PRP Records

Probable Primes Top 10000

(301737 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 ?
425133958^20825+20825^33958146651Hans Havermann12/2020
425226289^33178-33178^26289146640Frank Doornink03/2024
42532^487121-39523146639Enzo Doria09/2015
425461063^252+252^61063146637Hans Havermann12/2020
4255(7*2^486967+1)/39146591Lelio R Paula09/2015
425634099^19900+19900^34099146587Hans Havermann11/2020
42572^486893-79146570Yves Minet09/2017
425836818^9567+9567^36818146565Hans Havermann12/2020
42592^486840+1879141146554Enzo Doria08/2016
42602^486774-87146534Lelio R Paula12/2017
426138655^6176+6176^38655146530Hans Havermann11/2020
42628*10^146522-81146523Robert Price02/2021
426332820^29059+29059^32820146485Hans Havermann12/2020
426437261^8530+8530^37261146472Hans Havermann12/2020
426566953^154+154^66953146462Hans Havermann12/2020
426696^73877-95^73877146445Robert Price10/2015
42678*10^146421+81146422Robert Price08/2019
426833153^26090+26090^33153146420Hans Havermann11/2020
42692^486275+23961146384Enzo Doria10/2023
4270(12^135607-1)/18437127731146335Paul Vanderveen06/2025
4271(52^85259+1)/53146304Paul Bourdelais09/2017
4272179^64935+2146290Lelio R Paula10/2017
427332595^30758+30758^32595146285Hans Havermann11/2020
427434972^15157+15157^34972146205Hans Havermann12/2020
4275(16*10^146200+131)/3146201Robert Price03/2022
4276(19*10^146181-49)/3146182Robert Price05/2019
42772^485531-114621146160Enzo Doria05/2015
42782^485473-933075146142Paul Bourdelais06/2021
4279(2^485461-9)/4249146135Lelio R Paula09/2015
4280(22*10^146130-193)/9146131Robert Price07/2022
42812^485389+81887146117Enzo Doria08/2016
428232554^30773+30773^32554146108Hans Havermann11/2020
428328075^32844-32844^28075146101Frank Doornink06/2024
4284(10^146063+71)/9146063Serge Batalov07/2015
42852*10^146051-63146052Robert Price01/2022
4286(2^485119+7)/2745146032Lelio R Paula09/2015
4287(22*10^146029+257)/9146030Robert Price06/2018
42887*10^145982-53145983Robert Price06/2020
42892^484743+1872923145923Enzo Doria05/2016
429033140^25287+25287^33140145913Hans Havermann01/2021
429137875^7112+7112^37875145895Hans Havermann01/2021
429230542^32529-32529^30542145890Frank Doornink06/2024
429332862^27473+27473^32862145872Hans Havermann01/2021
4294V(1046652)/2093303145817Serge Batalov07/2024
429532836^27587+27587^32836145815Hans Havermann01/2021
42962^484341+1879157145802Enzo Doria08/2016
42972*10^145784-91145785Robert Price04/2020
42982^484271-51145781Lelio R Paula11/2017
4299(188*10^145750-11)/3145752Robert Price02/2022
430070^78989-69^78989145743Robert Price01/2014
430151^85334+2145714Robert Price07/2015
430210^2^72843+72843^2^10145687Henri Lifchitz03/2025
43032^483886-1857101145665Enzo Doria10/2015
430429312^32607-32607^29312145657Frank Doornink06/2024
430533350^23307+23307^33350145656Hans Havermann01/2021
4306(19*10^145585+131)/3145586Robert Price06/2020
430731815^32332-32332^31815145580Frank Doornink01/2024
43082^483563-1863457145567Enzo Doria12/2015
43094*10^145563-69145564Robert Price01/2022
43102^483516-1861409145553Enzo Doria11/2015
43112^483384-115019145514Enzo Doria06/2015
