PRP Records

Probable Primes Top 10000

(291192 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
37512^415259+77243125006Enzo Doria05/2016
3752(67*10^124990+77)/9124991Robert Price10/2021
37532^415144-3683124971Yves Minet10/2011
37542^415092+111546435124956Paul Bourdelais10/2021
375531936^8173+8173^31936124946Hans Havermann03/2021
37565^178715-4124916Tyler NeSmith07/2021
375729767^15700+15700^29767124900Hans Havermann03/2021
37582^414874+79124890Lelio R Paula01/2015
3759(2^414765+7)/1389124854Lelio R Paula05/2014
37602^414618+79459124813Enzo Doria06/2016
3761(61*10^124809-1)/3124811Robert Price01/2020
3762(29*10^124765-71)/3124766Robert Price07/2021
37632^414432-1846709124757Enzo Doria07/2015
37642*10^124751-51124752Robert Price04/2018
3765(56*10^124735+367)/9124736Robert Price06/2019
3766(13*2^414274-1)/153124708Lelio R Paula05/2014
3767(23*10^124690+37)/3124691Robert Price02/2022
376856*10^124656-3124658Robert Price03/2020
3769(7*10^124648+197)/3124649Robert Price07/2018
37712^414032-5124637Henri Lifchitz07/2006
37702^414032+1872331124637Enzo Doria05/2016
377237373^2158+2158^37373124604Hans Havermann03/2021
377329811^15112+15112^29811124590Hans Havermann03/2021
377414120^30009-30009^14120124533Norbert Schneider02/2015
377529757^15296+15296^29757124521Hans Havermann03/2021
377635056^3561+3561^35056124504Hans Havermann03/2021
377740588^1167+1167^40588124487Hans Havermann02/2021
3778(85*10^124485-49)/9124486Robert Price12/2020
377964^68909-63^68909124463Robert Price07/2013
378035016^3581+3581^35016124448Hans Havermann03/2021
37812^413387+76253124442Enzo Doria04/2016
378228749^21298+21298^28749124436Hans Havermann03/2021
37832^413352+524287124432Paul Underwood09/2018
3784287117#+391613124424Nicolas PALAU01/2017
3785(4*10^124420+83)/3124421Robert Price02/2018
378634578^3965+3965^34578124421Hans Havermann03/2021
3787(68*10^124392-329)/9124393Robert Price03/2021
3788(27*2^413207-1)/108335124385Lelio R Paula05/2014
378910^124383+58407124384Patrick De Geest08/2021
379110^124383-8000001124383Robert Price04/2021
379010^124383-5801124383Patrick De Geest08/2021
3792(41*10^124335-383)/9124336Robert Price11/2018
3793(304*10^124329-43)/9124331Robert Price02/2020
379434716^3811+3811^34716124320Hans Havermann03/2021
37952^412868-120599124286Paul Bourdelais02/2012
379610^124248+899089124249Patrick De Geest05/2021
379810^124248-1000001124248Robert Price08/2020
379710^124248-501903124248Patrick De Geest05/2021
379945^75145-2124231Lelio R Paula08/2015
380029901^14272+14272^29901124224Hans Havermann03/2021
38012^412645-112213124219Enzo Doria06/2014
380229837^14500+14500^29837124163Hans Havermann03/2021
380328074^26455+26455^28074124158Hans Havermann03/2021
38042^412248+74611124100Enzo Doria04/2016
3805(22*10^124096-13)/9124097Robert Price06/2018
3806(455*10^124093+31)/9124095Robert Price06/2021
38072^412192-3329124083Yves Minet12/2014
3808(25*2^412191-1)/23124082Lelio R Paula05/2014
3810(25*10^124076-67)/3124077Robert Price06/2019
380928132^25735+25735^28132124077Hans Havermann03/2021
3811F(593689)124074Henri Lifchitz01/2005
