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 ?
375128302^23269+23269^28302123589Hans Havermann03/2021
37522^410540-115079123585Enzo Doria06/2015
3753(7*10^123563+107)/3123564Robert Price02/2018
37549*10^123549+89123550Robert Price11/2019
3755(197*10^123545+7)/3123547Robert Price12/2020
3756(3*2^410392-1)/9229123537Lelio R Paula05/2014
3757(29*10^123510+277)/9123511Robert Price11/2021
375828118^24687+24687^28118123508Hans Havermann03/2021
375939994^1225+1225^39994123507Hans Havermann03/2021
37602^410206-113081123485Enzo Doria07/2014
3761(25*2^410192+1)/10397123478Lelio R Paula04/2014
376228974^18215+18215^28974123442Hans Havermann03/2021
376328901^18618+18618^28901123406Hans Havermann03/2021
37642^409909-189123395Enzo Doria05/2014
37652^409896-109043123391Enzo Doria04/2014
37662^409890+75409123390Enzo Doria04/2016
376781254^33+33^81254123386Hans Havermann03/2021
376833463^4854+4854^33463123348Hans Havermann03/2021
376934061^4182+4182^34061123348Hans Havermann03/2021
3770133^58076-2123345Lelio R Paula10/2017
3771F(590041)123311Henri Lifchitz01/2005
3772(82*10^123299+377)/9123300Robert Price03/2022
37732^409566-113501123292Enzo Doria08/2014
37742^409533+77747123282Enzo Doria05/2016
37752^409436-112799123253Enzo Doria06/2014
377628212^23321+23321^28212123223Hans Havermann03/2021
37772^409225+1873787123189Enzo Doria06/2016
37782^409174+73009123174Enzo Doria04/2016
37792^409058-112685123139Enzo Doria06/2014
3780(13*10^123137-61)/3123138Robert Price11/2018
37814*10^123113+21123114Robert Price12/2018
37822^408778+77689123055Enzo Doria05/2016
37832^408690-75123028Lelio R Paula11/2013
378428327^22032+22032^28327123026Hans Havermann03/2021
3785(29*10^122996+673)/9122997Robert Price12/2018
3786(65*10^122994-101)/9122995Robert Price01/2022
37872^408574-2787341122994Enzo Doria03/2016
37883*10^122977+37122978Robert Price08/2018
3789(7*10^122976-67)/3122977Robert Price10/2021
3790Phi(157825,10)122961Maksym Voznyy06/2015
3791(68*10^122933-419)/9122934Robert Price07/2019
379229712^13721+13721^29712122931Hans Havermann03/2021
3793(13*2^408283+1)/1665122904Lelio R Paula05/2014
3794(266*10^122872-17)/3122874Robert Price07/2020
3795(16*10^122871+77)/3122872Robert Price03/2019
379630395^11022+11022^30395122865Hans Havermann03/2021
37974*10^122859-69122860Robert Price01/2022
3798(10^122857+167)/3122857Robert Price05/2021
379933331^4852+4852^33331122856Hans Havermann03/2021
3800(11*2^408100-1)/35122850Lelio R Paula04/2014
3801(19*10^122836-43)/3122837Robert Price05/2019
380228420^20969+20969^28420122820Hans Havermann03/2021
3803(16*10^122818+179)/3122819Robert Price11/2021
380429865^12934+12934^29865122797Hans Havermann03/2021
3805(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
3806(32*10^122733-77)/9122734Robert Price06/2018
3807(21*2^407604-1)/215122701Lelio R Paula04/2014
3809(22*10^122681+161)/3122682Robert Price05/2019
380829513^14350+14350^29513122682Hans Havermann03/2021
3810(21*2^407433-1)/13122650Lelio R Paula04/2014
3811(26*10^122625-131)/3122626Robert Price10/2019
381227925^24562+24562^27925122599Hans Havermann03/2021
