robert Price08/2021
95872^325717-364598051Lelio R Paula07/2016
9588(2^325704+718)/298047Stefano Morozzi09/2020
9589(15679^23371-1)/1567898045Serge Batalov06/2022
9590(23342^22441-1)/2334198022Serge Batalov06/2022
959123968^12293+12293^2396898021Hans Havermann11/2019
9593(23*2^325583-1)/2198011Lelio R Paula02/2014
9592(128678^19321-1)/(128678^139-1)98011Ryan Propper11/2023
9594(7*10^98007-13)/398008Robert Price06/2016
9595(2^325544+1110)/297999Stefano Morozzi09/2020
95962^325512-45995997989Enzo Doria05/2015
9597(2^325492+682)/297983Stefano Morozzi09/2020
9598(3^205354-8)/1797978Lelio R Paula09/2013
95992^325433+7681797966Enzo Doria05/2016
96005*10^97963+8197964Robert Price08/2017
9601(9996^24649-1)/(9996^157-1)97964Ryan Propper11/2023
9602(13208^23773-1)/1320797961Serge Batalov06/2022
96032^325390-10906197953Enzo Doria04/2014
9604(55*10^97940+323)/997941Robert Price10/2021
960513^87921+2497940Lelio R Paula08/2016
960610^97930+18827797931Patrick De Geest09/2022
960810^97930-700000197930Robert Price06/2021
960710^97930-6695197930Patrick De Geest09/2022
9609961^32831-960^3283197926Jean-Louis Charton02/2011
9610(17968^23017-1)/1796797922Serge Batalov06/2022
9611(3337^27793-1)/333697922Serge Batalov06/2022
961322600^21499+21499^2260097913Hans Havermann05/2020
9612(18703^22921-1)/1870297913Serge Batalov06/2022
96142^325215+1290997900Lelio R Paula07/2016
961522619^21286+21286^2261997898Hans Havermann04/2020
9616(126852^19321-1)/(126852^139-1)97892Ryan Propper11/2023
9617(85*10^97876-49)/997877Robert Price12/2020
96187*10^97874-6997875Robert Price01/2017
96195*10^97869-6397870Robert Price04/2021
9620(643*32^65022-23)/3197870Eric Chen04/2023
9622(17^79537+5^79537)/2297865Robert Price06/2013
962115^83212+2297865Lelio R Paula08/2016
96232^325087-10905797861Enzo Doria04/2014
96242^325074+187065797858Enzo Doria05/2016
96262^325066-211197855Yves Minet08/2013
9625CopelandErdos(97855)97855Eric W. Weisstein10/2015
9627(8694^24841-1)/869397851Serge Batalov06/2022
9628(21159^22621-1)/2115897843Serge Batalov06/2022
962926660^4677+4677^2666097842Hans Havermann12/2019
963018^77944-8997841Lelio R Paula07/2016
9631119^47136+11897833Norbert Schneider09/2018
96326^125720-1766397830Enzo Doria02/2013
9633(73640^20101-1)/7363997829Serge Batalov06/2022
96342^324972-206997827Yves Minet05/2013
96352^324958-469197823Yves Minet05/2019
9636(8087^25033-1)/808697820Serge Batalov06/2022
96372^324944-278831997818Enzo Doria03/2016
963822845^19112+19112^2284597807Hans Havermann10/2019
9639(2^324898+1270)/297804Stefano Morozzi09/2020
96414*10^97799-997800Erik Branger11/2013
96402^324882+57729457597800Lelio R Paula09/2016
96422^324863-186792197794Enzo Doria04/2016
96436^125662-1847397785Enzo Doria03/2013
964412^90604+1197779Lelio R Paula07/2016
9645(29*10^97751+49)/397752Robert Price09/2021
9646(37108^21391-1)/3710797741Serge Batalov06/2022
96475^139830+2497737Lelio R Paula04/2016
9648(2^324672+1198)/297736Stefano Morozzi09/2020
9649(101*10^97724+7)/997726Robert Price02/2022
96502^324612+115597718Lelio R Paula07/2016
9651(2^324597+3542)/297714Stefano Morozzi09/2020
965219^76404-4497702Lelio R Paula07/2016
9653(5939^25889-1)/593897694Serge Batalov06/2022
96552^324505-298397686Yves Minet04/2011
9654(7740^25121-1)/773997686Serge Batalov06/2022
9656(144^45259+1)/14597684Paul Bourdelais08/2019
9657(31*2^324496-1)/4597683Lelio R Paula02/2014
9658(11234^24109-1)/1123397651Serge Batalov06/2022
96596^125488-1784397649Enzo Doria02/2013
9660(2^324350+3198)/297639Stefano Morozzi09/2020
9661(75638^20011-1)/7563797624Serge Batalov06/2022
96627^115515-297622Lelio R Paula09/2013
9663(15672^23269-1)/1567197613Serge Batalov06/2022
9664(89^50069-1)/8897603Paul Bourdelais08/2017
96656^125418-597595Lelio R Paula11/2014
9666(2^324193+3522)/297592Stefano Morozzi09/2020
9667(2422^28837-1)/242197587Serge Batalov06/2022
9668(2^324172+666)/297586Stefano Morozzi09/2020
96692^324091+11154643597562Paul Bourdelais10/2021