3812(11*2^412161+1)/19124073Lelio R Paula05/2014
381335364^3215+3215^35364124028Hans Havermann03/2021
3815(266*10^124022-11)/3124024Robert Price04/2020
381429987^13674+13674^29987124024Hans Havermann03/2021
38162^411932-111546435124004Paul Bourdelais10/2021
38172^411884-113279123990Enzo Doria07/2014
3818(2^411832+1)/257123972Lelio R Paula05/2014
3819(2^411833+2)/514123972Stefano Morozzi03/2020
3820(26*10^123970-89)/9123971Robert Price06/2018
38212^411790-1853531123962Enzo Doria08/2015
3822(5^177337+1)/6123953Paul Bourdelais11/2008
3823(101*10^123950+7)/9123952Robert Price02/2022
38242^411711-113257123938Enzo Doria07/2014
3825(23*2^411675-1)/3123928Lelio R Paula05/2014
382636289^2598+2598^36289123914Hans Havermann03/2021
3827(11*10^123899-179)/3123900Robert Price09/2018
382832276^6879+6879^32276123860Hans Havermann02/2021
38292^411325-351103123822Enzo Doria06/2015
3830(646*10^123817+11)/9123819Robert Price10/2021
383130738^10643+10643^30738123784Hans Havermann03/2021
383231074^9607+9607^31074123755Hans Havermann03/2021
38332^411052+1872481123739Enzo Doria05/2016
383434365^3986+3986^34365123733Hans Havermann03/2021
38352^410997+39123723Lelio R Paula05/2014
3836(649^43987-1)/648123700Michael Stocker05/2020
3837(148*10^123688-1)/3123690Robert Price03/2020
383836825^2284+2284^36825123684Hans Havermann03/2021
383929582^15171+15171^29582123683Hans Havermann03/2021
384010^123671+3593037123672Paul Bourdelais10/2021
38418*10^123657+87123658Robert Price10/2019
384230505^11302+11302^30505123642Hans Havermann03/2021
384329956^13401+13401^29956123633Hans Havermann03/2021
3844155^56438+154123618Norbert Schneider01/2019
38452^410596-39123602Lelio R Paula05/2014
3846(41*10^123600-221)/9123601Robert Price10/2021
384728995^18302+18302^28995123592Hans Havermann03/2021
384828302^23269+23269^28302123589Hans Havermann03/2021
38492^410540-115079123585Enzo Doria06/2015
3850(7*10^123563+107)/3123564Robert Price02/2018
38519*10^123549+89123550Robert Price11/2019
3852(197*10^123545+7)/3123547Robert Price12/2020
3853(3*2^410392-1)/9229123537Lelio R Paula05/2014
3854(29*10^123510+277)/9123511Robert Price11/2021
385528118^24687+24687^28118123508Hans Havermann03/2021
385639994^1225+1225^39994123507Hans Havermann03/2021
38572^410206-113081123485Enzo Doria07/2014
3858(25*2^410192+1)/10397123478Lelio R Paula04/2014
385928974^18215+18215^28974123442Hans Havermann03/2021
386028901^18618+18618^28901123406Hans Havermann03/2021
38612^409909-189123395Enzo Doria05/2014
38622^409896-109043123391Enzo Doria04/2014
38632^409890+75409123390Enzo Doria04/2016
386481254^33+33^81254123386Hans Havermann03/2021
386533463^4854+4854^33463123348Hans Havermann03/2021
386634061^4182+4182^34061123348Hans Havermann03/2021
3867133^58076-2123345Lelio R Paula10/2017
3868F(590041)123311Henri Lifchitz01/2005
3869(82*10^123299+377)/9123300Robert Price03/2022
38702^409566-113501123292Enzo Doria08/2014
38712^409533+77747123282Enzo Doria05/2016
38722^409436-112799123253Enzo Doria06/2014
387328212^23321+23321^28212123223Hans Havermann03/2021
38742^409225+1873787123189Enzo Doria06/2016
