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 ?
400128974^18215+18215^28974123442Hans Havermann03/2021
400228901^18618+18618^28901123406Hans Havermann03/2021
40032^409909-189123395Enzo Doria05/2014
40042^409896-109043123391Enzo Doria04/2014
40052^409890+75409123390Enzo Doria04/2016
400681254^33+33^81254123386Hans Havermann03/2021
400733463^4854+4854^33463123348Hans Havermann03/2021
400834061^4182+4182^34061123348Hans Havermann03/2021
4009133^58076-2123345Lelio R Paula10/2017
4010F(590041)123311Henri Lifchitz01/2005
4011(82*10^123299+377)/9123300Robert Price03/2022
40122^409566-113501123292Enzo Doria08/2014
40132^409533+77747123282Enzo Doria05/2016
40142^409436-112799123253Enzo Doria06/2014
401528212^23321+23321^28212123223Hans Havermann03/2021
40162^409225+1873787123189Enzo Doria06/2016
40172^409174+73009123174Enzo Doria04/2016
40182^409058-112685123139Enzo Doria06/2014
4019(13*10^123137-61)/3123138Robert Price11/2018
40204*10^123113+21123114Robert Price12/2018
40212^408778+77689123055Enzo Doria05/2016
40222^408690-75123028Lelio R Paula11/2013
402328327^22032+22032^28327123026Hans Havermann03/2021
4024(29*10^122996+673)/9122997Robert Price12/2018
4025(65*10^122994-101)/9122995Robert Price01/2022
40262^408574-2787341122994Enzo Doria03/2016
40273*10^122977+37122978Robert Price08/2018
4028(7*10^122976-67)/3122977Robert Price10/2021
4029Phi(157825,10)122961Maksym Voznyy06/2015
4030(68*10^122933-419)/9122934Robert Price07/2019
403129712^13721+13721^29712122931Hans Havermann03/2021
4032(13*2^408283+1)/1665122904Lelio R Paula05/2014
4033(266*10^122872-17)/3122874Robert Price07/2020
4034(16*10^122871+77)/3122872Robert Price03/2019
403530395^11022+11022^30395122865Hans Havermann03/2021
40364*10^122859-69122860Robert Price01/2022
4037(10^122857+167)/3122857Robert Price05/2021
403833331^4852+4852^33331122856Hans Havermann03/2021
4039(11*2^408100-1)/35122850Lelio R Paula04/2014
4040(19*10^122836-43)/3122837Robert Price05/2019
404128420^20969+20969^28420122820Hans Havermann03/2021
4042(16*10^122818+179)/3122819Robert Price11/2021
404329865^12934+12934^29865122797Hans Havermann03/2021
4044(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
4045(32*10^122733-77)/9122734Robert Price06/2018
4046(21*2^407604-1)/215122701Lelio R Paula04/2014
4048(22*10^122681+161)/3122682Robert Price05/2019
404729513^14350+14350^29513122682Hans Havermann03/2021
4049(21*2^407433-1)/13122650Lelio R Paula04/2014
4050(26*10^122625-131)/3122626Robert Price10/2019
405127925^24562+24562^27925122599Hans Havermann03/2021
4052(73*10^122592-1)/9122593Robert Price01/2015
4053(5*10^122592+91)/3122593Robert Price04/2018
405436751^2166+2166^36751122589Hans Havermann03/2021
4055(85*10^122585-1)/3122587Robert Price02/2020
405629368^14931+14931^29368122585Hans Havermann03/2021
40572^407179-112075122574Enzo Doria06/2014
4058(21*2^407131+1)/207517523122552Lelio R Paula04/2014
4059(66^67349+1)/67122543Paul Bourdelais09/2017
4060(646*10^122533+11)/9122535Robert Price10/2021
40612^407008-1867919122522Enzo Doria04/2016
406211^117642-300122512Enzo Doria10/2012
