PRP Records

Probable Primes Top 10000

(294627 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 ?
4751(68*10^124392-329)/9124393Robert Price03/2021
4752(27*2^413207-1)/108335124385Lelio R Paula05/2014
475310^124383+58407124384Patrick De Geest08/2021
475510^124383-8000001124383Robert Price04/2021
475410^124383-5801124383Patrick De Geest08/2021
4756(41*10^124335-383)/9124336Robert Price11/2018
4757(304*10^124329-43)/9124331Robert Price02/2020
475834716^3811+3811^34716124320Hans Havermann03/2021
47592^412868-120599124286Paul Bourdelais02/2012
476010^124248+899089124249Patrick De Geest05/2021
476210^124248-1000001124248Robert Price08/2020
476110^124248-501903124248Patrick De Geest05/2021
476345^75145-2124231Lelio R Paula08/2015
476429901^14272+14272^29901124224Hans Havermann03/2021
47652^412645-112213124219Enzo Doria06/2014
476629837^14500+14500^29837124163Hans Havermann03/2021
476728074^26455+26455^28074124158Hans Havermann03/2021
47682^412285+213317124111Enzo Doria09/2023
47692^412248+74611124100Enzo Doria04/2016
4770(22*10^124096-13)/9124097Robert Price06/2018
4771(455*10^124093+31)/9124095Robert Price06/2021
47722^412192-3329124083Yves Minet12/2014
4773(25*2^412191-1)/23124082Lelio R Paula05/2014
4775(25*10^124076-67)/3124077Robert Price06/2019
477428132^25735+25735^28132124077Hans Havermann03/2021
4776F(593689)124074Henri Lifchitz01/2005
4777(11*2^412161+1)/19124073Lelio R Paula05/2014
477835364^3215+3215^35364124028Hans Havermann03/2021
4780(266*10^124022-11)/3124024Robert Price04/2020
477929987^13674+13674^29987124024Hans Havermann03/2021
47812^411932-111546435124004Paul Bourdelais10/2021
47822^411884-113279123990Enzo Doria07/2014
4783(2^411832+1)/257123972Lelio R Paula05/2014
4784(2^411833+2)/514123972Stefano Morozzi03/2020
4785(26*10^123970-89)/9123971Robert Price06/2018
47862^411790-1853531123962Enzo Doria08/2015
4787(5^177337+1)/6123953Paul Bourdelais11/2008
4788(101*10^123950+7)/9123952Robert Price02/2022
47892^411711-113257123938Enzo Doria07/2014
4790(23*2^411675-1)/3123928Lelio R Paula05/2014
479136289^2598+2598^36289123914Hans Havermann03/2021
4792(11*10^123899-179)/3123900Robert Price09/2018
479332276^6879+6879^32276123860Hans Havermann02/2021
47942^411325-351103123822Enzo Doria06/2015
4795(646*10^123817+11)/9123819Robert Price10/2021
479630738^10643+10643^30738123784Hans Havermann03/2021
479731074^9607+9607^31074123755Hans Havermann03/2021
47982^411052+1872481123739Enzo Doria05/2016
479934365^3986+3986^34365123733Hans Havermann03/2021
48002^410997+39123723Lelio R Paula05/2014
4801(649^43987-1)/648123700Michael Stocker05/2020
4802(148*10^123688-1)/3123690Robert Price03/2020
480336825^2284+2284^36825123684Hans Havermann03/2021
480429582^15171+15171^29582123683Hans Havermann03/2021
480510^123671+3593037123672Paul Bourdelais10/2021
48068*10^123657+87123658Robert Price10/2019
480730505^11302+11302^30505123642Hans Havermann03/2021
480829956^13401+13401^29956123633Hans Havermann03/2021
4809155^56438+154123618Norbert Schneider01/2019
48102^410596-39123602Lelio R Paula05/2014
4811(41*10^123600-221)/9123601Robert Price10/2021