38752^409174+73009123174Enzo Doria04/2016
38762^409058-112685123139Enzo Doria06/2014
3877(13*10^123137-61)/3123138Robert Price11/2018
38784*10^123113+21123114Robert Price12/2018
38792^408778+77689123055Enzo Doria05/2016
38802^408690-75123028Lelio R Paula11/2013
388128327^22032+22032^28327123026Hans Havermann03/2021
3882(29*10^122996+673)/9122997Robert Price12/2018
3883(65*10^122994-101)/9122995Robert Price01/2022
38842^408574-2787341122994Enzo Doria03/2016
38853*10^122977+37122978Robert Price08/2018
3886(7*10^122976-67)/3122977Robert Price10/2021
3887Phi(157825,10)122961Maksym Voznyy06/2015
3888(68*10^122933-419)/9122934Robert Price07/2019
388929712^13721+13721^29712122931Hans Havermann03/2021
3890(13*2^408283+1)/1665122904Lelio R Paula05/2014
3891(266*10^122872-17)/3122874Robert Price07/2020
3892(16*10^122871+77)/3122872Robert Price03/2019
389330395^11022+11022^30395122865Hans Havermann03/2021
38944*10^122859-69122860Robert Price01/2022
3895(10^122857+167)/3122857Robert Price05/2021
389633331^4852+4852^33331122856Hans Havermann03/2021
3897(11*2^408100-1)/35122850Lelio R Paula04/2014
3898(19*10^122836-43)/3122837Robert Price05/2019
389928420^20969+20969^28420122820Hans Havermann03/2021
3900(16*10^122818+179)/3122819Robert Price11/2021
390129865^12934+12934^29865122797Hans Havermann03/2021
3902(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
3903(32*10^122733-77)/9122734Robert Price06/2018
3904(21*2^407604-1)/215122701Lelio R Paula04/2014
3906(22*10^122681+161)/3122682Robert Price05/2019
390529513^14350+14350^29513122682Hans Havermann03/2021
3907(21*2^407433-1)/13122650Lelio R Paula04/2014
3908(26*10^122625-131)/3122626Robert Price10/2019
390927925^24562+24562^27925122599Hans Havermann03/2021
3910(73*10^122592-1)/9122593Robert Price01/2015
3911(5*10^122592+91)/3122593Robert Price04/2018
391236751^2166+2166^36751122589Hans Havermann03/2021
3913(85*10^122585-1)/3122587Robert Price02/2020
391429368^14931+14931^29368122585Hans Havermann03/2021
39152^407179-112075122574Enzo Doria06/2014
3916(21*2^407131+1)/207517523122552Lelio R Paula04/2014
3917(66^67349+1)/67122543Paul Bourdelais09/2017
3918(646*10^122533+11)/9122535Robert Price10/2021
39192^407008-1867919122522Enzo Doria04/2016
392011^117642-300122512Enzo Doria10/2012
3921(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
39222^406949+72197122504Enzo Doria04/2016
3923(19*10^122501+149)/3122502Robert Price05/2019
392428632^18977+18977^28632122495Hans Havermann03/2021
392531815^7076+7076^31815122481Hans Havermann03/2021
39262^406826-65122467Lelio R Paula11/2013
39272^406821-2797363122466Enzo Doria04/2016
3928(7*10^122456-331)/9122456Robert Price03/2022
39292^406758-17122447Lelio R Paula11/2013
393029941^12282+12282^29941122437Hans Havermann03/2021
3931(30^82883-1)/29122427Robert Price12/2011
393227496^27577+27577^27496122422Norbert Schneider12/2020
393328732^18215+18215^28732122411Hans Havermann03/2021
3934(2^406583-1)/813167122388Jens K. Andersen02/2009
39354*10^122377+19122378Robert Price10/2018
393628227^21634+21634^28227122368Hans Havermann03/2021
3937Phi(246362,10)122365Makoto Kamada09/2019