3813(73*10^122592-1)/9122593Robert Price01/2015
3814(5*10^122592+91)/3122593Robert Price04/2018
381536751^2166+2166^36751122589Hans Havermann03/2021
3816(85*10^122585-1)/3122587Robert Price02/2020
381729368^14931+14931^29368122585Hans Havermann03/2021
38182^407179-112075122574Enzo Doria06/2014
3819(21*2^407131+1)/207517523122552Lelio R Paula04/2014
3820(66^67349+1)/67122543Paul Bourdelais09/2017
3821(646*10^122533+11)/9122535Robert Price10/2021
38222^407008-1867919122522Enzo Doria04/2016
382311^117642-300122512Enzo Doria10/2012
3824(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
38252^406949+72197122504Enzo Doria04/2016
3826(19*10^122501+149)/3122502Robert Price05/2019
382728632^18977+18977^28632122495Hans Havermann03/2021
382831815^7076+7076^31815122481Hans Havermann03/2021
38292^406826-65122467Lelio R Paula11/2013
38302^406821-2797363122466Enzo Doria04/2016
3831(7*10^122456-331)/9122456Robert Price03/2022
38322^406758-17122447Lelio R Paula11/2013
383329941^12282+12282^29941122437Hans Havermann03/2021
3834(30^82883-1)/29122427Robert Price12/2011
383527496^27577+27577^27496122422Norbert Schneider12/2020
383628732^18215+18215^28732122411Hans Havermann03/2021
3837(2^406583-1)/813167122388Jens K. Andersen02/2009
38384*10^122377+19122378Robert Price10/2018
383928227^21634+21634^28227122368Hans Havermann03/2021
3840Phi(246362,10)122365Makoto Kamada09/2019
38413*10^122345-97122346Robert Price07/2018
384297^61575-2122336Lelio R Paula12/2014
38432*10^122319+47122320Robert Price12/2021
3844208^52765+52765^208122313Norbert Schneider11/2020
38452^406298+2799109122308Enzo Doria04/2016
38467*10^122294+57122295Robert Price06/2019
3847(27*2^406241-1)/10277122289Lelio R Paula04/2014
38482^406229-1849993122288Enzo Doria08/2015
38493*10^122274+7122275Robert Price07/2015
38502^406117+1876577122254Enzo Doria07/2016
385129308^14835+14835^29308122253Hans Havermann03/2021
385228119^22268+22268^28119122253Hans Havermann03/2021
385332167^6312+6312^32167122240Hans Havermann03/2021
38543^256199-2^256199122238Mike Oakes06/2005
385527678^26053+26053^27678122223Hans Havermann03/2021
38562^405992-78557122216Jorge Menendez03/2018
3857(8*10^122203+43)/3122204Robert Price06/2018
3858(58*10^122170+329)/9122171Robert Price05/2019
38592^405774+179149122151Enzo Doria06/2016
3860(218*10^122109+7)/9122111Robert Price06/2022
386129189^15246+15246^29189122103Hans Havermann03/2021
386334*10^122082-9122084Robert Price06/2020
386233442^4473+4473^33442122084Hans Havermann03/2021
38645*10^122082+41122083Robert Price03/2019
386531849^6808+6808^31849122078Hans Havermann03/2021
38672^405514-3311122072Yves Minet12/2014
38682^405514-115511122072Enzo Doria07/2015
386623*10^122070-7122072Robert Price02/2020
38692^405422-113261122045Enzo Doria07/2014
38702^405173+71237121970Enzo Doria04/2016
3871(154*10^121953+17)/9121955Robert Price06/2022
3872(34*10^121924+191)/9121925Robert Price08/2021
3873(2^405016+1)/257121920Lelio R Paula04/2014
387428557^18590+18590^28557121918Hans Havermann03/2021
387528641^18002+18002^28641121877Hans Havermann03/2021
38762^404858+71329121875Enzo Doria04/2016