481228995^18302+18302^28995123592Hans Havermann03/2021
481328302^23269+23269^28302123589Hans Havermann03/2021
48142^410540-115079123585Enzo Doria06/2015
4815(7*10^123563+107)/3123564Robert Price02/2018
48169*10^123549+89123550Robert Price11/2019
4817(197*10^123545+7)/3123547Robert Price12/2020
4818(3*2^410392-1)/9229123537Lelio R Paula05/2014
48192^410342+212449123526Enzo Doria08/2023
4820(29*10^123510+277)/9123511Robert Price11/2021
482128118^24687+24687^28118123508Hans Havermann03/2021
482239994^1225+1225^39994123507Hans Havermann03/2021
48232^410206-113081123485Enzo Doria07/2014
4824(25*2^410192+1)/10397123478Lelio R Paula04/2014
482528974^18215+18215^28974123442Hans Havermann03/2021
482628901^18618+18618^28901123406Hans Havermann03/2021
48272^409909-189123395Enzo Doria05/2014
48282^409896-109043123391Enzo Doria04/2014
48292^409890+75409123390Enzo Doria04/2016
483081254^33+33^81254123386Hans Havermann03/2021
483133463^4854+4854^33463123348Hans Havermann03/2021
483234061^4182+4182^34061123348Hans Havermann03/2021
4833133^58076-2123345Lelio R Paula10/2017
4834F(590041)123311Henri Lifchitz01/2005
4835(82*10^123299+377)/9123300Robert Price03/2022
48362^409566-113501123292Enzo Doria08/2014
48372^409533+77747123282Enzo Doria05/2016
48382^409436-112799123253Enzo Doria06/2014
483928212^23321+23321^28212123223Hans Havermann03/2021
48402^409225+1873787123189Enzo Doria06/2016
48412^409174+73009123174Enzo Doria04/2016
48422^409058-112685123139Enzo Doria06/2014
4843(13*10^123137-61)/3123138Robert Price11/2018
48444*10^123113+21123114Robert Price12/2018
48452^408778+77689123055Enzo Doria05/2016
48462^408690-75123028Lelio R Paula11/2013
484728327^22032+22032^28327123026Hans Havermann03/2021
4848(29*10^122996+673)/9122997Robert Price12/2018
4849(65*10^122994-101)/9122995Robert Price01/2022
48502^408574-2787341122994Enzo Doria03/2016
48513*10^122977+37122978Robert Price08/2018
4852(7*10^122976-67)/3122977Robert Price10/2021
4853Phi(157825,10)122961Maksym Voznyy06/2015
485425493^27902-27902^25493122948Frank Doornink02/2024
4855(68*10^122933-419)/9122934Robert Price07/2019
485629712^13721+13721^29712122931Hans Havermann03/2021
4857(13*2^408283+1)/1665122904Lelio R Paula05/2014
4858(266*10^122872-17)/3122874Robert Price07/2020
4859(16*10^122871+77)/3122872Robert Price03/2019
486030395^11022+11022^30395122865Hans Havermann03/2021
48614*10^122859-69122860Robert Price01/2022
4862(10^122857+167)/3122857Robert Price05/2021
486333331^4852+4852^33331122856Hans Havermann03/2021
4864(11*2^408100-1)/35122850Lelio R Paula04/2014
4865(19*10^122836-43)/3122837Robert Price05/2019
486628420^20969+20969^28420122820Hans Havermann03/2021
4867(16*10^122818+179)/3122819Robert Price11/2021
486829865^12934+12934^29865122797Hans Havermann03/2021
4869(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
4870(32*10^122733-77)/9122734Robert Price06/2018
4871(21*2^407604-1)/215122701Lelio R Paula04/2014
4873(22*10^122681+161)/3122682Robert Price05/2019
487229513^14350+14350^29513122682Hans Havermann03/2021
4874(21*2^407433-1)/13122650Lelio R Paula04/2014
