PRP Records

Probable Primes Top 10000

(291910 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 ?
3751(78^67141-1)/77127036Paul Bourdelais09/2017
3752(14*10^127014-137)/3127015Robert Price04/2021
375331436^10965+10965^31436127002Hans Havermann03/2021
375428905^24758+24758^28905127001Hans Havermann03/2021
37552^421860-113285126993Enzo Doria07/2014
3756(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
3757(2^421827-7)/11126982Lelio R Paula05/2015
375811^121910-840126957Enzo Doria12/2012
3759(56*10^126935+187)/9126936Robert Price10/2021
376028915^24538+24538^28915126933Hans Havermann03/2021
3761(29*10^126928-77)/3126929Robert Price02/2020
3762(259*10^126919-1)/3126921Robert Price12/2020
376310^126919+204567126920Patrick De Geest05/2021
3764(2^421617+100280245065)126920Paul Bourdelais05/2022
376510^126919-100001126919Robert Price07/2020
376628340^28503+28503^28340126907Norbert Schneider02/2021
3767(71^68539+1)/72126882Paul Bourdelais09/2017
3768(5*10^126871-119)/3126872Robert Price03/2018
3769331^50339-10004126846Enzo Doria07/2012
37702^421363-2790757126843Enzo Doria03/2016
3771(106*10^126839-1)/3126841Serge Batalov12/2014
377237938^2203+2203^37938126828Hans Havermann03/2021
3773(13*10^126819+77)/9126820Robert Price07/2022
3774(7*2^421243+1)/39126807Lelio R Paula05/2014
3775(14*10^126784-83)/3126785Robert Price12/2018
37762^421161-286183126783Enzo Doria06/2015
3777(106*10^126726+17)/3126728Robert Price04/2021
377830718^13347+13347^30718126724Hans Havermann03/2021
37792^420939-113935126716Enzo Doria10/2014
3780177^56363-2126703Lelio R Paula10/2017
37812^420741-113659126656Enzo Doria08/2014
37822^420694-21126642Lelio R Paula05/2017
3783(13*10^126638+437)/9126639Robert Price04/2018
3784(167*10^126637-17)/3126639Robert Price03/2020
37854*10^126625+87126626Robert Price08/2018
3786(31*2^420556+1)/7126601Lelio R Paula05/2014
37877*10^126600-99126601Robert Price06/2019
37882^420424-59189126561Enzo Doria10/2015
378928717^25534+25534^28717126560Hans Havermann03/2021
3790(86*10^126542+103)/9126543Robert Price12/2021
379128922^23655+23655^28922126503Hans Havermann03/2021
37922^420126+71893126471Enzo Doria04/2016
3793(43*10^126441+47)/9126442Robert Price12/2018
37948*10^126408+71126409Robert Price05/2022
37952^419866+1877059126393Enzo Doria07/2016
379629315^20484+20484^29315126390Hans Havermann03/2021
379729433^19676+19676^29433126384Hans Havermann03/2021
3798F(604711)126377Henri Lifchitz02/2005
37992^419757+72707126360Enzo Doria04/2016
38002^419720-21569126349Enzo Doria07/2013
38012^419637+29126324Henri Lifchitz02/2006
380231004^11865+11865^31004126319Hans Havermann03/2021
38032^419612+1876741126316Enzo Doria07/2016
38042^419520+2793271126289Enzo Doria03/2016
3805(2^419447-5)/369126264Lelio R Paula05/2014
38062^419328-1859939126231Enzo Doria03/2016
38072^419282-1851507126217Enzo Doria08/2015
3808(133*10^126212+17)/3126214Robert Price11/2021
38092^419251+1866143126208Enzo Doria03/2016
381011^121185+2126202Robert Price05/2014
381128203^28352+28352^28203126175Norbert Schneider01/2021
3812(23*2^419036-1)/1393126141Lelio R Paula05/2014
