PRP Records

Probable Primes Top 10000

(303412 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 ?
525131112^29499+29499^31112139065Hans Havermann05/2021
52522*10^139043-63139044Robert Price01/2022
525336390^6613+6613^36390139025Hans Havermann04/2021
525430554^30989-30989^30554138988Frank Doornink05/2024
52552*10^138975+33138976Robert Price11/2021
525642437^1882+1882^42437138966Hans Havermann05/2021
525732151^20990+20990^32151138958Hans Havermann05/2021
525832154^20933+20933^32154138933Hans Havermann04/2021
525931082^29499+29499^31082138931Hans Havermann04/2021
526030573^30962-30962^30573138876Frank Doornink05/2024
52612^461228+1870441138844Enzo Doria05/2016
52622^461204-113675138837Enzo Doria08/2014
5263(397227*29^94935-19)/28138837Eric Chen06/2025
5264(2^461139-7)/47138815Lelio R Paula08/2015
5265(17*10^138812-521)/9138813Robert Price04/2018
52663*10^138811-11138812Robert Price07/2018
526729109^31088-31088^29109138778Frank Doornink05/2024
5268(28*10^138768+173)/3138769Robert Price12/2019
5269(17*2^460963+1)/124051613138757Lelio R Paula08/2015
5270(379*10^138737-1)/9138739Robert Price02/2020
5271(43*10^138648+101)/9138649Robert Price11/2018
52722^460567-113541138645Enzo Doria08/2014
52732^460539+224789138637Enzo Doria07/2024
5274(10^138622+161)/9138622Robert Price09/2021
52757*10^138604+3138605Robert Price08/2015
5276(133*10^138600+17)/3138602Robert Price11/2021
527733912^12203+12203^33912138581Hans Havermann05/2021
52782^460330+69138574Lelio R Paula09/2017
5279(17*10^138569-77)/3138570Robert Price08/2019
528031186^27725+27725^31186138556Hans Havermann05/2021
5281(41^85909-3^85909)/38138552Robert Price09/2025
5282(16*10^138545+89)/3138546Robert Price03/2021
528339753^3056+3056^39753138546Hans Havermann05/2021
528431282^26847+26847^31282138545Hans Havermann05/2021
52856*10^138520-37138521Robert Price02/2021
52882^460078-69581138498Enzo Doria12/2015
528631830^22447+22447^31830138498Hans Havermann05/2021
5287Phi(237987,2^3)138498Henri Lifchitz12/2025
528937384^5065+5065^37384138492Hans Havermann05/2021
529028736^31055-31055^28736138457Frank Doornink05/2024
529134774^9585+9585^34774138456Hans Havermann05/2021
529210^138444-5001138444Robert Price12/2021
52932^459768+1531138404Lelio R Paula06/2012
5294(266*10^138328-17)/3138330Robert Price07/2020
529527200^31193-31193^27200138328Frank Doornink01/2024
52962024^41836+2025138319Henri Lifchitz01/2025
529728782^31019-31019^28782138318Frank Doornink05/2024
529832963^15696+15696^32963138306Hans Havermann05/2021
52992^459343-113611138277Enzo Doria08/2014
5300(28*10^138240+113)/3138241Robert Price03/2020
53012^459199+1874393138233Enzo Doria06/2016
530233339^14002+14002^33339138230Hans Havermann05/2021
530330137^30860-30860^30137138226Frank Doornink05/2024
53042^459063-345307138192Enzo Doria06/2015
53052*10^138162-43138163Robert Price04/2018
53062^458927-112747138151Enzo Doria06/2014
53072^458927-69217138151Enzo Doria11/2015
530830907^29458+29458^30907138130Hans Havermann05/2021
530932882^15837+15837^32882138094Hans Havermann05/2021
531039252^3295+3295^39252138083Hans Havermann05/2021
531133789^12190+12190^33789138062Hans Havermann06/2021
5312555555*2^458524+1513138036Darren Bedwell08/2009
531328095^31028-31028^28095138033Frank Doornink05/2024
531430931^29002+29002^30931138028Hans Havermann05/2021
53152^458465+2^32+1138012T. D. Noe06/2007
531632206^19275+19275^32206138003Hans Havermann05/2021
53172^458321-113053137969Enzo Doria07/2014
53186^177298+323137965Riley Fisher03/2023
53192^458298+79459137962Enzo Doria06/2016
532030254^30789-30789^30254137959Frank Doornink05/2024
53212^458248-21815137947Enzo Doria07/2013
53222^458194+1876549137931Enzo Doria07/2016
5323(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
5324(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
5325(793*10^137887+53)/9137889Robert Price01/2022
53262^457937+57137853Lelio R Paula09/2017
532728714^30921-30921^28714137849Frank Doornink05/2024
5328(8*10^137845+13)/3137846Robert Price06/2018
53292^457822+105137819Donovan Johnson06/2006
53302^457754-113711137798Enzo Doria09/2014
533111^132315-360137792Enzo Doria09/2012
5332(2^659318)%L(659318)137787Henri Lifchitz05/2025
533332072^19689+19689^32072137725Hans Havermann06/2021