38772^404813-114703121861Enzo Doria04/2015
38782^404764+77791121847Enzo Doria05/2016
387928830^16841+16841^28830121847Hans Havermann03/2021
3880(4*10^121825+89)/3121826Robert Price08/2021
3881317^48694+48694^317121787Norbert Schneider08/2015
38822^404536-115259121778Enzo Doria06/2015
38832^404501-631121767Yves Minet07/2012
38845*10^121764-69121765Robert Price02/2021
388528236^20485+20485^28236121738Hans Havermann02/2021
3886(382*10^121694-31)/9121696Robert Price06/2022
388763^67620+2121672Lelio R Paula08/2015
3888(16*10^121633+167)/3121634Robert Price06/2019
388929955^11494+11494^29955121632Hans Havermann02/2021
3890(17*10^121621+1)/9121622Serge Batalov05/2010
389131088^8163+8163^31088121612Hans Havermann02/2021
3892(15*2^403912+1)/271121589Lelio R Paula05/2014
3893(10^121543-79)/3121543Robert Price01/2018
38942^403676+76831121519Enzo Doria05/2016
3895(7*10^121487+143)/3121488Robert Price03/2018
389627965^22086+22086^27965121484Hans Havermann02/2021
3897(893*10^121470+7)/9121472Robert Price06/2021
3898(206*10^121462-11)/3121464Robert Price02/2022
3899(77*10^121455+67)/9121456Robert Price12/2021
39002^403363-113635121425Enzo Doria08/2014
3901(17*10^121418-113)/3121419Robert Price06/2021
39022^403336-1861469121417Enzo Doria03/2016
390327929^22186+22186^27929121382Hans Havermann02/2021
3904p(24442)#/2-64121381Robert Price04/2017
390511^116555-720121380Enzo Doria11/2012
39062^403100-461267121346Enzo Doria07/2015
39072^403093-112213121344Enzo Doria06/2014
390829404^13385+13385^29404121340Hans Havermann02/2021
390928106^20745+20745^28106121332Hans Havermann02/2021
3910(316^48539+1)/317121330Eric Chen10/2017
3911(23*10^121320-71)/3121321Robert Price07/2020
39122^403004+1866361121317Enzo Doria03/2016
39132^402953+89121301Lelio R Paula10/2013
39142^402944-2788319121299Enzo Doria03/2016
3915(44*10^121297-719)/9121298Robert Price12/2018
3916(27*2^402865+1)/5121276Lelio R Paula04/2014
39172^402828-113183121264Enzo Doria07/2014
3918(17*10^121242+1)/9121243Serge Batalov05/2010
3919(15*2^402757+1)/101121242Lelio R Paula05/2014
39212^402715+1874223121230Enzo Doria06/2016
3920(35*10^121229-593)/9121230Robert Price07/2018
3922(91^61879+1)/92121222Paul Bourdelais09/2017
392328719^16568+16568^28719121174Hans Havermann02/2021
39247*10^121144+9121145Robert Price09/2015
392527490^25467+25467^27490121121Hans Havermann02/2021
392634575^3182+3182^34575121106Hans Havermann02/2021
39275*10^121100-37121101Robert Price11/2021
392829954^10935+10935^29954120979Hans Havermann02/2021
392933585^3992+3992^33585120946Hans Havermann02/2021
393040296^1003+1003^40296120941Hans Havermann02/2021
39312^401725-113251120932Enzo Doria07/2014
3932(15*2^401677-1)/19120917Lelio R Paula05/2014
39332^401652+73711120910Enzo Doria04/2016
3934(2^401632+3)/79120902Lelio R Paula04/2014
393540450^973+973^40450120870Hans Havermann01/2021
393610^120841+88417120842Patrick De Geest04/2020
393710^120841-123456789120841Robert Price02/2020
393810^120841-176853120841Patrick De Geest04/2020
39392^401406-2791331120836Enzo Doria03/2016
3940(28^83497+1)/29120832Robert Price07/2013