38132^418851+23126087Robert Price09/2015
3814(2^418849-9)/2681126083Lelio R Paula05/2014
38152^418829+167126081Lelio R Paula01/2012
381631037^11530+11530^31037126067Hans Havermann03/2021
38174*10^126064-69126065Robert Price01/2022
3818(31*2^418782-1)/75891126063Lelio R Paula05/2014
3819(19*2^418754-1)/15126058Lelio R Paula05/2014
3820(35*10^126048-323)/9126049Robert Price10/2021
382133016^6551+6551^33016126000Hans Havermann03/2021
38222^418548-111546435125996Paul Bourdelais10/2021
382334736^4227+4227^34736125954Hans Havermann03/2021
38242^418319-109501125927Enzo Doria04/2014
38252^418316-112373125926Enzo Doria06/2014
382640398^1309+1309^40398125919Hans Havermann03/2021
3827(8*10^125894-29)/3125895Robert Price07/2018
3828(26*10^125886-413)/9125887Robert Price05/2018
382955*10^125847+9125849Robert Price03/2022
38304*10^125832+57125833Robert Price05/2022
38312^417968+1869811125821Enzo Doria06/2016
38322^417902+63125802Lelio R Paula09/2015
3833(10^125792-91)/9125792Serge Batalov12/2014
383430438^13573+13573^30438125791Hans Havermann03/2021
383532867^6714+6714^32867125782Hans Havermann03/2021
383631155^10892+10892^31155125777Hans Havermann03/2021
3837(35*10^125754-593)/9125755Robert Price07/2018
383830455^13464+13464^30455125754Hans Havermann03/2021
3839(32*10^125751-77)/9125752Robert Price06/2018
38402^417704+77011125742Enzo Doria05/2016
384129755^16816+16816^29755125737Hans Havermann03/2021
3842(22*10^125734+203)/9125735Robert Price10/2021
384329918^15915+15915^29918125710Hans Havermann03/2021
3844(10^125706+149)/3125706Serge Batalov12/2014
384528531^25368+25368^28531125659Hans Havermann03/2021
38462^417419-115309125656Enzo Doria07/2015
3847(46*10^125642+593)/9125643Robert Price04/2022
38482^417300+77281125620Enzo Doria05/2016
384930638^12537+12537^30638125561Hans Havermann03/2021
38502^417095-1657125559Yves Minet07/2014
385130162^14525+14525^30162125538Hans Havermann03/2021
3852(56*10^125535+583)/9125536Robert Price08/2021
3853(23*10^125517-179)/3125518Robert Price06/2022
38549*10^125516+29125517Robert Price03/2022
3855(88*10^125492-637)/9125493Robert Price11/2020
385628958^21525+21525^28958125474Hans Havermann02/2021
38582^416773-25125462Lelio R Paula09/2015
3857(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
385933889^5032+5032^33889125449Hans Havermann03/2021
3860(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
3861(11*2^416691+1)/43125436Lelio R Paula05/2014
3862(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
38632^416641-2*416641+1125422Robert Price05/2018
386433392^5697+5697^33392125409Hans Havermann03/2021
3865(21*2^416566-1)/17125399Lelio R Paula05/2014
38662^416530+1870429125389Enzo Doria05/2016
3867(56*10^125385+691)/9125386Robert Price05/2019
386827953^28198+28198^27953125381Norbert Schneider01/2021
386931074^10837+10837^31074125381Hans Havermann03/2021
387033745^5194+5194^33745125380Hans Havermann03/2021
38712^416490+1875109125376Enzo Doria09/2016
387228360^26331+26331^28360125365Hans Havermann03/2021
38732^416416-114929125354Enzo Doria05/2015
3874(77*10^125330-293)/9125331Robert Price09/2019
3875(172*10^125292-1)/9125294Serge Batalov12/2014
