PRP Records

Probable Primes Top 10000

(293510 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 ?
4501(316^48539+1)/317121330Eric Chen10/2017
4502(23*10^121320-71)/3121321Robert Price07/2020
45032^403004+1866361121317Enzo Doria03/2016
45042^402953+89121301Lelio R Paula10/2013
45052^402944-2788319121299Enzo Doria03/2016
4506(44*10^121297-719)/9121298Robert Price12/2018
4507(27*2^402865+1)/5121276Lelio R Paula04/2014
45082^402828-113183121264Enzo Doria07/2014
4509(17*10^121242+1)/9121243Serge Batalov05/2010
4510(15*2^402757+1)/101121242Lelio R Paula05/2014
45122^402715+1874223121230Enzo Doria06/2016
4511(35*10^121229-593)/9121230Robert Price07/2018
4513(91^61879+1)/92121222Paul Bourdelais09/2017
451428719^16568+16568^28719121174Hans Havermann02/2021
45157*10^121144+9121145Robert Price09/2015
451627490^25467+25467^27490121121Hans Havermann02/2021
451734575^3182+3182^34575121106Hans Havermann02/2021
45185*10^121100-37121101Robert Price11/2021
451929954^10935+10935^29954120979Hans Havermann02/2021
452033585^3992+3992^33585120946Hans Havermann02/2021
452140296^1003+1003^40296120941Hans Havermann02/2021
45222^401725-113251120932Enzo Doria07/2014
4523(15*2^401677-1)/19120917Lelio R Paula05/2014
45242^401652+73711120910Enzo Doria04/2016
4525(2^401632+3)/79120902Lelio R Paula04/2014
452640450^973+973^40450120870Hans Havermann01/2021
4527(8*10^120851-11)/3120852Robert Price07/2023
452810^120841+88417120842Patrick De Geest04/2020
452910^120841-123456789120841Robert Price02/2020
453010^120841-176853120841Patrick De Geest04/2020
45312^401406-2791331120836Enzo Doria03/2016
4532(28^83497+1)/29120832Robert Price07/2013
4533(22*10^120828+161)/3120829Robert Price05/2019
45342^401369+1867367120825Enzo Doria03/2016
4535(5*10^120821+43)/3120822Robert Price12/2021
4536(10^120782+29)/3120782Serge Batalov12/2014
45372^401215-1657120778Yves Minet07/2014
45382^401159+53120761Lelio R Paula10/2013
453927782^22179+22179^27782120739Hans Havermann01/2021
454032974^4585+4585^32974120730Hans Havermann02/2021
45412^401031-113047120723Enzo Doria07/2014
454230598^8813+8813^30598120713Hans Havermann02/2021
4543(71*10^120703-287)/9120704Robert Price09/2019
4544(29*2^400909-1)/303120685Lelio R Paula04/2014
454534793^2940+2940^34793120675Hans Havermann02/2021
4546(2^400846+538)/2120667Stefano Morozzi09/2020
4547(166*10^120654+11)/3120656Robert Price03/2021
454834066^3481+3481^34066120652Hans Havermann02/2021
45498*10^120637-27120638Robert Price10/2021
4550(2^400709+3546)/2120626Stefano Morozzi09/2020
4551(2^400700+3126)/2120623Stefano Morozzi09/2020
4552(2^400693+2634)/2120621Stefano Morozzi09/2020
45539*10^120617-61120618Robert Price06/2021
4554(29*10^120590-71)/3120591Robert Price07/2021
45552^400571-15120584Lelio R Paula10/2013
4556(10^120574+359)/9120574Serge Batalov12/2014
4557(8*10^120552-17)/9120552Serge Batalov11/2022
455827431^24810+24810^27431120550Hans Havermann02/2021
45592^400424-216413120540Enzo Doria04/2013
456029090^13911+13911^29090120531Hans Havermann02/2021
4561(2^400346+1722)/2120516Stefano Morozzi09/2020
456227899^20868+20868^27899120510Hans Havermann02/2021