4876(26*10^122625-131)/3122626Robert Price10/2019
4875(643*33^80753+3709)/32122626Eric Chen12/2023
487727925^24562+24562^27925122599Hans Havermann03/2021
4878(73*10^122592-1)/9122593Robert Price01/2015
4879(5*10^122592+91)/3122593Robert Price04/2018
488036751^2166+2166^36751122589Hans Havermann03/2021
4881(85*10^122585-1)/3122587Robert Price02/2020
488229368^14931+14931^29368122585Hans Havermann03/2021
48832^407179-112075122574Enzo Doria06/2014
4884(21*2^407131+1)/207517523122552Lelio R Paula04/2014
4885(66^67349+1)/67122543Paul Bourdelais09/2017
4886(646*10^122533+11)/9122535Robert Price10/2021
48872^407008-1867919122522Enzo Doria04/2016
488811^117642-300122512Enzo Doria10/2012
4889(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
48902^406949+72197122504Enzo Doria04/2016
4891(19*10^122501+149)/3122502Robert Price05/2019
489228632^18977+18977^28632122495Hans Havermann03/2021
489331815^7076+7076^31815122481Hans Havermann03/2021
48942^406826-65122467Lelio R Paula11/2013
48952^406821-2797363122466Enzo Doria04/2016
4896(7*10^122456-331)/9122456Robert Price03/2022
48972^406758-17122447Lelio R Paula11/2013
489829941^12282+12282^29941122437Hans Havermann03/2021
4899(30^82883-1)/29122427Robert Price12/2011
490027496^27577+27577^27496122422Norbert Schneider12/2020
490128732^18215+18215^28732122411Hans Havermann03/2021
4902(2^406583-1)/813167122388Jens K. Andersen02/2009
49034*10^122377+19122378Robert Price10/2018
490428227^21634+21634^28227122368Hans Havermann03/2021
4905Phi(246362,10)122365Makoto Kamada09/2019
49063*10^122345-97122346Robert Price07/2018
490797^61575-2122336Lelio R Paula12/2014
49082*10^122319+47122320Robert Price12/2021
4909208^52765+52765^208122313Norbert Schneider11/2020
49112^406298+2799109122308Enzo Doria04/2016
49102^406296+213691122308Enzo Doria09/2023
49127*10^122294+57122295Robert Price06/2019
4913(27*2^406241-1)/10277122289Lelio R Paula04/2014
49142^406229-1849993122288Enzo Doria08/2015
49153*10^122274+7122275Robert Price07/2015
49162^406117+1876577122254Enzo Doria07/2016
491729308^14835+14835^29308122253Hans Havermann03/2021
491828119^22268+22268^28119122253Hans Havermann03/2021
491932167^6312+6312^32167122240Hans Havermann03/2021
49203^256199-2^256199122238Mike Oakes06/2005
492127678^26053+26053^27678122223Hans Havermann03/2021
49222^405992-78557122216Jorge Menendez03/2018
4923(8*10^122203+43)/3122204Robert Price06/2018
4924(58*10^122170+329)/9122171Robert Price05/2019
49252^405774+179149122151Enzo Doria06/2016
49262^405693+20417122126Enzo Doria07/2023
4927(218*10^122109+7)/9122111Robert Price06/2022
492829189^15246+15246^29189122103Hans Havermann03/2021
493034*10^122082-9122084Robert Price06/2020
492933442^4473+4473^33442122084Hans Havermann03/2021
49315*10^122082+41122083Robert Price03/2019
493231849^6808+6808^31849122078Hans Havermann03/2021
49342^405514-3311122072Yves Minet12/2014
49352^405514-115511122072Enzo Doria07/2015
493323*10^122070-7122072Robert Price02/2020
49362^405422-113261122045Enzo Doria07/2014
49372^405173+71237121970Enzo Doria04/2016
4938fibonacci(583574)+2121960Jon Grantham08/2023