38762^416134+1865899125269Enzo Doria03/2016
3877153^57337-152125264Norbert Schneider12/2018
3878(599*10^125224+13)/9125226Robert Price02/2022
3879(9*2^415992+1)/13560845125220Lelio R Paula05/2014
388030054^14657+14657^30054125207Hans Havermann03/2021
3881(23^91943-1)/22125201Robert Price01/2012
38822^415884-933075125194Paul Bourdelais06/2021
388343125^27010-106125185Enzo Doria08/2012
3884(38*10^125166+349)/9125167Robert Price10/2018
388510^125166-5001125166Robert Price12/2021
38862^415765-112603125158Enzo Doria06/2014
38878*10^125088-13125089Robert Price08/2019
3888(25*10^125076-13)/3125077Robert Price09/2019
3889(11*10^125054+73)/3125055Robert Price08/2021
3890(29*10^125021-113)/3125022Robert Price10/2019
38912^415290-113591125015Enzo Doria08/2014
38922^415276-460919125011Enzo Doria06/2015
38932^415259+77243125006Enzo Doria05/2016
3894(67*10^124990+77)/9124991Robert Price10/2021
38952^415144-3683124971Yves Minet10/2011
38962^415092+111546435124956Paul Bourdelais10/2021
389731936^8173+8173^31936124946Hans Havermann03/2021
38985^178715-4124916Tyler NeSmith07/2021
389929767^15700+15700^29767124900Hans Havermann03/2021
39002^414874+79124890Lelio R Paula01/2015
3901(2^414765+7)/1389124854Lelio R Paula05/2014
39022^414618+79459124813Enzo Doria06/2016
3903(61*10^124809-1)/3124811Robert Price01/2020
3904(29*10^124765-71)/3124766Robert Price07/2021
39052^414432-1846709124757Enzo Doria07/2015
39062*10^124751-51124752Robert Price04/2018
3907(56*10^124735+367)/9124736Robert Price06/2019
3908(13*2^414274-1)/153124708Lelio R Paula05/2014
3909(23*10^124690+37)/3124691Robert Price02/2022
391056*10^124656-3124658Robert Price03/2020
3911(7*10^124648+197)/3124649Robert Price07/2018
39132^414032-5124637Henri Lifchitz07/2006
39122^414032+1872331124637Enzo Doria05/2016
391437373^2158+2158^37373124604Hans Havermann03/2021
391529811^15112+15112^29811124590Hans Havermann03/2021
391614120^30009-30009^14120124533Norbert Schneider02/2015
391729757^15296+15296^29757124521Hans Havermann03/2021
391835056^3561+3561^35056124504Hans Havermann03/2021
391940588^1167+1167^40588124487Hans Havermann02/2021
3920(85*10^124485-49)/9124486Robert Price12/2020
392164^68909-63^68909124463Robert Price07/2013
392235016^3581+3581^35016124448Hans Havermann03/2021
39232^413387+76253124442Enzo Doria04/2016
392428749^21298+21298^28749124436Hans Havermann03/2021
39252^413352+524287124432Paul Underwood09/2018
3926287117#+391613124424Nicolas PALAU01/2017
3927(4*10^124420+83)/3124421Robert Price02/2018
392834578^3965+3965^34578124421Hans Havermann03/2021
3929(68*10^124392-329)/9124393Robert Price03/2021
3930(27*2^413207-1)/108335124385Lelio R Paula05/2014
393110^124383+58407124384Patrick De Geest08/2021
393310^124383-8000001124383Robert Price04/2021
393210^124383-5801124383Patrick De Geest08/2021
3934(41*10^124335-383)/9124336Robert Price11/2018
3935(304*10^124329-43)/9124331Robert Price02/2020
393634716^3811+3811^34716124320Hans Havermann03/2021
39372^412868-120599124286Paul Bourdelais02/2012
393810^124248+899089124249Patrick De Geest05/2021
394010^124248-1000001124248Robert Price08/2020
