PRP Records

Probable Primes Top 10000

(295158 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 ?
500134061^4182+4182^34061123348Hans Havermann03/2021
5002133^58076-2123345Lelio R Paula10/2017
5003F(590041)123311Henri Lifchitz01/2005
5004(82*10^123299+377)/9123300Robert Price03/2022
50052^409566-113501123292Enzo Doria08/2014
50062^409533+77747123282Enzo Doria05/2016
50072^409436-112799123253Enzo Doria06/2014
500828212^23321+23321^28212123223Hans Havermann03/2021
50092^409225+1873787123189Enzo Doria06/2016
50102^409174+73009123174Enzo Doria04/2016
50112^409058-112685123139Enzo Doria06/2014
5012(13*10^123137-61)/3123138Robert Price11/2018
50134*10^123113+21123114Robert Price12/2018
50142^408778+77689123055Enzo Doria05/2016
50152^408690-75123028Lelio R Paula11/2013
501628327^22032+22032^28327123026Hans Havermann03/2021
5017(29*10^122996+673)/9122997Robert Price12/2018
5018(65*10^122994-101)/9122995Robert Price01/2022
50192^408574-2787341122994Enzo Doria03/2016
50203*10^122977+37122978Robert Price08/2018
5021(7*10^122976-67)/3122977Robert Price10/2021
5022Phi(157825,10)122961Maksym Voznyy06/2015
502325493^27902-27902^25493122948Frank Doornink02/2024
502426749^27768-27768^26749122938Frank Doornink03/2024
5025(68*10^122933-419)/9122934Robert Price07/2019
502629712^13721+13721^29712122931Hans Havermann03/2021
5027(13*2^408283+1)/1665122904Lelio R Paula05/2014
5028(266*10^122872-17)/3122874Robert Price07/2020
5029(16*10^122871+77)/3122872Robert Price03/2019
503030395^11022+11022^30395122865Hans Havermann03/2021
50314*10^122859-69122860Robert Price01/2022
5032(10^122857+167)/3122857Robert Price05/2021
503333331^4852+4852^33331122856Hans Havermann03/2021
5034(11*2^408100-1)/35122850Lelio R Paula04/2014
5035(19*10^122836-43)/3122837Robert Price05/2019
503628420^20969+20969^28420122820Hans Havermann03/2021
5037(16*10^122818+179)/3122819Robert Price11/2021
503829865^12934+12934^29865122797Hans Havermann03/2021
5039(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
5040(32*10^122733-77)/9122734Robert Price06/2018
5041(21*2^407604-1)/215122701Lelio R Paula04/2014
5043(22*10^122681+161)/3122682Robert Price05/2019
504229513^14350+14350^29513122682Hans Havermann03/2021
5044(21*2^407433-1)/13122650Lelio R Paula04/2014
5045(26*10^122625-131)/3122626Robert Price10/2019
5046(643*33^80753+3709)/32122626Eric Chen12/2023
504727925^24562+24562^27925122599Hans Havermann03/2021
5048(73*10^122592-1)/9122593Robert Price01/2015
5049(5*10^122592+91)/3122593Robert Price04/2018
505036751^2166+2166^36751122589Hans Havermann03/2021
5051(85*10^122585-1)/3122587Robert Price02/2020
505229368^14931+14931^29368122585Hans Havermann03/2021
50532^407179-112075122574Enzo Doria06/2014
5054(21*2^407131+1)/207517523122552Lelio R Paula04/2014
5055(66^67349+1)/67122543Paul Bourdelais09/2017
5056(646*10^122533+11)/9122535Robert Price10/2021
50572^407008-1867919122522Enzo Doria04/2016
505811^117642-300122512Enzo Doria10/2012
5059(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
50602^406949+72197122504Enzo Doria04/2016
5061(19*10^122501+149)/3122502Robert Price05/2019