3941(22*10^120828+161)/3120829Robert Price05/2019
39422^401369+1867367120825Enzo Doria03/2016
3943(5*10^120821+43)/3120822Robert Price12/2021
3944(10^120782+29)/3120782Serge Batalov12/2014
39452^401215-1657120778Yves Minet07/2014
39462^401159+53120761Lelio R Paula10/2013
394727782^22179+22179^27782120739Hans Havermann01/2021
394832974^4585+4585^32974120730Hans Havermann02/2021
39492^401031-113047120723Enzo Doria07/2014
395030598^8813+8813^30598120713Hans Havermann02/2021
3951(71*10^120703-287)/9120704Robert Price09/2019
3952(29*2^400909-1)/303120685Lelio R Paula04/2014
395334793^2940+2940^34793120675Hans Havermann02/2021
3954(2^400846+538)/2120667Stefano Morozzi09/2020
3955(166*10^120654+11)/3120656Robert Price03/2021
395634066^3481+3481^34066120652Hans Havermann02/2021
39578*10^120637-27120638Robert Price10/2021
3958(2^400709+3546)/2120626Stefano Morozzi09/2020
3959(2^400700+3126)/2120623Stefano Morozzi09/2020
3960(2^400693+2634)/2120621Stefano Morozzi09/2020
39619*10^120617-61120618Robert Price06/2021
3962(29*10^120590-71)/3120591Robert Price07/2021
39632^400571-15120584Lelio R Paula10/2013
3964(10^120574+359)/9120574Serge Batalov12/2014
396527431^24810+24810^27431120550Hans Havermann02/2021
39662^400424-216413120540Enzo Doria04/2013
396729090^13911+13911^29090120531Hans Havermann02/2021
3968(2^400346+1722)/2120516Stefano Morozzi09/2020
396927899^20868+20868^27899120510Hans Havermann02/2021
397033740^3729+3729^33740120506Hans Havermann02/2021
3971(17*2^400200-1)/587120471Lelio R Paula05/2014
39722^400166+1874899120462Enzo Doria06/2016
3973(2^400165+1602)/2120462Stefano Morozzi09/2020
397437078^1771+1771^37078120438Hans Havermann02/2021
3975(2^400084+1638)/2120437Stefano Morozzi09/2020
3976(3*2^400045-1)/865120424Lelio R Paula04/2014
3977(2^399974+2790)/2120404Stefano Morozzi02/2021
39782^399966+73759120402Enzo Doria04/2016
3979(2^399961+2306)/2120400Stefano Morozzi02/2021
3980(112*10^120395-1)/3120397Serge Batalov12/2014
39812^399918-95120388Lelio R Paula04/2013
3982(28*10^120381-67)/3120382Robert Price10/2020
3983(49*10^120380-139)/9120381Robert Price03/2019
3984(2^399874+2194)/2120374Stefano Morozzi09/2020
39852^399792-1849259120350Enzo Doria08/2015
39869*10^120342-7120343Robert Price09/2015
3987(2^399751+786)/2120337Stefano Morozzi09/2020
3988(331*10^120332-7)/9120334Robert Price04/2022
3989(13*10^120306-37)/3120307Robert Price01/2019
3990(23*10^120299+37)/3120300Robert Price02/2022
3991(2^399604+3070)/2120293Stefano Morozzi09/2020
3992(2^399549+1062)/2120276Stefano Morozzi09/2020
39932^399526-1861721120270Enzo Doria11/2015
3994(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
399532016^5687+5687^32016120217Hans Havermann01/2021
3996(205*10^120212-1)/3120214Robert Price11/2021
39972^399322-2798111120208Enzo Doria04/2016
399830438^8867+8867^30438120163Hans Havermann02/2021
400072^64693-71^64693120157Robert Price03/2014
3999(17*10^120156-161)/9120157Robert Price02/2021


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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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