4312(259*10^145501-1)/3145503Robert Price12/2020
4313(19*10^145499-61)/3145500Robert Price05/2019
43142^483302-3221145489Lelio R Paula12/2012
4315(23*10^145463+61)/3145464Robert Price01/2022
431635523^12434+12434^35523145453Hans Havermann01/2021
4317(29121^32761-1)/(29121^181-1)145444Ryan Propper11/2023
43182^483046+1874029145412Enzo Doria06/2016
43192^482991-2789317145395Enzo Doria12/2015
43202^482978-2789711145391Enzo Doria12/2015
43212^482966-2789711145388Enzo Doria12/2015
43222^482817-1858843145343Enzo Doria10/2015
4323235*29^99378+4145333Eric Chen06/2025
43242^482751-113635145323Enzo Doria08/2014
43252^482705-459763145309Enzo Doria05/2015
4326(4^241306+11)/3145281Robert Price03/2017
4327(238*10^145276-1)/3145278Robert Price04/2020
4328(19*2^482534+1)/7145258Lelio R Paula09/2015
432953^84239-52^84239145252Robert Price01/2013
4330U(1042497)145243Serge Batalov07/2024
43312^482386+212419145213Enzo Doria08/2023
433247952^1067+1067^47952145207Hans Havermann01/2021
4333(2^482333+5)/9287145193Lelio R Paula09/2015
43342^482087+72623145123Enzo Doria04/2016
43352^482016-286565145102Enzo Doria07/2015
4336(19*10^145093+101)/3145094Robert Price09/2019
43372^481956+121145084Stefano Morozzi04/2021
433827535^32676-32676^27535145078Frank Doornink06/2024
43392^481840+15145049Robert Price09/2015
4340(23*10^145040+7)/3145041Robert Price05/2023
43412^481801-481801145037Henri Lifchitz03/2005
43422^481775+1869083145029Enzo Doria05/2016
434329^99167+2145022Ray Chandler08/2011
43442^481663+1875653144996Enzo Doria07/2016
43458*10^144977+27144978Robert Price09/2021
434629840^32393-32393^29840144953Frank Doornink06/2024
434736486^9379+9379^36486144929Hans Havermann12/2020
434831580^32209-32209^31580144922Frank Doornink01/2024
434935111^13378+13378^35111144882Hans Havermann01/2021
43502^481149-459073144841Enzo Doria05/2015
43512^481113+181419144830Boyan Hu04/2024
435234619^15246+15246^34619144817Hans Havermann01/2021
43532^481045-113215144809Enzo Doria07/2014
4354(64*10^144797+287)/9144798Robert Price04/2019
435527320^32629-32629^27320144758Frank Doornink06/2024
43562^480859-113695144753Enzo Doria09/2014
4357(106*10^144744+17)/3144746Robert Price04/2021
43587*10^144742-27144743Robert Price11/2022
43592^480766-2787191144725Enzo Doria11/2015
4360(21*27^101106-151)/26144720Curtis Bright05/2015
436128915^32438-32438^28915144710Frank Doornink06/2024
43622^480678+1874239144699Enzo Doria06/2016
4363(8*10^144683+1)/9144683Serge Batalov05/2010
4364L(692147)144651Henri Lifchitz10/2008
4365(76*10^144648+77)/9144649Robert Price10/2019
436632672^26721+26721^32672144635Hans Havermann01/2021
436731478^32153-32153^31478144625Frank Doornink01/2024
43682^480417+35144620Robert Price11/2015
43692^480296-59879144584Enzo Doria10/2015
437033157^22878+22878^33157144546Hans Havermann12/2020
437127520^32541-32541^27520144471Frank Doornink06/2024
437245494^1497+1497^45494144454Hans Havermann12/2020
43732^479844+3144448Donovan Johnson06/2006
437433442^20803+20803^33442144407Hans Havermann01/2021
4375(441*33^95095-3833)/32144405Eric Chen12/2023
437631892^32061-32061^31892144393Norbert Schneider01/2023