456333740^3729+3729^33740120506Hans Havermann02/2021
4564(17*2^400200-1)/587120471Lelio R Paula05/2014
45652^400166+1874899120462Enzo Doria06/2016
4566(2^400165+1602)/2120462Stefano Morozzi09/2020
456737078^1771+1771^37078120438Hans Havermann02/2021
4568(2^400084+1638)/2120437Stefano Morozzi09/2020
4569(3*2^400045-1)/865120424Lelio R Paula04/2014
45702^399999+54173120412Norman Luhn08/2023
4571(2^399974+2790)/2120404Stefano Morozzi02/2021
45722^399966+73759120402Enzo Doria04/2016
4573(2^399961+2306)/2120400Stefano Morozzi02/2021
4574(112*10^120395-1)/3120397Serge Batalov12/2014
45752^399918-95120388Lelio R Paula04/2013
4576(28*10^120381-67)/3120382Robert Price10/2020
4577(49*10^120380-139)/9120381Robert Price03/2019
4578(2^399874+2194)/2120374Stefano Morozzi09/2020
45792^399792-1849259120350Enzo Doria08/2015
45809*10^120342-7120343Robert Price09/2015
4581(2^399751+786)/2120337Stefano Morozzi09/2020
4582(331*10^120332-7)/9120334Robert Price04/2022
4583(13*10^120306-37)/3120307Robert Price01/2019
4584(23*10^120299+37)/3120300Robert Price02/2022
4585(2^399604+3070)/2120293Stefano Morozzi09/2020
4586(2^399549+1062)/2120276Stefano Morozzi09/2020
45872^399526-1861721120270Enzo Doria11/2015
4588(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
458932016^5687+5687^32016120217Hans Havermann01/2021
4590(205*10^120212-1)/3120214Robert Price11/2021
45912^399322-2798111120208Enzo Doria04/2016
459230438^8867+8867^30438120163Hans Havermann02/2021
45933^251841-5*2^251841120159Jon Grantham08/2023
459572^64693-71^64693120157Robert Price03/2014
4594(17*10^120156-161)/9120157Robert Price02/2021
45962^399111-28489120145Enzo Doria08/2015
4597(2^399014+1318)/2120115Stefano Morozzi02/2021
459830254^9333+9333^30254120110Hans Havermann02/2021
459930882^7745+7745^30882120101Hans Havermann02/2021
46002^398877+105120074Donovan Johnson01/2006
4601(101*10^120072-87)/7120074Hans Havermann02/2015
4602(88^61751+1)/89120072Paul Bourdelais09/2017
46032^398710+57120024Lelio R Paula04/2013
4604(2^398698+1138)/2120020Stefano Morozzi09/2020
46052^398691-115057120018Enzo Doria06/2015
4606L(574219)120005Renaud Lifchitz03/2004
46072^398571+60413119982Yves Minet03/2011
460828623^15538+15538^28623119971Hans Havermann02/2021
4609p(24179)#/2-64119949Robert Price04/2017
46102^398448+1872001119945Enzo Doria05/2016
4611(191*10^119941-17)/3119943Robert Price11/2021
4612634^42803+42803^634119938Norbert Schneider07/2019
461331083^7220+7220^31083119935Hans Havermann01/2021
4614(68*10^119931-11)/3119933Robert Price01/2020
46158*10^119930-3119931Ray Chandler04/2011
4616(2^398398+774)/2119930Stefano Morozzi09/2020
4617(10^119880+179)/9119880Serge Batalov12/2014
4618(9*2^398145+1)/73119853Lelio R Paula04/2014
4619(10^119836+77)/3119836Robert Price01/2018
462028179^17870+17870^28179119821Hans Havermann02/2021
46212^398029+1872527119819Enzo Doria05/2016
462233142^4119+4119^33142119802Hans Havermann01/2021
46232^397897-113541119779Enzo Doria08/2014
462428636^15171+15171^28636119728Hans Havermann02/2021
4625(2^397696+1042)/2119719Stefano Morozzi09/2020
4627(19*10^119716+101)/3119717Robert Price09/2019
