PRP Records

Probable Primes Top 10000

(301429 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 ?
6751(749^38809+1)/(749^197+1)110990Martin Hopf11/2023
67522^368641-460303110972Enzo Doria06/2015
67532^368619-109087110966Enzo Doria04/2014
6754(74*10^110961+313)/9110962Robert Price06/2019
675525258^24711+24711^25258110956Hans Havermann11/2020
6756(2^368539+1290)/2110941Stefano Morozzi01/2021
67573*2^368489+7110927Lelio R Paula09/2014
6758(14*10^110922+61)/3110923Robert Price12/2018
675997411!4-2110913Robert Price07/2017
6760(301*10^110903+23)/9110905Robert Price06/2021
6761(9179*2^368330-1)/35110881Lelio R Paula05/2015
676225830^19619+19619^25830110880Hans Havermann10/2020
6763(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
676426022^18191+18191^26022110850Hans Havermann10/2020
6765(2^368211+2250)/2110843Stefano Morozzi01/2021
6766(37*10^110813+251)/9110814Robert Price09/2021
67672^368050-64875110795Lelio R Paula05/2017
67682^368048+25110794Lelio R Paula02/2013
6769(2^368017+2262)/2110784Stefano Morozzi02/2021
677069^60239-2110771Lelio R Paula10/2013
6771(23*2^367952+1)/15717110762Lelio R Paula03/2014
67722^367924-69110757Lelio R Paula02/2013
6773(23*10^110738+61)/3110739Robert Price01/2022
6774(2^367779+3750)/2110713Stefano Morozzi01/2021
67752^367709-109723110692Enzo Doria04/2014
67762^367687+213413110685Enzo Doria09/2023
6777(3*2^367644-1)/107110671Lelio R Paula03/2014
6778(2^367626+3514)/2110667Stefano Morozzi09/2020
6779(1288676*34^72242-455)/33110642Eric Chen03/2023
6780379*10^110616+9110619Jason Yuen01/2025
6781(23*2^367398+1)/57963110595Lelio R Paula03/2014
6782140^51515-139110558Norbert Schneider04/2019
67832^367215+1879223110543Enzo Doria09/2016
678425782^19375+19375^25782110534Hans Havermann10/2020
678526117^17058+17058^26117110526Hans Havermann10/2020
67862^367141+41110521Lelio R Paula02/2013
67872^367126+29835110516Lelio R Paula05/2017
6788(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
6789(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
6790(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
6791(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
6792(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
6793(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
6794(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
6795(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
6796(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
6797(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
6798(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
67993*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
68003*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
68013*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
68023*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
68033*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
68043*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
68053*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
68067*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
68077*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
68087*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
68097*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
68107*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
68117*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
68127*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
68137*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
68147*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
68157*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
68167*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
68177*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
68187*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
68197*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
68207*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
6821(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
6822(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
6823(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
6824(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
6825(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
6826(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