4377(27*2^479642+1)/733144386Lelio R Paula08/2015
4378(56*10^144380+169)/9144381Robert Price03/2022
437944917^1638+1638^44917144378Hans Havermann12/2020
4380(21*2^479605-1)/11144376Lelio R Paula09/2015
4381(11^138641-1)/6631590024336120710144361Paul Vanderveen05/2025
4382(56*10^144336+583)/9144337Robert Price08/2021
43835*2^479430-3144324Jon Grantham07/2023
43842^479348-2792219144299Enzo Doria02/2016
438531134^32111-32111^31134144283Frank Doornink01/2024
43863^302389-6242144277Enzo Doria05/2014
438731665^32056-32056^31665144271Frank Doornink01/2024
438833778^18641+18641^33778144248Hans Havermann01/2021
438929083^32312-32312^29083144230Frank Doornink06/2024
43902*10^144220-3144221Robert Price07/2015
439125313^32750-32750^25313144210Frank Doornink01/2024
43922^478904-109109144165Enzo Doria04/2014
439343698^1987+1987^43698144125Hans Havermann12/2020
439479^75948+75948144121Kellen Shenton06/2023
439526941^32522-32522^26941144086Frank Doornink06/2024
439636128^9723+9723^36128144072Hans Havermann01/2021
439732817^24518+24518^32817144050Hans Havermann12/2020
4398(772*10^144036-7)/9144038Robert Price06/2022
439934295^15828+15828^34295144020Hans Havermann01/2021
44002^478337-115333143994Enzo Doria07/2015
4401(7*2^478330-1)/3143993Lelio R Paula08/2015
440288^74047-87^74047143984Robert Price05/2015
440333242^21441+21441^33242143980Hans Havermann01/2021
4404(19*10^143963+467)/9143964Robert Price02/2018
4405(71^77761+1)/72143954Paul Bourdelais09/2017
440633490^19859+19859^33490143939Hans Havermann01/2021
4407(853*10^143931-7)/9143933Robert Price07/2021
44082^478088+27143919Robert Price11/2015
4409(8*10^143898-137)/3143899Robert Price03/2022
44107*10^143857-93143858Robert Price08/2020
44113*10^143844+61143845Robert Price09/2020
441241358^3005+3005^41358143837Hans Havermann01/2021
44132^477475-22071143735Enzo Doria07/2013
44142^477417-22123143717Enzo Doria07/2013
44152^477359-3577143700Yves Minet03/2017
441639435^4402+4402^39435143688Hans Havermann01/2021
4417(14*10^143662-71)/3143663Robert Price12/2018
44186^184614+5143658Paul Bourdelais01/2021
441946371^1252+1252^46371143640Hans Havermann12/2020
442034975^12748+12748^34975143588Hans Havermann01/2021
44212^476936-396765143573Enzo Doria07/2013
44222^476888-2791229143558Enzo Doria01/2016
44232^476868-1859939143552Enzo Doria11/2015
442440807^3294+3294^40807143548Hans Havermann12/2020
4425755^49878+49878^755143547Norbert Schneider04/2019
4426(19^112247-4^112247)/15143536Robert Price03/2021
442735561^10872+10872^35561143536Hans Havermann06/2021
442837637^6492+6492^37637143487Hans Havermann05/2021
442961567^214+214^61567143477Hans Havermann05/2021
443025933^32504-32504^25933143468Frank Doornink03/2024
44312^476558-113627143459Enzo Doria08/2014
44322^476478-45143435Lelio R Paula11/2017
443336380^8757+8757^36380143423Hans Havermann06/2021
443432510^25707+25707^32510143371Hans Havermann05/2021
44358*10^143361+17143362Robert Price07/2021
4436(2^475854+9)/73143245Lelio R Paula08/2015
44372^475813-113239143234Enzo Doria07/2014
4438(19*10^143212+137)/3143213Robert Price03/2022
443932218^27849+27849^32218143203Hans Havermann04/2021