96702^324076+115597557Lelio R Paula07/2016
9671(2^324074+9)/1397555Lelio R Paula10/2013
9672(11*10^97539-71)/397540Robert Price04/2022
9673(55459*2^323993+1)/2197536Lelio R Paula07/2014
967413^87557-12^8755797534Jean-Louis Charton12/2008
96752^323946+7393997518Enzo Doria04/2016
96762^323937+186694797515Enzo Doria03/2016
9677(98339^19531-1)/9833897508Serge Batalov06/2022
96796^125290-1853397495Enzo Doria03/2013
9678(2^323870+1650)/297495Stefano Morozzi09/2020
96802^323845+10197488Lelio R Paula12/2012
968118^77662+6597487Lelio R Paula07/2016
968222634^20265+20265^2263497479Hans Havermann04/2020
9683(5533^26041-1)/553297467Serge Batalov06/2022
96842^323772+7677197466Enzo Doria05/2016
96852^323765-11221397463Enzo Doria06/2014
968622730^19389+19389^2273097457Hans Havermann02/2020
96872^323720-655597450Lelio R Paula07/2016
96882^323694-186040197442Enzo Doria03/2016
968920^74886+397429Lelio R Paula06/2016
969024476^9561+9561^2447697427Hans Havermann01/2020
9691(2^323623+1766)/297420Stefano Morozzi09/2020
9692(3250^27739-1)/324997413Serge Batalov06/2022
96943*10^97399+7397400Robert Price04/2016
96937^115252-5097400Lelio R Paula07/2016
9695(4715^26513-1)/471497392Serge Batalov06/2022
96962^323521+21331797390Enzo Doria09/2023
9697224737#+39358197389Nicolas PALAU12/2016
9698(119374^19321-1)/(119374^139-1)97386Ryan Propper11/2023
9699(2^323468+3186)/297374Stefano Morozzi09/2020
9700(2^323456+538)/297370Stefano Morozzi09/2020
970123277^15236+15236^2327797365Hans Havermann07/2020
9703(26*10^97353+31)/397354Robert Price07/2016
9702(2^323403+3510)/297354Stefano Morozzi09/2020
970423756^12519+12519^2375697342Hans Havermann07/2020
970510^97335+27164197336Patrick De Geest09/2022
970710^97335-400000197335Robert Price07/2021
970610^97335-9819397335Patrick De Geest09/2022
9708(637*10^97331+11)/997333Robert Price10/2021
970923991^11402+11402^2399197332Hans Havermann07/2020
971061^54517-60^5451797331Jean-Louis Charton09/2005
9711(38*10^97329+187)/997330Robert Price11/2017
9712(31147^21661-1)/3114697328Serge Batalov06/2022
971386455!4+897319Robert Price09/2019
971422591^20310+20310^2259197316Hans Havermann06/2020
97152^323261-43117397312Harrison Mesh06/2022
9716(3996^27017-1)/399597302Serge Batalov06/2022
971725101^7520+7520^2510197297Hans Havermann05/2020
9718(233*10^97294+7)/397296Robert Price03/2022
9719p(19982)#/2-102497293Robert Price09/2017
9720(65*10^97288+277)/997289Robert Price08/2021
97216^125021-8597286Lelio R Paula08/2016
97222^323164-4735597283Lelio R Paula07/2016
9723(3^203902+4)/3605101515797276Lelio R Paula09/2013
97242^323054-655597249Lelio R Paula07/2016
972522822^18247+18247^2282297249Hans Havermann02/2020
97269*10^97247-2997248Robert Price05/2017
972724382^9735+9735^2438297244Hans Havermann02/2020
9728(31*10^97242+41)/997243Robert Price04/2015
9729GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
973012^90098-4197233Lelio R Paula07/2016
97312^322928-21692997212Enzo Doria05/2014
9732(16731^23017-1)/1673097209Serge Batalov06/2022
97333*10^97205-6197206Robert Price04/2021
9734(7*2^322896-1)/5797201Lelio R Paula02/2014
9735(35*10^97194-341)/997195Robert Price08/2021
9736(4872^26357-1)/487197194Serge Batalov06/2022
9737(2^322897+5)/314610748997193Lelio R Paula10/2013
9738(796*10^97183-31)/997185Robert Price07/2022
9739(2^322789+2214)/297169Stefano Morozzi09/2020
97402^322725+7576197150Enzo Doria04/2016
9741(13*2^322686+1)/11997138Lelio R Paula11/2013
9742(2175^29101-1)/217497121Serge Batalov06/2022
974322402^21639+21639^2240297118Hans Havermann07/2020
974423399^14128+14128^2339997108Hans Havermann06/2020
9745(2892^28057-1)/289197108Serge Batalov06/2022
9746(9578^24391-1)/957797104Serge Batalov06/2022
9747(2^322525+2606)/297090Stefano Morozzi09/2020
9748(9563^24391-1)/956297087Serge Batalov06/2022
9749(41*10^97085+373)/997086Robert Price04/2017
9750(2^322473+854)/297074Stefano Morozzi02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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