6827(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
6828(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
6829(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
6830(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
6831(11*10^110496+49)/3110497Robert Price07/2018
683225447^21958+21958^25447110481Hans Havermann11/2020
6833(31*2^366976+1)/7110472Lelio R Paula03/2014
68347*10^110468-23110469Robert Price07/2019
68355*3^231464-2^231464110438Jon Grantham08/2023
68362^366853+5711110434Lelio R Paula05/2017
6837(21181*2^366833+1)/3110432Lelio R Paula07/2014
68382^366816+315110423Lelio R Paula05/2017
68392^366775-2787037110411Enzo Doria03/2016
6840(112*10^110405-1)/3110407Serge Batalov12/2014
68412^366751+2797553110404Enzo Doria03/2016
684225276^23331+23331^25276110404Hans Havermann10/2020
68432^366748+255110403Lelio R Paula05/2017
68442^366738-2985110400Yves Minet09/2014
6845(23*2^366739+1)/74575110396Lelio R Paula03/2014
6846(2^366722+1314)/2110395Stefano Morozzi02/2021
68472^366716+1871791110393Enzo Doria05/2016
6848(239*23^81066-349)/22110391Eric Chen08/2023
68492^366695+1334025110387Henri Lifchitz10/2024
68502^366649+1871687110373Enzo Doria05/2016
68512^366629-351205110367Enzo Doria06/2015
6852(31*10^110363+257)/9110364Robert Price12/2021
6853(17*19^86292-215)/18110347Eric Chen01/2023
68552^366558+1874479110345Enzo Doria06/2016
685425132^24581+24581^25132110345Hans Havermann10/2020
6856(2^366539+770)/2110339Stefano Morozzi09/2020
685726368^15285+15285^26368110331Hans Havermann10/2020
6858(23*10^110290+19)/3110291Robert Price07/2019
685918^87853-4409110280Enzo Doria03/2013
686028490^7419+7419^28490110267Hans Havermann11/2020
68612^366218-23110243Lelio R Paula02/2013
6862(21*2^366193-1)/197110235Lelio R Paula03/2014
68632^366178-343991110231Enzo Doria07/2015
686412^102123-11110210Riley Fisher09/2023
6865(725*35^71368+16649)/34110199Eric Chen05/2025
686625777^18798+18798^25777110174Hans Havermann10/2020
68672^365944+1871341110161Enzo Doria05/2016
68682^365838-461267110129Enzo Doria07/2015
686930152^4491+4491^30152110126Hans Havermann11/2020
68702^365802+23359110118Enzo Doria10/2023
687110^110111+464019110112Patrick De Geest05/2021
687210^110111-40001110111Robert Price01/2021
68732^365763-6555110106Lelio R Paula04/2017
6874(2^365689+2^182845+1)/511008311/2006
68752^365666-459161110077Enzo Doria05/2015
68763*10^110076-7110077Robert Price08/2015
687713^98785-72110041Lelio R Paula03/2017
6879(25^78707+1)/26110027Robert Price06/2013
6878(7*10^110027-277)/9110027Robert Price02/2022
6880(16*10^110014-73)/3110015Robert Price07/2020
6881(7*10^110006-151)/9110006Robert Price02/2018
68826^141361-7110001Lelio R Paula11/2014
688310^110000+8029681110001Hayden Chesnut11/2024
688410^110000+2044477110001Hayden Chesnut11/2024
688510^110000+76407110001Hayden Chesnut11/2024
688610^110000+167311110001Hayden Chesnut11/2024
688720^84536+81109984Lelio R Paula03/2017
68885*2^365347-9109982Lelio R Paula09/2014
68899*6^141303+7109957Lelio R Paula11/2014
689027635^9522+9522^27635109953Hans Havermann11/2020
689178^58099+77109929Norbert Schneider02/2015
68922*10^109928-7109929Robert Price10/2015
689330580^3933+3933^30580109927Hans Havermann11/2020
689426380^14689+14689^26380109926Hans Havermann11/2020
6895(2^365161+1130)/2109925Stefano Morozzi09/2020
6896(27*2^365137-1)/2021109916Lelio R Paula03/2014
689729^75157-30109910Anonymous09/2024
6898(4441*29^75152-24)/7109905Curtis Bright05/2015
6899(2^365087+7)/6015109899Lelio R Paula01/2014
6900(2^365069+3774)/2109897Stefano Morozzi02/2021
690129652^5083+5083^29652109894Mark Rodenkirch10/2020
6902(2^365049+722)/2109891Stefano Morozzi09/2020
6903(35*10^109888-89)/9109889Robert Price02/2022
690418^87533-11109878Lelio R Paula04/2017
69052^364982-5109871Henri Lifchitz04/2006
69063*10^109861+59109862Robert Price08/2018
69075*10^109860-69109861Robert Price02/2021
69082^364936-1867979109857Enzo Doria04/2016
690927013^11652+11652^27013109846Hans Havermann10/2020
69102^364867-112087109836Enzo Doria06/2014
69114^182415-85061109825Mike Oakes06/2011
6912(2^364809+1034)/2109819Stefano Morozzi09/2020
691324972^24972-8323^8323109814Henri Lifchitz10/2024
6914(53*10^109809-287)/9109810Robert Price02/2022
6915(52*10^109807-133)/9109808Robert Price09/2021