506228632^18977+18977^28632122495Hans Havermann03/2021
506331815^7076+7076^31815122481Hans Havermann03/2021
50642^406826-65122467Lelio R Paula11/2013
50652^406821-2797363122466Enzo Doria04/2016
5066(7*10^122456-331)/9122456Robert Price03/2022
50672^406758-17122447Lelio R Paula11/2013
506829941^12282+12282^29941122437Hans Havermann03/2021
5069(30^82883-1)/29122427Robert Price12/2011
507027496^27577+27577^27496122422Norbert Schneider12/2020
507128732^18215+18215^28732122411Hans Havermann03/2021
5072(2^406583-1)/813167122388Jens K. Andersen02/2009
50734*10^122377+19122378Robert Price10/2018
507428227^21634+21634^28227122368Hans Havermann03/2021
5075Phi(246362,10)122365Makoto Kamada09/2019
50763*10^122345-97122346Robert Price07/2018
507797^61575-2122336Lelio R Paula12/2014
50782*10^122319+47122320Robert Price12/2021
5079208^52765+52765^208122313Norbert Schneider11/2020
50812^406298+2799109122308Enzo Doria04/2016
50802^406296+213691122308Enzo Doria09/2023
50827*10^122294+57122295Robert Price06/2019
5083(27*2^406241-1)/10277122289Lelio R Paula04/2014
50842^406229-1849993122288Enzo Doria08/2015
50853*10^122274+7122275Robert Price07/2015
50862^406117+1876577122254Enzo Doria07/2016
508729308^14835+14835^29308122253Hans Havermann03/2021
508828119^22268+22268^28119122253Hans Havermann03/2021
508932167^6312+6312^32167122240Hans Havermann03/2021
50903^256199-2^256199122238Mike Oakes06/2005
509127678^26053+26053^27678122223Hans Havermann03/2021
50922^405992-78557122216Jorge Menendez03/2018
5093(8*10^122203+43)/3122204Robert Price06/2018
5094(58*10^122170+329)/9122171Robert Price05/2019
50952^405774+179149122151Enzo Doria06/2016
50962^405693+20417122126Enzo Doria07/2023
5097(218*10^122109+7)/9122111Robert Price06/2022
509829189^15246+15246^29189122103Hans Havermann03/2021
510034*10^122082-9122084Robert Price06/2020
509933442^4473+4473^33442122084Hans Havermann03/2021
51015*10^122082+41122083Robert Price03/2019
510231849^6808+6808^31849122078Hans Havermann03/2021
51042^405514-3311122072Yves Minet12/2014
51052^405514-115511122072Enzo Doria07/2015
510323*10^122070-7122072Robert Price02/2020
51062^405422-113261122045Enzo Doria07/2014
51072^405173+71237121970Enzo Doria04/2016
5108fibonacci(583574)+2121960Jon Grantham08/2023
5109(154*10^121953+17)/9121955Robert Price06/2022
5110(34*10^121924+191)/9121925Robert Price08/2021
5111(2^405016+1)/257121920Lelio R Paula04/2014
511228557^18590+18590^28557121918Hans Havermann03/2021
511328641^18002+18002^28641121877Hans Havermann03/2021
51142^404858+71329121875Enzo Doria04/2016
51152^404813-114703121861Enzo Doria04/2015
51162^404764+77791121847Enzo Doria05/2016
511728830^16841+16841^28830121847Hans Havermann03/2021
5118(4*10^121825+89)/3121826Robert Price08/2021
5119317^48694+48694^317121787Norbert Schneider08/2015
51202^404536-115259121778Enzo Doria06/2015
51212^404501-631121767Yves Minet07/2012
51225*10^121764-69121765Robert Price02/2021
512328236^20485+20485^28236121738Hans Havermann02/2021
5124(382*10^121694-31)/9121696Robert Price06/2022
512563^67620+2121672Lelio R Paula08/2015
5126(25*34^79445-28062367)/33121669Eric Chen08/2023