4939(154*10^121953+17)/9121955Robert Price06/2022
4940(34*10^121924+191)/9121925Robert Price08/2021
4941(2^405016+1)/257121920Lelio R Paula04/2014
494228557^18590+18590^28557121918Hans Havermann03/2021
494328641^18002+18002^28641121877Hans Havermann03/2021
49442^404858+71329121875Enzo Doria04/2016
49452^404813-114703121861Enzo Doria04/2015
49462^404764+77791121847Enzo Doria05/2016
494728830^16841+16841^28830121847Hans Havermann03/2021
4948(4*10^121825+89)/3121826Robert Price08/2021
4949317^48694+48694^317121787Norbert Schneider08/2015
49502^404536-115259121778Enzo Doria06/2015
49512^404501-631121767Yves Minet07/2012
49525*10^121764-69121765Robert Price02/2021
495328236^20485+20485^28236121738Hans Havermann02/2021
4954(382*10^121694-31)/9121696Robert Price06/2022
495563^67620+2121672Lelio R Paula08/2015
4956(25*34^79445-28062367)/33121669Eric Chen08/2023
4957(13*33^80110-121453)/32121648Eric Chen12/2023
4958(16*10^121633+167)/3121634Robert Price06/2019
495929955^11494+11494^29955121632Hans Havermann02/2021
4960(17*10^121621+1)/9121622Serge Batalov05/2010
496131088^8163+8163^31088121612Hans Havermann02/2021
4962(15*2^403912+1)/271121589Lelio R Paula05/2014
4963(10^121543-79)/3121543Robert Price01/2018
49642^403676+76831121519Enzo Doria05/2016
4965(7*10^121487+143)/3121488Robert Price03/2018
496627965^22086+22086^27965121484Hans Havermann02/2021
4967(893*10^121470+7)/9121472Robert Price06/2021
4968(206*10^121462-11)/3121464Robert Price02/2022
4969(77*10^121455+67)/9121456Robert Price12/2021
49702^403363-113635121425Enzo Doria08/2014
497125531^27552-27552^25531121424Frank Doornink02/2024
4972(17*10^121418-113)/3121419Robert Price06/2021
49732^403336-1861469121417Enzo Doria03/2016
497427929^22186+22186^27929121382Hans Havermann02/2021
4975p(24442)#/2-64121381Robert Price04/2017
497611^116555-720121380Enzo Doria11/2012
49772^403100-461267121346Enzo Doria07/2015
49782^403093-112213121344Enzo Doria06/2014
497929404^13385+13385^29404121340Hans Havermann02/2021
498028106^20745+20745^28106121332Hans Havermann02/2021
4981(316^48539+1)/317121330Eric Chen10/2017
4982(23*10^121320-71)/3121321Robert Price07/2020
49832^403004+1866361121317Enzo Doria03/2016
49842^402953+89121301Lelio R Paula10/2013
49852^402944-2788319121299Enzo Doria03/2016
4986(44*10^121297-719)/9121298Robert Price12/2018
4987(27*2^402865+1)/5121276Lelio R Paula04/2014
49882^402828-113183121264Enzo Doria07/2014
4989(17*10^121242+1)/9121243Serge Batalov05/2010
4990(15*2^402757+1)/101121242Lelio R Paula05/2014
49922^402715+1874223121230Enzo Doria06/2016
4991(35*10^121229-593)/9121230Robert Price07/2018
4993(91^61879+1)/92121222Paul Bourdelais09/2017
499428719^16568+16568^28719121174Hans Havermann02/2021
49957*10^121144+9121145Robert Price09/2015
499627490^25467+25467^27490121121Hans Havermann02/2021
499734575^3182+3182^34575121106Hans Havermann02/2021
49985*10^121100-37121101Robert Price11/2021
499925592^27467-27467^25592121078Frank Doornink02/2024
500029954^10935+10935^29954120979Hans Havermann02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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