533426529^31132-31132^26529137720Frank Doornink03/2024
533544592^1225+1225^44592137707Hans Havermann05/2021
533628986^30857-30857^28986137690Frank Doornink05/2024
53372^457347-37137676Lelio R Paula09/2017
53382^457322-2786393137668Enzo Doria10/2015
5339gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
5340Phi(699340M,10)137664Anonymous03/2025
534134015^11134+11134^34015137647Hans Havermann06/2021
53422^457240-59939137643Enzo Doria10/2015
5343(856*10^137633-1)/9137635Robert Price03/2020
534436232^6289+6289^36232137631Hans Havermann05/2021
53452^457120-21575137607Enzo Doria07/2013
5346(11*2^456978+1)/15137564Lelio R Paula07/2015
534730963^27722+27722^30963137564Hans Havermann04/2021
534833722^12003+12003^33722137562Hans Havermann06/2021
5349(7*25^98399+10613)/12137556Curtis Bright05/2015
535041901^1918+1918^41901137555Hans Havermann06/2021
5351(7*10^137551-1)/3137552Robert Price08/2022
535232930^15021+15021^32930137539Hans Havermann05/2021
535331178^25785+25785^31178137538Hans Havermann05/2021
5354419^52446+52446^419137525Norbert Schneider11/2020
53552^456813+214175137515Enzo Doria10/2023
53562^456796-113513137510Enzo Doria08/2014
535731788^21137+21137^31788137485Hans Havermann04/2021
5358(7*2^456655+1)/39137467Lelio R Paula07/2015
535927151^31004-31004^27151137466Frank Doornink01/2024
53602^456503-114361137422Enzo Doria01/2015
5361(11*2^456387+1)/19137386Lelio R Paula07/2015
536230618^30618-5^5137352Serge Batalov04/2024
536336248^6147+6147^36248137332Hans Havermann05/2021
536431986^19651+19651^31986137329Hans Havermann05/2021
53652^456167+22313137320Enzo Doria09/2023
536631817^20656+20656^31817137292Hans Havermann05/2021
5367(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
5368(71*10^137250+1)/9137251Serge Batalov05/2010
53692^455922+76249137247Enzo Doria05/2016
537031310^24171+24171^31310137241Hans Havermann05/2021
537114^119741-119741^14137239Serge Batalov04/2016
537235014^8297+8297^35014137218Hans Havermann05/2021
5373(19*2^455760+1)/3455137196Lelio R Paula07/2015
5375124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
5374124^65536+57^65536137195Serge Batalov03/2018
53762^455689+72677137177Enzo Doria04/2016
5377(17948!)^2+Prime(17948)137118Robert Price08/2014
537831287^24128+24128^31287137116Hans Havermann05/2021
5379(37^87421-1)/36137093Robert Price03/2012
538036233^6070+6070^36233137077Hans Havermann05/2021
5381(8*10^137073-17)/9137073Serge Batalov11/2022
538238418^3697+3697^38418137070Hans Havermann04/2021
53832^455323-57137066Lelio R Paula09/2017
5384(56*10^137019+583)/9137020Robert Price08/2021
538525017^31148-31148^25017136997Frank Doornink12/2023
5386(73*17^111333-9)/16136991Curtis Bright05/2015
53872^455025-112723136977Enzo Doria06/2014
538833876^11039+11039^33876136959Hans Havermann05/2021
5389(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
5390(251^57059-1)/250136921Anonymous04/2024
539135142^7873+7873^35142136919Hans Havermann05/2021
5392(4997*31^91805-1)/2136918Eric Chen05/2024
539366*10^136894+7136896Robert Price07/2020
539428766^30697-30697^28766136875Frank Doornink05/2024
53952^454675-1777136871Yves Minet10/2011
539631676^20931+20931^31676136866Hans Havermann05/2021
53973*10^136829+29136830Robert Price05/2018
53984*10^136813-57136814Robert Price10/2018
5399(6092*28^94536-143)/9136812Curtis Bright05/2015
5400fibonacci(654572)-2136798Jon Grantham08/2023
540137359^4588+4588^37359136795Hans Havermann05/2021
54022^454348-53136773Lelio R Paula09/2017
540331^91680-2136729Lelio R Paula05/2017
54042^454199-113697136728Enzo Doria09/2014
540530785^27622+27622^30785136725Hans Havermann05/2021
540632973^14014+14014^32973136725Hans Havermann05/2021
54087*10^136716+69136717Robert Price07/2019
540736002^6273+6273^36002136717Hans Havermann05/2021
54096*10^136692+53136693Robert Price05/2020
5410Phi(568997,2)136692Henri Lifchitz02/2026
5411(13*10^136687+47)/3136688Robert Price10/2018
5412F(2*453976)%(2^453976)136661Henri Lifchitz06/2025
54132^453935-2791357136649Enzo Doria01/2016
54142^453906-69131136640Enzo Doria11/2015
541533232^12915+12915^33232136620Hans Havermann05/2021
54162^453791+1873913136605Enzo Doria06/2016
541734166^9951+9951^34166136592Hans Havermann05/2021