5127(13*33^80110-121453)/32121648Eric Chen12/2023
5128(16*10^121633+167)/3121634Robert Price06/2019
512929955^11494+11494^29955121632Hans Havermann02/2021
5130(17*10^121621+1)/9121622Serge Batalov05/2010
513131088^8163+8163^31088121612Hans Havermann02/2021
5132(15*2^403912+1)/271121589Lelio R Paula05/2014
5133(211^52301-1)/210121560Anonymous04/2024
5134(10^121543-79)/3121543Robert Price01/2018
51352^403676+76831121519Enzo Doria05/2016
5136(7*10^121487+143)/3121488Robert Price03/2018
513727965^22086+22086^27965121484Hans Havermann02/2021
5138(893*10^121470+7)/9121472Robert Price06/2021
5139(206*10^121462-11)/3121464Robert Price02/2022
514026282^27481-27481^26282121457Frank Doornink03/2024
5141(77*10^121455+67)/9121456Robert Price12/2021
51422^403363-113635121425Enzo Doria08/2014
514325531^27552-27552^25531121424Frank Doornink02/2024
5144(17*10^121418-113)/3121419Robert Price06/2021
51452^403336-1861469121417Enzo Doria03/2016
514627929^22186+22186^27929121382Hans Havermann02/2021
5147p(24442)#/2-64121381Robert Price04/2017
514811^116555-720121380Enzo Doria11/2012
51492^403100-461267121346Enzo Doria07/2015
51502^403093-112213121344Enzo Doria06/2014
515129404^13385+13385^29404121340Hans Havermann02/2021
515228106^20745+20745^28106121332Hans Havermann02/2021
5153(316^48539+1)/317121330Eric Chen10/2017
5154(23*10^121320-71)/3121321Robert Price07/2020
51552^403004+1866361121317Enzo Doria03/2016
51562^402953+89121301Lelio R Paula10/2013
51572^402944-2788319121299Enzo Doria03/2016
5158(44*10^121297-719)/9121298Robert Price12/2018
5159(27*2^402865+1)/5121276Lelio R Paula04/2014
51602^402828-113183121264Enzo Doria07/2014
5161(17*10^121242+1)/9121243Serge Batalov05/2010
5162(15*2^402757+1)/101121242Lelio R Paula05/2014
51642^402715+1874223121230Enzo Doria06/2016
5163(35*10^121229-593)/9121230Robert Price07/2018
5165(91^61879+1)/92121222Paul Bourdelais09/2017
516628719^16568+16568^28719121174Hans Havermann02/2021
51677*10^121144+9121145Robert Price09/2015
516827490^25467+25467^27490121121Hans Havermann02/2021
516934575^3182+3182^34575121106Hans Havermann02/2021
51705*10^121100-37121101Robert Price11/2021
517125592^27467-27467^25592121078Frank Doornink02/2024
517229954^10935+10935^29954120979Hans Havermann02/2021
517333585^3992+3992^33585120946Hans Havermann02/2021
517440296^1003+1003^40296120941Hans Havermann02/2021
51752^401725-113251120932Enzo Doria07/2014
5176(15*2^401677-1)/19120917Lelio R Paula05/2014
51772^401652+73711120910Enzo Doria04/2016
5178(2^401632+3)/79120902Lelio R Paula04/2014
517940450^973+973^40450120870Hans Havermann01/2021
5180(8*10^120851-11)/3120852Robert Price07/2023
518110^120841+88417120842Patrick De Geest04/2020
518210^120841-123456789120841Robert Price02/2020
518310^120841-176853120841Patrick De Geest04/2020
51842^401406-2791331120836Enzo Doria03/2016
5185(28^83497+1)/29120832Robert Price07/2013
5186(22*10^120828+161)/3120829Robert Price05/2019
51872^401369+1867367120825Enzo Doria03/2016
5188(5*10^120821+43)/3120822Robert Price12/2021
518926990^27263-27263^26990120808Frank Doornink03/2024