393910^124248-501903124248Patrick De Geest05/2021
394145^75145-2124231Lelio R Paula08/2015
394229901^14272+14272^29901124224Hans Havermann03/2021
39432^412645-112213124219Enzo Doria06/2014
394429837^14500+14500^29837124163Hans Havermann03/2021
394528074^26455+26455^28074124158Hans Havermann03/2021
39462^412248+74611124100Enzo Doria04/2016
3947(22*10^124096-13)/9124097Robert Price06/2018
3948(455*10^124093+31)/9124095Robert Price06/2021
39492^412192-3329124083Yves Minet12/2014
3950(25*2^412191-1)/23124082Lelio R Paula05/2014
3952(25*10^124076-67)/3124077Robert Price06/2019
395128132^25735+25735^28132124077Hans Havermann03/2021
3953F(593689)124074Henri Lifchitz01/2005
3954(11*2^412161+1)/19124073Lelio R Paula05/2014
395535364^3215+3215^35364124028Hans Havermann03/2021
3957(266*10^124022-11)/3124024Robert Price04/2020
395629987^13674+13674^29987124024Hans Havermann03/2021
39582^411932-111546435124004Paul Bourdelais10/2021
39592^411884-113279123990Enzo Doria07/2014
3960(2^411832+1)/257123972Lelio R Paula05/2014
3961(2^411833+2)/514123972Stefano Morozzi03/2020
3962(26*10^123970-89)/9123971Robert Price06/2018
39632^411790-1853531123962Enzo Doria08/2015
3964(5^177337+1)/6123953Paul Bourdelais11/2008
3965(101*10^123950+7)/9123952Robert Price02/2022
39662^411711-113257123938Enzo Doria07/2014
3967(23*2^411675-1)/3123928Lelio R Paula05/2014
396836289^2598+2598^36289123914Hans Havermann03/2021
3969(11*10^123899-179)/3123900Robert Price09/2018
397032276^6879+6879^32276123860Hans Havermann02/2021
39712^411325-351103123822Enzo Doria06/2015
3972(646*10^123817+11)/9123819Robert Price10/2021
397330738^10643+10643^30738123784Hans Havermann03/2021
397431074^9607+9607^31074123755Hans Havermann03/2021
39752^411052+1872481123739Enzo Doria05/2016
397634365^3986+3986^34365123733Hans Havermann03/2021
39772^410997+39123723Lelio R Paula05/2014
3978(649^43987-1)/648123700Michael Stocker05/2020
3979(148*10^123688-1)/3123690Robert Price03/2020
398036825^2284+2284^36825123684Hans Havermann03/2021
398129582^15171+15171^29582123683Hans Havermann03/2021
398210^123671+3593037123672Paul Bourdelais10/2021
39838*10^123657+87123658Robert Price10/2019
398430505^11302+11302^30505123642Hans Havermann03/2021
398529956^13401+13401^29956123633Hans Havermann03/2021
3986155^56438+154123618Norbert Schneider01/2019
39872^410596-39123602Lelio R Paula05/2014
3988(41*10^123600-221)/9123601Robert Price10/2021
398928995^18302+18302^28995123592Hans Havermann03/2021
399028302^23269+23269^28302123589Hans Havermann03/2021
39912^410540-115079123585Enzo Doria06/2015
3992(7*10^123563+107)/3123564Robert Price02/2018
39939*10^123549+89123550Robert Price11/2019
3994(197*10^123545+7)/3123547Robert Price12/2020
3995(3*2^410392-1)/9229123537Lelio R Paula05/2014
3996(29*10^123510+277)/9123511Robert Price11/2021
399728118^24687+24687^28118123508Hans Havermann03/2021
399839994^1225+1225^39994123507Hans Havermann03/2021
39992^410206-113081123485Enzo Doria07/2014
4000(25*2^410192+1)/10397123478Lelio R Paula04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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