5418(21*2^453740-1)/2735136588Lelio R Paula07/2015
541931102^24635+24635^31102136587Hans Havermann05/2021
5420580^49413+49413^580136550Norbert Schneider02/2019
54212^453503-2788297136519Enzo Doria11/2015
542234989^7958+7958^34989136486Hans Havermann12/2020
5423(2*10^136484+187)/9136484Robert Price06/2022
5424(5^653025)%L(653025)136475Henri Lifchitz06/2025
542531007^25158+25158^31007136452Hans Havermann11/2020
54262^453267-113827136447Enzo Doria09/2014
542732234^17085+17085^32234136435Hans Havermann12/2020
54282^453102+1877629136398Enzo Doria08/2016
542931016^24981+24981^31016136397Hans Havermann12/2020
5430(62*10^136384-791)/9136385Robert Price06/2019
543134171^9798+9798^34171136382Hans Havermann12/2020
5432(17*10^136354-113)/3136355Robert Price06/2021
543332756^14541+14541^32756136350Hans Havermann11/2020
543432205^17086+17086^32205136313Hans Havermann12/2020
5435(25*10^136303+161)/3136304Robert Price09/2019
543635337^7196+7196^35337136299Hans Havermann12/2020
5437(182*10^136291+1)/3136293Robert Price02/2020
5438(88*10^136234+83)/9136235Robert Price03/2022
543923*10^136225-7136227Robert Price02/2020
5440L(651821)136223Henri Lifchitz09/2008
544125519^30908-30908^25519136208Frank Doornink02/2024
54422^452460+77701136205Enzo Doria05/2016
54432^452440-114755136199Enzo Doria04/2015
544428625^30558-30558^28625136190Frank Doornink05/2024
544532286^16489+16489^32286136157Hans Havermann11/2020
5446(47*10^136141+493)/9136142Robert Price03/2019
544727140^30699-30699^27140136108Frank Doornink01/2024
5448Phi(199391,-5)136098Henri Lifchitz12/2025
544940392^2339+2339^40392136082Hans Havermann12/2020
54502*10^136057-43136058Robert Price04/2018
54512^451971+21563136057Enzo Doria08/2023
5452(2^451956-5)/181136051Lelio R Paula07/2015
54532^451947-22165136050Enzo Doria07/2013
5454(3^451810)%(2^451810)136008Henri Lifchitz06/2025
54552^451787-21805136002Enzo Doria07/2013
54562^451734-112817135986Enzo Doria06/2014
5457(11*2^451714+1)/75135979Lelio R Paula07/2015
54582^451705-21879135977Enzo Doria07/2013
5459(4666^37249-1)/(4666^193-1)135957Ryan Propper11/2023
54602^451560-112349135934Enzo Doria06/2014
54612^451530+45135925Lelio R Paula08/2017
546226594^30719-30719^26594135925Frank Doornink03/2024
546331622^19875+19875^31622135922Hans Havermann11/2020
5464(25*10^135906-73)/3135907Robert Price09/2019
54652^451450-21743135900Enzo Doria07/2013
5466(7*10^135879+11)/9135879Tyler Busby01/2023
546735218^7199+7199^35218135846Hans Havermann11/2020
546835661^6446+6446^35661135844Hans Havermann11/2020
5469(7*33^89453-4743239)/32135835Eric Chen12/2023
547031869^18248+18248^31869135801Hans Havermann12/2020
5471(77*10^135789+157)/9135790Robert Price05/2022
5472Phi(286219,-3)135763Henri Lifchitz12/2025
54732^450958+60529135752Enzo Doria08/2023
54742^450805+65135706Lelio R Paula08/2017
547510^135669+21135670Boyan Hu12/2024
547630761^25728+25728^30761135669Hans Havermann12/2020
54772*10^135663+69135664Robert Price06/2020
547833962^9867+9867^33962135651Hans Havermann11/2020
547934474^8605+8605^34474135647Hans Havermann11/2020
548034501^8508+8508^34501135583Hans Havermann12/2020
548135487^6614+6614^35487135577Hans Havermann12/2020
5482(13725^32768+1)/131074135573Lelio R Paula03/2012
5483(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
5485(5^193939+1)/6135557Paul Bourdelais12/2008
5484Phi(193939,-5)135557Henri Lifchitz12/2025
5486(76*10^135553-49)/9135554Robert Price07/2022
54875*3^284077+2^284077135540Jon Grantham08/2023
5488(844*10^135527-7)/9135529Robert Price05/2021
548927191^30560-30560^27191135517Frank Doornink01/2024
549040387^2260+2260^40387135463Hans Havermann12/2020
54912^449944-113247135447Enzo Doria07/2014
5492Phi(70509,-1105)135418Henri Lifchitz12/2025
54932^449770-113247135395Enzo Doria07/2014
54942^449637-21471135355Enzo Doria07/2013
549526061^30650-30650^26061135351Frank Doornink03/2024
54962^449571-75135335Lelio R Paula08/2017
5497(14*10^135301-53)/3135302Robert Price12/2018
5498(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
5499(13*10^135279+437)/9135280Robert Price04/2018
55002^449330-35135262Lelio R Paula08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 14 2026 17:13 (Time in France)

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