462629563^11208+11208^29563119717Hans Havermann02/2021
46282^397655-933075119707Paul Bourdelais06/2021
4629(21*2^397661-1)/27593119705Lelio R Paula04/2014
463028243^17308+17308^28243119701Hans Havermann02/2021
463177*10^119688+3119690Robert Price06/2020
4632(2^397504+1698)/2119661Stefano Morozzi09/2020
4633(58^67853-1)/57119653Paul Bourdelais09/2017
46342^397426+73849119638Enzo Doria04/2016
46358*10^119509+29119510Robert Price11/2021
46362^396933-112723119489Enzo Doria06/2014
463711^114738-150119488Enzo Doria10/2012
4638(4*10^119474+149)/9119474Robert Price04/2018
46392^396790-21119446Lelio R Paula04/2013
464032061^5300+5300^32061119405Hans Havermann01/2021
4641(2^396633-7)/5119398Lelio R Paula04/2014
464227382^22913+22913^27382119388Hans Havermann03/2021
4643(2^396577+2522)/2119382Stefano Morozzi09/2020
4644(2^396492+2230)/2119356Stefano Morozzi01/2021
4645(47*10^119354+259)/9119355Robert Price03/2022
4647105^59050+104119352Norbert Schneider11/2016
4646126^56824-125119352Norbert Schneider12/2018
46482^396469+111546435119350Paul Bourdelais10/2021
4649139^55690-138119345Norbert Schneider04/2019
4650790^41179+41179^790119322Norbert Schneider04/2019
46512^396374+73729119321Enzo Doria04/2016
465288*10^119295+3119297Robert Price05/2020
46532^396258-459491119286Enzo Doria05/2015
4654(2^396248+3126)/2119283Stefano Morozzi09/2020
46552^396128-396128-1119247Karsten Bonath06/2018
4656(893*10^119228+7)/9119230Robert Price06/2021
4657(31*10^119229+257)/9119230Robert Price12/2021
4658(28*10^119206-67)/3119207Robert Price10/2020
4659(2^395986+5)/76881119199Lelio R Paula04/2014
466011^114458+6119196Paul Bourdelais02/2021
4661(23*2^395942-1)/91119190Lelio R Paula04/2014
4662(2^395902+202)/2119179Stefano Morozzi09/2020
4663(2^395825+582)/2119155Stefano Morozzi09/2020
4664(2^395733+1130)/2119128Stefano Morozzi09/2020
466529548^10725+10725^29548119091Hans Havermann02/2021
4666(11*2^395548+1)/3119073Lelio R Paula04/2014
4667(30^80599+1)/31119054Robert Price07/2013
4668(232*10^119047+17)/3119049Robert Price04/2021
4669(43*10^119024-403)/9119025Robert Price01/2019
4670(4*10^119021+47)/3119022Robert Price01/2022
4671fibonacci(569433)+3119005Jon Grantham08/2023
467226603^26888-26888^26603118978Norbert Schneider07/2021
46736*10^118964+43118965Robert Price07/2020
4674(8*10^118960+49)/3118961Robert Price05/2020
467531253^6402+6402^31253118959Hans Havermann02/2021
4676(194*10^118925-17)/3118927Robert Price09/2020
46772^395062-109121118926Enzo Doria04/2014
46782^395055-4627118924Yves Minet05/2019
4679(2^395054+702)/2118923Stefano Morozzi09/2020
46802^395018-224141118913Harrison Mesh06/2022
4681(2^395011+2526)/2118910Stefano Morozzi09/2020
4682(2^394918+78557)/3118882Lelio R Paula01/2015
4683(2^394858+1018)/2118864Stefano Morozzi09/2020
4684(77*10^118862-149)/9118863Robert Price03/2022
4685(16*10^118852+77)/3118853Robert Price03/2019
4686fibonacci(568658)-2118843Jon Grantham08/2023
4687(2^394739+3)/1883118826Lelio R Paula04/2014
468810^118772+163599118773Patrick De Geest02/2021
469010^118772-40000000001118772Robert Price09/2020
468910^118772-207603118772Patrick De Geest02/2021