4440580*33^94296+19143193Eric Chen12/2023
44412^475624-114059143178Enzo Doria11/2014
4442(11*2^475553-7)/15143156Renaud Lifchitz03/2011
44432^475480-2786129143134Enzo Doria10/2015
444433912^16621+16621^33912143131Hans Havermann05/2021
4445(19*10^143129-43)/3143130Robert Price05/2019
444631830^31373+31373^31830143126Hans Havermann05/2021
44472^475392+1334025143108Henri Lifchitz01/2025
44486*10^143105-53143106Robert Price05/2021
4449(14*10^143097+73)/3143098Robert Price12/2018
44502^475299-111937143080Enzo Doria05/2014
445135488^10753+10753^35488143071Hans Havermann04/2021
445229695^31986-31986^29695143064Frank Doornink06/2024
44532^475160-2797859143038Enzo Doria04/2016
4454(2^475069+3)/395143008Lelio R Paula08/2015
44552^475027-461437142998Enzo Doria07/2015
4456(2^474958+78557)/3142977Lelio R Paula07/2015
4457(8*10^142932+43)/3142933Robert Price06/2018
445835055^11942+11942^35055142922Hans Havermann05/2021
445937650^6239+6239^37650142887Hans Havermann05/2021
4460(54^82471-1)/53142871Paul Bourdelais09/2017
446131205^31784-31784^31205142845Frank Doornink01/2024
4462(11*2^474432-1)/95142818Lelio R Paula09/2015
44632^474417-59923142814Enzo Doria10/2015
44644*10^142810-21142811Robert Price09/2018
446532287^26494+26494^32287142811Hans Havermann06/2021
446637162^6965+6965^37162142811Hans Havermann06/2021
4467(34*10^142805-601)/9142806Robert Price07/2022
446837456^6493+6493^37456142799Hans Havermann05/2021
446935141^11572+11572^35141142793Hans Havermann05/2021
447032231^26908+26908^32231142780Hans Havermann05/2021
4471(3*2^474166+1)/7142738Lelio R Paula08/2015
44722^474053+2897142705Lelio R Paula08/2012
4473(10^142699+359)/9142699Serge Batalov12/2014
447426073^32312-32312^26073142696Frank Doornink03/2024
4475898^48311-897^48311142676Jean-Louis Charton12/2012
44762^473740-1856639142610Enzo Doria09/2015
4477(25*10^142573-403)/9142574Robert Price12/2020
44782^473617-114223142573Enzo Doria12/2014
447936115^8856+8856^36115142555Hans Havermann05/2021
4480fibonacci(682007)+4142531Jon Grantham08/2023
44812^473257+1873217142465Enzo Doria06/2016
4482(19*2^473242+1)/11142461Lelio R Paula09/2015
448332750^22371+22371^32750142453Hans Havermann06/2021
4484(61*10^142446-1)/3142448Robert Price01/2020
4485(14*10^142440+61)/3142441Robert Price12/2018
4486(10^142425+359)/9142425Serge Batalov12/2014
44872^473101+773027142418Enzo Doria05/2016
4488(13*2^472838-1)/3142340Lelio R Paula09/2015
4489(17*2^472789-1)/187347142320Lelio R Paula09/2015
449036915^7162+7162^36915142309Hans Havermann05/2021
44912^472634-109511142278Enzo Doria04/2014
449231870^28997+28997^31870142216Hans Havermann06/2021
4493(48^84589+1)/49142213Robert Price01/2014
44947*10^142189+87142190Robert Price07/2019
44952^472258+7142164Lelio R Paula08/2015
449640135^3484+3484^40135142162Hans Havermann05/2021
44979*33^93598+26142131Eric Chen12/2023
4498(23*10^142105+91)/3142106Robert Price08/2019
4499tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
4500(11*2^471913-1)/21142060Lelio R Paula09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 13 2025 09:00 (Time in France)

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