4063(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
40642^406949+72197122504Enzo Doria04/2016
4065(19*10^122501+149)/3122502Robert Price05/2019
406628632^18977+18977^28632122495Hans Havermann03/2021
406731815^7076+7076^31815122481Hans Havermann03/2021
40682^406826-65122467Lelio R Paula11/2013
40692^406821-2797363122466Enzo Doria04/2016
4070(7*10^122456-331)/9122456Robert Price03/2022
40712^406758-17122447Lelio R Paula11/2013
407229941^12282+12282^29941122437Hans Havermann03/2021
4073(30^82883-1)/29122427Robert Price12/2011
407427496^27577+27577^27496122422Norbert Schneider12/2020
407528732^18215+18215^28732122411Hans Havermann03/2021
4076(2^406583-1)/813167122388Jens K. Andersen02/2009
40774*10^122377+19122378Robert Price10/2018
407828227^21634+21634^28227122368Hans Havermann03/2021
4079Phi(246362,10)122365Makoto Kamada09/2019
40803*10^122345-97122346Robert Price07/2018
408197^61575-2122336Lelio R Paula12/2014
40822*10^122319+47122320Robert Price12/2021
4083208^52765+52765^208122313Norbert Schneider11/2020
40842^406298+2799109122308Enzo Doria04/2016
40857*10^122294+57122295Robert Price06/2019
4086(27*2^406241-1)/10277122289Lelio R Paula04/2014
40872^406229-1849993122288Enzo Doria08/2015
40883*10^122274+7122275Robert Price07/2015
40892^406117+1876577122254Enzo Doria07/2016
409029308^14835+14835^29308122253Hans Havermann03/2021
409128119^22268+22268^28119122253Hans Havermann03/2021
409232167^6312+6312^32167122240Hans Havermann03/2021
40933^256199-2^256199122238Mike Oakes06/2005
409427678^26053+26053^27678122223Hans Havermann03/2021
40952^405992-78557122216Jorge Menendez03/2018
4096(8*10^122203+43)/3122204Robert Price06/2018
4097(58*10^122170+329)/9122171Robert Price05/2019
40982^405774+179149122151Enzo Doria06/2016
4099(218*10^122109+7)/9122111Robert Price06/2022
410029189^15246+15246^29189122103Hans Havermann03/2021
410234*10^122082-9122084Robert Price06/2020
410133442^4473+4473^33442122084Hans Havermann03/2021
41035*10^122082+41122083Robert Price03/2019
410431849^6808+6808^31849122078Hans Havermann03/2021
41062^405514-3311122072Yves Minet12/2014
41072^405514-115511122072Enzo Doria07/2015
410523*10^122070-7122072Robert Price02/2020
41082^405422-113261122045Enzo Doria07/2014
41092^405173+71237121970Enzo Doria04/2016
4110(154*10^121953+17)/9121955Robert Price06/2022
4111(34*10^121924+191)/9121925Robert Price08/2021
4112(2^405016+1)/257121920Lelio R Paula04/2014
411328557^18590+18590^28557121918Hans Havermann03/2021
411428641^18002+18002^28641121877Hans Havermann03/2021
41152^404858+71329121875Enzo Doria04/2016
41162^404813-114703121861Enzo Doria04/2015
41172^404764+77791121847Enzo Doria05/2016
411828830^16841+16841^28830121847Hans Havermann03/2021
4119(4*10^121825+89)/3121826Robert Price08/2021
4120317^48694+48694^317121787Norbert Schneider08/2015
41212^404536-115259121778Enzo Doria06/2015
41222^404501-631121767Yves Minet07/2012
41235*10^121764-69121765Robert Price02/2021
412428236^20485+20485^28236121738Hans Havermann02/2021
4125(382*10^121694-31)/9121696Robert Price06/2022
412663^67620+2121672Lelio R Paula08/2015