39383*10^122345-97122346Robert Price07/2018
393997^61575-2122336Lelio R Paula12/2014
39402*10^122319+47122320Robert Price12/2021
3941208^52765+52765^208122313Norbert Schneider11/2020
39422^406298+2799109122308Enzo Doria04/2016
39437*10^122294+57122295Robert Price06/2019
3944(27*2^406241-1)/10277122289Lelio R Paula04/2014
39452^406229-1849993122288Enzo Doria08/2015
39463*10^122274+7122275Robert Price07/2015
39472^406117+1876577122254Enzo Doria07/2016
394829308^14835+14835^29308122253Hans Havermann03/2021
394928119^22268+22268^28119122253Hans Havermann03/2021
395032167^6312+6312^32167122240Hans Havermann03/2021
39513^256199-2^256199122238Mike Oakes06/2005
395227678^26053+26053^27678122223Hans Havermann03/2021
39532^405992-78557122216Jorge Menendez03/2018
3954(8*10^122203+43)/3122204Robert Price06/2018
3955(58*10^122170+329)/9122171Robert Price05/2019
39562^405774+179149122151Enzo Doria06/2016
3957(218*10^122109+7)/9122111Robert Price06/2022
395829189^15246+15246^29189122103Hans Havermann03/2021
396034*10^122082-9122084Robert Price06/2020
395933442^4473+4473^33442122084Hans Havermann03/2021
39615*10^122082+41122083Robert Price03/2019
396231849^6808+6808^31849122078Hans Havermann03/2021
39642^405514-3311122072Yves Minet12/2014
39652^405514-115511122072Enzo Doria07/2015
396323*10^122070-7122072Robert Price02/2020
39662^405422-113261122045Enzo Doria07/2014
39672^405173+71237121970Enzo Doria04/2016
3968(154*10^121953+17)/9121955Robert Price06/2022
3969(34*10^121924+191)/9121925Robert Price08/2021
3970(2^405016+1)/257121920Lelio R Paula04/2014
397128557^18590+18590^28557121918Hans Havermann03/2021
397228641^18002+18002^28641121877Hans Havermann03/2021
39732^404858+71329121875Enzo Doria04/2016
39742^404813-114703121861Enzo Doria04/2015
39752^404764+77791121847Enzo Doria05/2016
397628830^16841+16841^28830121847Hans Havermann03/2021
3977(4*10^121825+89)/3121826Robert Price08/2021
3978317^48694+48694^317121787Norbert Schneider08/2015
39792^404536-115259121778Enzo Doria06/2015
39802^404501-631121767Yves Minet07/2012
39815*10^121764-69121765Robert Price02/2021
398228236^20485+20485^28236121738Hans Havermann02/2021
3983(382*10^121694-31)/9121696Robert Price06/2022
398463^67620+2121672Lelio R Paula08/2015
3985(16*10^121633+167)/3121634Robert Price06/2019
398629955^11494+11494^29955121632Hans Havermann02/2021
3987(17*10^121621+1)/9121622Serge Batalov05/2010
398831088^8163+8163^31088121612Hans Havermann02/2021
3989(15*2^403912+1)/271121589Lelio R Paula05/2014
3990(10^121543-79)/3121543Robert Price01/2018
39912^403676+76831121519Enzo Doria05/2016
3992(7*10^121487+143)/3121488Robert Price03/2018
399327965^22086+22086^27965121484Hans Havermann02/2021
3994(893*10^121470+7)/9121472Robert Price06/2021
3995(206*10^121462-11)/3121464Robert Price02/2022
3996(77*10^121455+67)/9121456Robert Price12/2021
39972^403363-113635121425Enzo Doria08/2014
3998(17*10^121418-113)/3121419Robert Price06/2021
39992^403336-1861469121417Enzo Doria03/2016
400027929^22186+22186^27929121382Hans Havermann02/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!