691625708^18675+18675^25708109806Hans Havermann10/2020
6917(17^89227+16^89227)/33109788Robert Price08/2013
69182^364687-187109782Lelio R Paula01/2012
69192^364644+67109769Lelio R Paula01/2012
6920(9787*2^364625-1)/24947109763Lelio R Paula05/2015
6921(2^364616+5)/9109760Lelio R Paula01/2014
6922(55*10^109759+89)/9109760Robert Price03/2019
6923(14*32^72921+4171)/31109757Eric Chen04/2023
692412^101694+73109747Lelio R Paula03/2017
692513^98518-66109744Lelio R Paula03/2017
6926(35^71069+2^71069)/37109734Robert Price01/2025
6927(8*10^109721-269)/9109721Robert Price09/2021
69282^364478-113261109719Enzo Doria07/2014
6929(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
6930(24737*2^364454+1)/3109716Lelio R Paula07/2014
693127814^8777+8777^27814109681Hans Havermann10/2020
6932(62*10^109673+1)/9109674Serge Batalov11/2010
69333^229824+340109654Lelio R Paula03/2017
6934(16623*33^72206-8095)/16109649Eric Chen05/2023
6935(2*10^109645-71)/3109645Robert Price12/2017
6936V(786978)109644Serge Batalov07/2024
69372^364169-112813109626Enzo Doria06/2014
693828822^6359+6359^28822109622Hans Havermann11/2020
693910^109615+21109616Lelio R Paula03/2017
694010^109615-456267109615Patrick De Geest03/2017
6941522^40331-40331^522109607Norman Luhn09/2024
69422^364094-113109604Lelio R Paula01/2012
694325251^21898+21898^25251109600Hans Havermann11/2020
6944(4^182026+11)/3109591Robert Price02/2017
69452^364041-6883109588Lelio R Paula09/2011
694612^101545+11109586Lelio R Paula03/2017
694726536^13475+13475^26536109582Hans Havermann11/2020
69482^363842-2787101109528Enzo Doria03/2016
6949(2^363812+3570)/2109519Stefano Morozzi09/2020
6950(996^36527+1)/997109515Jinyuan Wang12/2024
6951(22699*2^363782+1)/763109511Lelio R Paula07/2014
69522^363769+5711109506Lelio R Paula04/2017
6953(31*2^363748+1)/49109499Lelio R Paula03/2014
695426^77372+25109480Anonymous09/2024
6955(2^363670+100280245065)109476Paul Bourdelais05/2022
6956p(22245)#/2-8109462Robert Price01/2017
69572^363556+55109442Lelio R Paula01/2012
6958(509*10^109414+31)/9109416Robert Price08/2022
6959(2^363437+1682)/2109406Stefano Morozzi09/2020
6960(55459*2^363411+1)/81109401Lelio R Paula07/2014
69612^363406+1871569109397Enzo Doria05/2016
6962(129^51829-1)/128109388Anonymous06/2024
6963(2^363370+1338)/2109385Stefano Morozzi02/2021
6964(2^363349+7)/9109378Lelio R Paula01/2014
6965(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
69663^229236+100109374Lelio R Paula03/2017
6967(2^363315+3258)/2109369Stefano Morozzi02/2021
69682^363268-58695109355Lelio R Paula04/2017
69692^363191-112321109332Enzo Doria06/2014
697026231^14718+14718^26231109327Hans Havermann10/2020
697125461^19672+19672^25461109326Hans Havermann10/2020
69724*10^109316-63109317Robert Price10/2018
69732^363120+3109311Donovan Johnson04/2006
6974(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
69752^363042-114641109287Enzo Doria04/2015
69762^363020-112793109280Enzo Doria06/2014
6977(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
6978(85*10^109253+203)/9109254Robert Price09/2020
697924990^23431+23431^24990109202Hans Havermann10/2020
6980(2^362746+3738)/2109198Stefano Morozzi09/2020
6981(2^362716+1282)/2109189Stefano Morozzi01/2021
6982(67607*2^362695+1)/70499109183Lelio R Paula07/2014
698325060^22737+22737^25060109180Hans Havermann10/2020
6984(9*2^362644+1)/5109167Lelio R Paula03/2014
69855^156181+38109166Lelio R Paula02/2017
6986(2^362623+3618)/2109161Stefano Morozzi09/2020
698725138^21993+21993^25138109157Hans Havermann10/2020
69884*10^109142+91109143Robert Price08/2018
69893^228750+68109142Lelio R Paula03/2017
6990(2^362561+786)/2109142Stefano Morozzi09/2020
6991(23*10^109113+61)/3109114Robert Price01/2022
69922*10^109100-49109101Robert Price09/2020
6993(10223*2^362376+1)/9109090Lelio R Paula07/2014
699465^60167-64^60167109078Robert Price08/2013
69957*3^228589-2109066Lelio R Paula09/2014
699624874^24243+24243^24874109063Hans Havermann11/2020
6997(17*10^109059-161)/9109060Robert Price02/2021
699829158^5495+5495^29158109050Hans Havermann11/2020
6999(78557*2^362188+1)/189109033Lelio R Paula07/2014
70002*7^129008+9109025Lelio R Paula11/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 21 2025 13:33 (Time in France)

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