4127(16*10^121633+167)/3121634Robert Price06/2019
412829955^11494+11494^29955121632Hans Havermann02/2021
4129(17*10^121621+1)/9121622Serge Batalov05/2010
413031088^8163+8163^31088121612Hans Havermann02/2021
4131(15*2^403912+1)/271121589Lelio R Paula05/2014
4132(10^121543-79)/3121543Robert Price01/2018
41332^403676+76831121519Enzo Doria05/2016
4134(7*10^121487+143)/3121488Robert Price03/2018
413527965^22086+22086^27965121484Hans Havermann02/2021
4136(893*10^121470+7)/9121472Robert Price06/2021
4137(206*10^121462-11)/3121464Robert Price02/2022
4138(77*10^121455+67)/9121456Robert Price12/2021
41392^403363-113635121425Enzo Doria08/2014
4140(17*10^121418-113)/3121419Robert Price06/2021
41412^403336-1861469121417Enzo Doria03/2016
414227929^22186+22186^27929121382Hans Havermann02/2021
4143p(24442)#/2-64121381Robert Price04/2017
414411^116555-720121380Enzo Doria11/2012
41452^403100-461267121346Enzo Doria07/2015
41462^403093-112213121344Enzo Doria06/2014
414729404^13385+13385^29404121340Hans Havermann02/2021
414828106^20745+20745^28106121332Hans Havermann02/2021
4149(316^48539+1)/317121330Eric Chen10/2017
4150(23*10^121320-71)/3121321Robert Price07/2020
41512^403004+1866361121317Enzo Doria03/2016
41522^402953+89121301Lelio R Paula10/2013
41532^402944-2788319121299Enzo Doria03/2016
4154(44*10^121297-719)/9121298Robert Price12/2018
4155(27*2^402865+1)/5121276Lelio R Paula04/2014
41562^402828-113183121264Enzo Doria07/2014
4157(17*10^121242+1)/9121243Serge Batalov05/2010
4158(15*2^402757+1)/101121242Lelio R Paula05/2014
41602^402715+1874223121230Enzo Doria06/2016
4159(35*10^121229-593)/9121230Robert Price07/2018
4161(91^61879+1)/92121222Paul Bourdelais09/2017
416228719^16568+16568^28719121174Hans Havermann02/2021
41637*10^121144+9121145Robert Price09/2015
416427490^25467+25467^27490121121Hans Havermann02/2021
416534575^3182+3182^34575121106Hans Havermann02/2021
41665*10^121100-37121101Robert Price11/2021
416729954^10935+10935^29954120979Hans Havermann02/2021
416833585^3992+3992^33585120946Hans Havermann02/2021
416940296^1003+1003^40296120941Hans Havermann02/2021
41702^401725-113251120932Enzo Doria07/2014
4171(15*2^401677-1)/19120917Lelio R Paula05/2014
41722^401652+73711120910Enzo Doria04/2016
4173(2^401632+3)/79120902Lelio R Paula04/2014
417440450^973+973^40450120870Hans Havermann01/2021
417510^120841+88417120842Patrick De Geest04/2020
417610^120841-123456789120841Robert Price02/2020
417710^120841-176853120841Patrick De Geest04/2020
41782^401406-2791331120836Enzo Doria03/2016
4179(28^83497+1)/29120832Robert Price07/2013
4180(22*10^120828+161)/3120829Robert Price05/2019
41812^401369+1867367120825Enzo Doria03/2016
4182(5*10^120821+43)/3120822Robert Price12/2021
4183(10^120782+29)/3120782Serge Batalov12/2014
41842^401215-1657120778Yves Minet07/2014
41852^401159+53120761Lelio R Paula10/2013
418627782^22179+22179^27782120739Hans Havermann01/2021
418732974^4585+4585^32974120730Hans Havermann02/2021
41882^401031-113047120723Enzo Doria07/2014
418930598^8813+8813^30598120713Hans Havermann02/2021
4190(71*10^120703-287)/9120704Robert Price09/2019