5190(10^120782+29)/3120782Serge Batalov12/2014
51912^401215-1657120778Yves Minet07/2014
51922^401159+53120761Lelio R Paula10/2013
519327782^22179+22179^27782120739Hans Havermann01/2021
519432974^4585+4585^32974120730Hans Havermann02/2021
51952^401031-113047120723Enzo Doria07/2014
519630598^8813+8813^30598120713Hans Havermann02/2021
5197(71*10^120703-287)/9120704Robert Price09/2019
519825671^27370-27370^25671120687Frank Doornink02/2024
5199(29*2^400909-1)/303120685Lelio R Paula04/2014
520034793^2940+2940^34793120675Hans Havermann02/2021
520126028^27329-27329^26028120670Frank Doornink03/2024
5202(2^400846+538)/2120667Stefano Morozzi09/2020
5203(166*10^120654+11)/3120656Robert Price03/2021
520434066^3481+3481^34066120652Hans Havermann02/2021
52058*10^120637-27120638Robert Price10/2021
5206(2^400709+3546)/2120626Stefano Morozzi09/2020
5207(2^400700+3126)/2120623Stefano Morozzi09/2020
5208(2^400693+2634)/2120621Stefano Morozzi09/2020
52099*10^120617-61120618Robert Price06/2021
5210(29*10^120590-71)/3120591Robert Price07/2021
52112^400571-15120584Lelio R Paula10/2013
5212(10^120574+359)/9120574Serge Batalov12/2014
5213(8*10^120552-17)/9120552Serge Batalov11/2022
521427431^24810+24810^27431120550Hans Havermann02/2021
52152^400424-216413120540Enzo Doria04/2013
521629090^13911+13911^29090120531Hans Havermann02/2021
5217(2^400346+1722)/2120516Stefano Morozzi09/2020
521827899^20868+20868^27899120510Hans Havermann02/2021
521933740^3729+3729^33740120506Hans Havermann02/2021
5220(17*2^400200-1)/587120471Lelio R Paula05/2014
52212^400166+1874899120462Enzo Doria06/2016
5222(2^400165+1602)/2120462Stefano Morozzi09/2020
522337078^1771+1771^37078120438Hans Havermann02/2021
5224(2^400084+1638)/2120437Stefano Morozzi09/2020
5225(3*2^400045-1)/865120424Lelio R Paula04/2014
52262^399999+54173120412Norman Luhn08/2023
5227(2^399974+2790)/2120404Stefano Morozzi02/2021
52282^399966+73759120402Enzo Doria04/2016
5229(2^399961+2306)/2120400Stefano Morozzi02/2021
5230(112*10^120395-1)/3120397Serge Batalov12/2014
52322^399918-95120388Lelio R Paula04/2013
52312^399918+214009120388Enzo Doria10/2023
5233(28*10^120381-67)/3120382Robert Price10/2020
5234(49*10^120380-139)/9120381Robert Price03/2019
5235(2^399874+2194)/2120374Stefano Morozzi09/2020
52362^399792-1849259120350Enzo Doria08/2015
52379*10^120342-7120343Robert Price09/2015
5238(2^399751+786)/2120337Stefano Morozzi09/2020
5239(331*10^120332-7)/9120334Robert Price04/2022
5240(13*10^120306-37)/3120307Robert Price01/2019
5241(23*10^120299+37)/3120300Robert Price02/2022
524225935^27254-27254^25935120297Frank Doornink03/2024
5243(2^399604+3070)/2120293Stefano Morozzi09/2020
5244(2^399549+1062)/2120276Stefano Morozzi09/2020
52452^399526-1861721120270Enzo Doria11/2015
5246(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
524732016^5687+5687^32016120217Hans Havermann01/2021
5248(205*10^120212-1)/3120214Robert Price11/2021
52492^399322-2798111120208Enzo Doria04/2016
525030438^8867+8867^30438120163Hans Havermann02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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