469126842^26577+26577^26842118763Hans Havermann02/2021
4692(2^394513+2034)/2118760Stefano Morozzi09/2020
4693(2^394473+2774)/2118748Stefano Morozzi02/2021
469427949^17710+17710^27949118734Hans Havermann02/2021
46952^394266+71389118686Enzo Doria04/2016
4696(10^118681-3^118681)/7118681Jon Grantham08/2023
46972^394215-51261118671Tony Prest / Never Odd Or Even04/2018
4698(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
4699(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
4700(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
4701(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
4702(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
470329201^11568+11568^29201118652Hans Havermann02/2021
4704(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
4705(2^394131+2214)/2118645Stefano Morozzi09/2020
4706(17*10^118635+13)/3118636Robert Price01/2019
47075^169727+2118635Lelio R Paula08/2013
47082^394034-3118617M. Frind & P. Underwood09/2002
4709(7*10^118607+179)/3118608Robert Price09/2018
47103^248572-6242118599Enzo Doria05/2014
4711(3*2^393964-1)/181118594Lelio R Paula04/2014
4712(49*10^118576-319)/9118577Robert Price10/2021
47137^140303-6118570Robert Price11/2014
4714(2^393864+2686)/2118565Stefano Morozzi09/2020
4715(2^393862+3150)/2118564Stefano Morozzi09/2020
4716(2^393849+3762)/2118561Stefano Morozzi01/2021
4717(529*10^118554-7)/9118556Robert Price08/2021
471826712^26777-26777^26712118534Norbert Schneider07/2021
4719(2^393661+2666)/2118504Stefano Morozzi09/2020
4720(2^393650+1614)/2118501Stefano Morozzi09/2020
472127655^19264+19264^27655118495Hans Havermann02/2021
472210^118485+469413118486Patrick De Geest05/2021
472310^118485-50001118485Robert Price08/2020
4724(2^393528+1030)/2118464Stefano Morozzi09/2020
47252^393427+75683118434Enzo Doria04/2016
47262^393376-114749118418Enzo Doria04/2015
4727(65*10^118417+493)/9118418Robert Price08/2021
472830960^6671+6671^30960118397Hans Havermann02/2021
4729(2^393234+2010)/2118375Stefano Morozzi09/2020
4730(2^393205+3030)/2118367Stefano Morozzi09/2020
4731(2^393191+2174)/2118362Stefano Morozzi09/2020
47322^393180+73118359Lelio R Paula04/2013
47333*2^393125+5118343Jon Grantham07/2023
473427546^19771+19771^27546118339Hans Havermann02/2021
4735p(23881)#/2+256118328Robert Price05/2017
4736(10^118324+359)/9118324Serge Batalov12/2014
4737(2^393048+570)/2118319Stefano Morozzi09/2020
4738p(23879)#/2+64118317Robert Price03/2017
47392^393033+20147118315Enzo Doria08/2023
47408*10^118308+59118309Robert Price11/2021
47419*10^118282+29118283Robert Price03/2022
4742(238*10^118265-1)/3118267Robert Price04/2020
4744(53*10^118216+1)/9118217Serge Batalov11/2010
4743(2^392707+1710)/2118217Stefano Morozzi09/2020
4745(7*2^392697+1)/15118214Renaud Lifchitz03/2011
4746(157^53819-1)/156118179Alexander Zhirkov06/2016
4747(2^392567+2750)/2118175Stefano Morozzi01/2021
474855*10^118172+3118174Robert Price07/2022
4749(19*2^392551+1)/3118171Lelio R Paula04/2014
475027185^22222+22222^27185118168Hans Havermann01/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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