4191(29*2^400909-1)/303120685Lelio R Paula04/2014
419234793^2940+2940^34793120675Hans Havermann02/2021
4193(2^400846+538)/2120667Stefano Morozzi09/2020
4194(166*10^120654+11)/3120656Robert Price03/2021
419534066^3481+3481^34066120652Hans Havermann02/2021
41968*10^120637-27120638Robert Price10/2021
4197(2^400709+3546)/2120626Stefano Morozzi09/2020
4198(2^400700+3126)/2120623Stefano Morozzi09/2020
4199(2^400693+2634)/2120621Stefano Morozzi09/2020
42009*10^120617-61120618Robert Price06/2021
4201(29*10^120590-71)/3120591Robert Price07/2021
42022^400571-15120584Lelio R Paula10/2013
4203(10^120574+359)/9120574Serge Batalov12/2014
4204(8*10^120552-17)/9120552Serge Batalov11/2022
420527431^24810+24810^27431120550Hans Havermann02/2021
42062^400424-216413120540Enzo Doria04/2013
420729090^13911+13911^29090120531Hans Havermann02/2021
4208(2^400346+1722)/2120516Stefano Morozzi09/2020
420927899^20868+20868^27899120510Hans Havermann02/2021
421033740^3729+3729^33740120506Hans Havermann02/2021
4211(17*2^400200-1)/587120471Lelio R Paula05/2014
42122^400166+1874899120462Enzo Doria06/2016
4213(2^400165+1602)/2120462Stefano Morozzi09/2020
421437078^1771+1771^37078120438Hans Havermann02/2021
4215(2^400084+1638)/2120437Stefano Morozzi09/2020
4216(3*2^400045-1)/865120424Lelio R Paula04/2014
4217(2^399974+2790)/2120404Stefano Morozzi02/2021
42182^399966+73759120402Enzo Doria04/2016
4219(2^399961+2306)/2120400Stefano Morozzi02/2021
4220(112*10^120395-1)/3120397Serge Batalov12/2014
42212^399918-95120388Lelio R Paula04/2013
4222(28*10^120381-67)/3120382Robert Price10/2020
4223(49*10^120380-139)/9120381Robert Price03/2019
4224(2^399874+2194)/2120374Stefano Morozzi09/2020
42252^399792-1849259120350Enzo Doria08/2015
42269*10^120342-7120343Robert Price09/2015
4227(2^399751+786)/2120337Stefano Morozzi09/2020
4228(331*10^120332-7)/9120334Robert Price04/2022
4229(13*10^120306-37)/3120307Robert Price01/2019
4230(23*10^120299+37)/3120300Robert Price02/2022
4231(2^399604+3070)/2120293Stefano Morozzi09/2020
4232(2^399549+1062)/2120276Stefano Morozzi09/2020
42332^399526-1861721120270Enzo Doria11/2015
4234(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
423532016^5687+5687^32016120217Hans Havermann01/2021
4236(205*10^120212-1)/3120214Robert Price11/2021
42372^399322-2798111120208Enzo Doria04/2016
423830438^8867+8867^30438120163Hans Havermann02/2021
424072^64693-71^64693120157Robert Price03/2014
4239(17*10^120156-161)/9120157Robert Price02/2021
42412^399111-28489120145Enzo Doria08/2015
4242(2^399014+1318)/2120115Stefano Morozzi02/2021
424330254^9333+9333^30254120110Hans Havermann02/2021
424430882^7745+7745^30882120101Hans Havermann02/2021
42452^398877+105120074Donovan Johnson01/2006
4246(101*10^120072-87)/7120074Hans Havermann02/2015
4247(88^61751+1)/89120072Paul Bourdelais09/2017
42482^398710+57120024Lelio R Paula04/2013
4249(2^398698+1138)/2120020Stefano Morozzi09/2020
42502^398691-115057120018Enzo Doria06/2015


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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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